depreciation under the company law
TRANSCRIPT
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Depreciation under the company law
he Commerce course consists of many subjects. They are studied
independently. But it is expected of the students to study all subjects as a
unit to take correct decisions in business. It is an attempt to make
commerce students to understand and apply the concepts that are studied under
various subjects to take correct decisions.
Module-I: Financial Accounting & Financial Applications:
Financial Statements are Trading and Profit and Loss statements, Balance sheet
statement and Cash Flow Statement. Most of the times they are prepared in
accounting form or statement form i.e. horizontal or vertical form. Controlling cost
is an important issue in costing. Some of the statistical tools are used for analysis
of past information for future predictions. Financial management is used for how
effectively and efficiently the funds are procured and used in the business.
Operation research is used to convert business problems into mathematical
problems and obtains mathematical solutions which help the business to take
optimal solutions to business problems. Mathematics is used in every business
decisions to narrow down the problems. Every business decisions have tax
implications. Management accounting has various techniques and tools to collect
information, which consists of Accounting, Costing, Statistics, Income tax, and
corporate tax impact on decisions, Financial Management, Economic
Applications. We have to study all subjects and the techniques available under
various subjects can be used at an appropriate time in order to take a correct
decision.
First, let us understand the basics of Financial Statements:
a) Balance Sheet Basics:
Balance Sheet is the snap shot of financial strength of any company at any point of
time. It gives the details of the assets and the liabilities of the company.
Understanding balance sheet is very important because it gives an idea of the
financial strength of the company at any given point of time. Following is the
balance sheet of SAST Ltd. for the year ending on 31st Mar' 2008:
As on 31-3-08
Assets
Gross Block 3978.55
Net Block 2790.57
Capital WIP 66.72
T
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Investments 454.33
Inventory 610.81
Receivables 1546.81
Other Current Assets 3673.67
Balance Sheet Total 9142.92
Liabilities
Equity Share Capital 434.12
Reserves 5815.65
Total Debt 2096.69
Creditors and Acceptances 393.91
Other current liab/prov. 402.55
Balance Sheet Total 9142.92
Let us take a look at each of its components.
1) Assets: Gross block is the sum total of all assets of the company valued at their cost of
acquisition. This is inclusive of the depreciation that is to be charged on each
asset.
Net block is the gross block less accumulated depreciation on assets. Net block is
actually what the assets are worth to the company.
Capital work in progress, sometimes at the end of the financial year, there is
some construction or installation going on in the company, which is not complete,
such installation is recorded in the books as capital work in progress because it is
asset for the business.
Investments If the company has made some investments out of its free cash, it is
recorded under the head investments.
Inventory is the stock of goods that a company has at any point of time.
Receivables include the debtors of the company, i.e., it includes all those accounts
which are to give money back to the company.
Other current assets include all the assets, which can be converted into cash
within a very short period of time like cash in bank etc.
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Equity Share capital is the owner's equity. It is the most permanent source and
risky of finance for the company.
Reserves include the free reserves of the company which are built out of the
genuine profits of the company. It is an internal source of capital. Together they
are known as net worth of the company.
Total debt includes the long term and the short debt of the company. Long term is
for a longer duration, usually for a period more than 3 years like debentures. Short
term debt is for a lesser duration, usually for less than a year like bank finance for
working capital.
Creditors are those entities to which the company owes money.
Other liabilities and provisions include all the liabilities that do not fall under
any of the above heads and various provisions made such as provision for tax,
provision for contingencies.
2) Role of Balance Sheet in Investment Decision making: The balance sheet is a snapshot of what the company's finances look like only on
the last day of the quarter/Six month/year. (It's much like if you take every
statement you received from every financial institution you have dealings with —
banks, brokerages, credit card issuers, mortgage banks, etc. — and listed the
closing balances of each account).
When reviewing the balance sheet, keep an eye on inventories and accounts
receivable. If inventories are growing too quickly, perhaps some of it is outdated
or obsolete. If the accounts receivable are growing faster than sales, then it might
indicate a problem, such as lax credit policies or poor internal controls. Finally,
take a look at the liability side of the balance sheet. Look at both long-term and
short-term debt. Have they increased? If so, why? How about accounts payable?
Read the comments made by management. They should have addressed anything
that looked unusual, such as a large increase in inventory. Management will also
usually make some statements about the future prospects of business. These
comments are only the opinion of management, so use them as such.
Investors can analyse the position each quarter to understand the problems and
trends of business.
3) Purpose of the Income Statement:
The primary purpose of the income statement is to report a company's earnings to
investors over a specific period of time. The income statement was referred to as
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the Profit and Loss (or P&L) statement, and has since evolved into the most well-
known and widely used financial report on BSE. Many times, investors make
decisions based entirely on the reported earnings from the income statement
without consulting the balance sheet or cash flow statements (which, while a
mistake, is a testament to how influential it is).
Using Income Statement Analysis to Calculate Expenses, Earnings, Financial
Ratios and Profit Margins.
To an enterprising investor, income statement analysis reveals much more than a
company's earnings. It provides important insights into how effectively
management is controlling expenses, the amount of interest income and expense,
and the taxes paid. Investors can use income statement analysis to calculate
financial ratios that will reveal the rate of return the business is earning on the
shareholders' retained earnings and assets; they can also compare a company's
profits to its competitors by examining various profit margins such as the gross
profit margin, operating profit margin, and net profit margin.
You must remember John Burr William‘s basic truth that a business is only worth
the profit that it will generate for its owners from now until doomsday, discounted
back to the present, adjusted for inflation. The income statement is the ―report
card‖ of those earnings, which ultimately determine the price you should be
willing to pay for a business.
Profit Loss Account
Rs. Crore
Mar ' 07
Operating income 13,683.90
Material consumed 1,889.00
Manufacturing expenses 120.50
Personnel expenses 5,764.50
Selling expenses -
Administrative expenses 2,655.40
Expenses capitalized -
Cost of sales 10,429.40
Operating profit 3,254.50
Other recurring income 288.70
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Adjusted PBDIT 3,543.20
Financial expenses 7.20
Depreciation 359.80
Other write offs -
Adjusted PBT 3,176.20
Tax charges 334.10
Adjusted PAT 2,842.10
Non recurring items -
Other non cash adjustments -
Reported net profit 2,842.10
Earnings before appropriation 2,842.10
Equity dividend 873.70
Preference dividend -
Dividend tax 126.80
Retained earnings 1,841.60
Cost of Goods Sold:
When reviewing your financial statement there are several key elements that
determine profit:
Net sales- the amount of sales during the reporting period. This amount reflects
the total value of merchandise sold to your customers. Markdowns are subtracted
and sales tax is not included in Net Sales. Some other caveats to remember is that
gains or losses from investments or from charging customers for alterations are not
included in Net Sales. This income is added below as Other Income. Also, Net
Sales assume an accrual basis for accounting. For example, if an item is sold on a
house charge that item is included in Net Sales even though the revenue has not
been fully collected. Should the monies never be collected then that becomes an
expense when it is determined un-collectable.
Cost of Goods Sold- this is sometimes referred to as Cost of Sales. Cost of Goods
Sold is what it actually costs a retailer for the goods that he sold during a given
period. The correct formula for determining Cost of Goods Sold for merchandise
is: Opening stock+Purchases-Closing stock
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Accountants will also include freight-in, as Generally Accepted Accounting
Principles requires that this expense directly related to bringing the merchandise
available to sell be included. Cash discounts are often also reflected as a separate
line item in the Cost of Goods section of the financial statement as a reduction in
purchases. This is particularly true for retailers who include discounts when
determining initial mark up. Generally Accepted Accounting Principles for
publicly held companies requires that they be reflected as a credit expense or other
income as a line item on the income statement. In smaller companies cash
discounts and incentives are immaterial and their placement on the financial
statement is at the discretion of the owner. It is important that whatever is included
be consistent over time.
Gross Profit: Net Sales minus Cost of Goods Sold. This is the money that is
available to pay other expenses, bills, salaries, taxes and profits.
Total Operating expenses: A list of all your expenses- occupancy, salaries, and
selling, general and administrative expenses. A dividend or distribution that the
owner takes is not included in operating expenses.
Net Profit/(Loss): Gross Profit minus operating expenses. This is what is
available for dividends, debt reduction, or Rupees to reinvest in the business.
Sometimes financial statements will calculate Cost of Goods Sold strictly as
purchases for the period. It is not quite that simple. Cost of Goods Sold is based on
goods available for sale during the period that is being reported. Goods available
for sale includes beginning inventory as well as merchandise purchased during the
period reviewed. Simply stating purchases instead of an accurate Cost of Goods
Sold calculation does not take into account beginning and ending inventory. For
example, merchandise theft impacts profits by raising Cost of Goods Sold. The
merchant pays for goods whether they are stolen or given away. This is reflected
in the difference of beginning and ending inventory and the accurate reflection of
these transactions would boost the Costs of Goods Sold. Showing only purchases
as Cost of Goods Sold distorts the profit and would result in decisions, like income
taxes to pay on a less accurate measurement.
How inventory is valued with the different acceptable methods, like LIFO, FIFO,
or Average Cost can have a direct impact on your financial statement
The following equation expresses how a company's inventory is determined.
Beginning inventory at cost + Purchases at cost – Ending inventory at cost = Cost of good sold
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Beginning Inventory + Net Purchases – Cost of Goods sold=Ending inventory
1. The Question of LIFO or FIFO: Which is preferable?
―Cost of goods sold is measured using the cost of the most recent additions to
inventory, and the inventory account always retains the oldest cost of items
purchased…‖―…cost flow may be very different from the actual physical flow of
goods…‖ Most US companies use this.
FIFO: ―the oldest costs in the inventory account are the first to be transferred to
cost of goods sold…‖FIFO…produces an inventory account balance that usually
comes the closest of the three method to approximating the replacement cost of the
inventory.‖
LIFO & FIFO: An Example:
1/01/03 Beginning Inventory: 15(3 units)
Purchases:
3/01/03: 14(2 units)
6/01/03: 27(3 Units)
10/01/03: 33(3 Units)
12/31/03: Ending Inventory: 2 units
Cost of Goods Available for Sale: 15+14+27+33=Rs.89
FIFO:
Ending Inventory: Rs.22
COGS: 15+14+27+11= Rs.67
LIFO
Ending Inventory: Rs.10
COGS: 33+27+14+5= 79
Are you one of those investors who doesn't look at how a company accounts
for its inventory?
For many companies, inventory represents a large (if not the largest) portion of
assets and, as such, makes up an important part of the balance sheet. It is,
therefore, crucial for investors who are analyzing stocks to understand how
inventory is valued.
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How Do We Value Inventory?
The accounting method that a company decides to use to determine the costs of
inventory can directly impact the balance sheet, income statement and statement of
cash flow. There are three inventory-costing methods that are widely used by both
public and private companies:
First-In, First-Out (FIFO): This method assumes that the first unit making its
way into inventory is the first sold. For example, let's say that a bakery produces
200 loaves of bread on Monday at a cost of Rs.10 each, and 200 more on Tuesday
at Rs.10.25 each. FIFO states that if the bakery sold 200 loaves on Wednesday,
the COGS is Rs.10 per loaf (recorded on the income statement) because that was
the cost of each of the first loaves in inventory. The Rs.10.25 loaves would be
allocated to ending inventory (appears on the balance sheet).
Last-in, First-out (LIFO): This method assumes that the last unit making its way
into inventory is sold first. The older inventory, therefore, is left over at the end of
the accounting period. For the 200 loaves sold on Wednesday, the same bakery
would assign RS.10.25 per loaf to COGS while the remaining Rs10 loaves would
be used to calculate the value of inventory at the end of the period.
Average Cost: This method is quite straightforward; it takes the weighted
average of all units available for sale during the accounting period and then uses
that average cost to determine the value of COGS and ending inventory. In our
bakery example, the average cost for inventory would be Rs.10.125 per unit,
calculated as [(200 x Rs.10) + (200 x Rs.10.25)]/400.
An important point in the examples above is that COGS appears on the income
statement, while ending inventory appears on the balance sheet under current
assets. (For more insight, see Reading the Balance Sheet.
Why is Inventory Important?
If inflation were nonexistent, then all three of the inventory valuation methods
would produce the exact same results. When prices are stable our bakery would be
able to produce all of its loafs of bread at Rs.10.25, and FIFO, LIFO and average
cost would give us a cost of Rs.10.125 per loaf.
Unfortunately, the world is more complicated. Over the long term, prices tend to
rise, which means the choice of accounting method can dramatically affect
valuation ratios.
If prices are rising, each of the accounting methods produces the
following results:
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FIFO gives us a better indication of the value of ending inventory (on the balance
sheet), but it also increases net income because inventory that might be several
years old is used to value the cost of goods sold. Increasing net income sounds
good, but remember that it also has the potential to increase the amount of taxes
that a company must pay.
LIFO isn't a good indicator of ending inventory value because the left over
inventory might be extremely old and, perhaps, obsolete. This results in a
valuation that is much lower than today's prices. LIFO results in lower net income
because cost of goods sold is higher.
Average cost produces results that fall somewhere between FIFO and LIFO.
(Note: if prices are decreasing then the complete opposite of the above is true.)
One thing to keep in mind is that companies are prevented from getting the best of
both worlds. If a company uses LIFO valuation when it files taxes, which results
in lower taxes when prices are increasing, it then must also use LIFO when it
reports financial results to shareholders. This lowers net income and, ultimately,
earnings per share.
Example: Let's examine the inventory of SAST Inc. to see how the different inventory
valuation methods can affect the financial analysis of a company.
Monthly Inventory Purchases*
Month Units Purchased Cost/Kg Total Value
January 1,000 Rs10 Rs10,000
February 1,000 Rs12 RS.12,000
March 1,000 Rs15 Rs.15,000
Total 3,000
Beginning Inventory = 1,000 units purchased at Rs.8 each (a total of 4,000
units)
Income Statement (simplified): January-March*
Item LIFO FIFO Average
Sales = 3,000 units @ Rs.20 each Rs.
60,000 .Rs.60,000 Rs.60,000
Beginning Inventory 8,000 8,000 8,000
Purchases 37,000 37,000 37,000
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Ending Inventory (appears on B/S)
*See calculation below 8,000 15,000 11,250
COGS Rs.37,000 Rs.30,000 Rs.33,750
Expenses 10,000 10,000 10,000
Net Income Rs.13,000 Rs.20,000 Rs.16,250
*Note: All calculations assume that there are 1,000 units left for ending
inventory: (4,000 units - 3,000 units sold = 1,000 units left)
What we are doing here is figuring out the ending inventory, the results of which
depend on the accounting method, in order to find out what COGS is. All we've
done is rearrange the above equation into the following:
Beginning Inventory + Net Purchases - Ending Inventory = Cost of Goods Sold
LIFO Ending Inventory Cost = 1,000 units X Rs.8 each = Rs.8,000
Remember that the last units in are sold first; therefore, we leave the oldest units
for ending inventory.
FIFO Ending Inventory Cost = 1,000 units X Rs.15 each = Rs.15,000
Remember that the first units in (the oldest ones) are sold first; therefore, we leave
the newest units for ending inventory.
Average Cost Ending Inventory = [(1,000 x 8) + (1,000 x 10) + (1,000 x 12) +
(1,000 x 15)]/4000 units = Rs.11.25 per unit
1,000 units X Rs.11.25 each = Rs.11,250
Remember that we take a weighted average of all the units in inventory.
Using the information above, we can calculate various performance and leverage
ratios. Let's assume the following:
Assets (not including inventory) Rs.150,000
Current assets (not including inventory) Rs.100,000
Current liabilities Rs.40,000
Total liabilities Rs.50,000
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Each inventory valuation method causes the various ratios to produce significantly
different results (excluding the effects of income taxes):
Ratio LIFO FIFO Average Cost
Debt-to-Asset 0.32 0.30 0.31
Working Capital 2.7 2.88 2.78
Inventory Turnover 7.5 4.0 5.3
Gross Profit Margin 38% 50% 44%
As you can see from the ratio results, inventory analysis can have a big effect on
the bottom line. Unfortunately, a company probably won't publish its entire
inventory situation in its financial statements. Companies are required,
however, to state in the notes to financial statements what inventory system they
use. By learning how these differences work, you will be better able to compare
companies within the same industry.
Conclusion: As a final note, many companies will also state that they use the "lower of cost or
market". This means that if inventory values were to plummet, their valuations
would represent the market value (or replacement cost) instead of FIFO, LIFO or
average cost.
Understanding inventory calculation might seem overwhelming, but it's something
you need to be aware of. Next time you're valuing a company, check out its
inventory; it might reveal more than you thought.
FIFO, LIFO -- does it matter? You bet it does, especially in inflationary times
Impossible as this may sound, inflation in material, labour, and other costs can
actually boost a company's cash flow.Return on capital employed might differ
from method to method. All it takes is an accounting sleight of hand. The magic
words? FIFO to LIFO. While that may sound like mumbo jumbo, all we're really
talking about is changing a business's method of accounting for its inventory costs.
Many accounting issues seem to have little to do with growing and running a
business. But this one is different. Inventory accounting -- and the key question of
whether a company recognizes inflation when accounting for costs -- has an
immediate impact on a company's reported profits, tax payments to Government
and, ultimately, its all-important cash flow. In an inflationary economy such as
ours, this issue is vital for growing businesses to examine, since most rely on an
accounting method that ignores inflation entirely and thus exposes them to
unnecessary costs.
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Case Study-1:
Consider the case of SAST Inc. manufacturer of scuba-diving equipment. After
the company switched to an inflation-sensitive method of accounting for inventory
costs in 2008, its cash flow increased on average by 10% annually. And the
higher inflation goes, the bigger the bang. Last year's cash-flow increase was close
to 25%.
Inflation wasn't always this painless for SAST. The company, founded back in
1954 by the late Sam -- an ex-marine who had invented an easy-breathing
regulator on his kitchen table -- grew to be one of the top names in its field, selling
nearly 5,000 items that range from masks and regulators to diving outfits. But
SAST remained small enough to be vulnerable to various types of inflation. By the
early 1980s its domestic labor costs were increasing at double-digit rates;
meanwhile, the costs of imports -- which added up to about 30% of its product line
-- had also been rising, although not as rapidly, thanks to the then-strong Rupee.
To David and chief financial officer Domnic inflation was just another cost of
doing business, albeit a painful and unpredictable one. But SAST's outside
accountants, Tim., had other ideas. "They came to me with a plan for us to switch
inventory accounting methods -- which some of their other clients had done -- and
said it would save taxes, therefore generating more cash," recalls Goldberg, an
accountant by training. "Frankly, I was worried that it would turn out to be a
gimmick," he confesses, "or an enormous paperwork headache for my staff."
Here's how the proposal worked: SAST, like most small to midsize businesses,
relied on FIFO (first in, first out) accounting for inventory expenses. Put simply,
every time SAST sold a piece of scuba-diving equipment -- which meant it could
write off the cost of producing the item against its profits -- the company would
look back in its records and write off the cost of producing the oldest item in
stock. In an inflationary environment, SAST's executives were in the worst
possible bind: their write-offs were artificially low, thanks to FIFO, but their
current expenses were quite high, because prices were rising.
SAST's outside accountants wanted to switch to the LIFO (last in, first out)
method. "That would bring their write-offs in line with current expenses," explains
Tim partner who now works most closely with the company. "Best of all, it would
accomplish the goal of increasing their write-offs -- always desirable, since this
would cut their tax bill."
The difference between FIFO and LIFO was clear. If it cost Rs.5 to produce the
oldest mask in stock and Rs.10 to produce the newest, SAST would be able to
write off Rs.10 each time it sold a mask under the LIFO method. Under FIFO,
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only Rs.5 could be written off. It sounded great. But there were plenty of
complications -- the kind that worry a financial officer with a small staff and a big
payroll to handle each week. "There were all these accounting decisions we would
have to make -- and it all sounded very, very complex," Tim says, shaking his
head.
So he took the proposal to his chief executive officer, whose response was
admirably straightforward. "He basically didn't understand it," Tim recalls, "but
said he didn't need to understand all those obscure accounting details. All he
wanted to know was whether it made financial sense for us. If I was convinced
that it did, he would do it."
After analyzing some of Tim initial projections, Tim was ready to make the leap.
His fear of hassles, though, was not out of line. LIFO does require more record
keeping than FIFO, especially in the early stages. For companies with large
inventories or limited computer capabilities, this can be a problem, and
unfortunately, SAST fit into both categories. But by the end of the first fiscal year,
the company found that financial rewards had outweighed the extra paperwork.
Analyse the above case with respect to method of valuation of inventory.
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Important adjustments in Final Accounts:
(a) Goods destroyed due to fire and goods are partly insured.
(b) Goods are destroyed due to fire and insurance company compensated-
Accounting treatment and tax implications.
(c) Plant and machinery destroyed due to fire and insurance company
compensated –accounting treatment and tax implications.
(d) Asset purchased enter into purchases account and Sale of building
entered into sales account- Accounting treatment and financial
implications
(e) Goods distributed as free sample for advertisement.
(f) Goods are sent on approval basis- Accounting and balance sheet effect.
(g) Wages paid to erect a machinery entered into wages account.
(h) Closing stock is given in the trial balance-treatment in final accounts.
(i) Outstanding expenses, prepaid expenses given in the trial balance-How
do you adjust?
(j) Provision for bad and doubtful debts, Reserves, provision for tax,
provision for dividend etc- tax treatment and accounting treatments.
(k) Tax paid by the owner -tax treatment and accounting treatment
(l) Advance payment of tax
(m) Prepaid expenses , outstanding expenses new provision for bad debts
and closing stock given in the trial balance.
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CHAPTER FIRST
DEPRECIATION Depreciation under Company Law, Accounting Standards
and the Income-Tax Act, Tax Planning and
Depreciation’s Impact on Finance such as lease/hire purchase/own.
epreciation is an allocation of past investment cash flows to expense
and has no impact on the statement of cash flows. Depreciation is a
significant operating expense and does not involve current cash
expenditure as cash flows are of the past; it is very important expenditure
like material and labour.
If an asset generates cash inflows over its life cannot be considered as
income until enough provision is made for its replacement. Depreciation is
the systematic allocation of the past cash flows over time.
The requirements of the Companies Act are applicable only to companies. In
the case of other entities, such as partnership firms, proprietary concerns and
so on, there is no law governing the charging of depreciation. The ICAI
made it mandatory for auditors to ensure compliance with the Accounting
Standards while carrying out attest functions. It is significant to note that
Accounting Standard (AS) 6 on depreciation does not suggest any rate of
depreciation.
Depreciation Amount: While company law requires 95 per cent of cost of an asset to be depreciated
over its life, the Income-Tax Act does not stipulate such a condition. But AS
6 requires that the historic cost of the asset less its estimated realizable value
to be depreciated over its useful life. The method of depreciation should be
followed consistently.
Deferment of Depreciation: Schedule XIV of the Companies Act lays down the schedule of the
depreciation rates to be charged by companies. It allows companies to
charge rates of depreciation independent of it. Section 205 suggests that a
company can postpone charging of depreciation until the company proposes
to pay dividends. (A note is, at times, appended to the balance sheet and the
auditor puts in his qualification under Section 211(3) a, b and c). But a
D
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dividend-paying company has to write off all previous years depreciation on
its assets and losses before declaring any dividends.
Thus, while there is a possibility that a company may postpone depreciation,
the I-T Act does not allow such a deviation. Following a recent amendment,
assessees will have to compulsorily provide for depreciation, there being a
loss notwithstanding.
Rigid Provisions: The depreciation rates mentioned in Schedule XIV are the minimum rates
and a company may choose to charge more than the rates specified therein.
If company uses higher rate, does it amount to non-compliance with AS 6?
Perhaps the company justifies increased rate of depreciation by providing a
basis for charging an increased rate of depreciation.
Methods of depreciation: While AS 6 does not suggest any method of
depreciation, company law provides an option between the straight-line and
written-down value (WDV) methods. But under income tax, one has to only
follow Block Asset method along with the WDV method.
Concept of Block of Assets: The I-T Act provides for charging of depreciation on a block of assets.
Under company law, each asset is considered independently. Any profit on
sale of assets is reduced from the block of assets, whereas for accounting
purposes, the profits are to be transferred to profit and loss (P&L) account.
Time Concept: Company law requires depreciation to be charged on time basis, say only
four months used during the current period, then depreciation for the current
year is only for four months. Under income tax, depreciation is allowed at
the normal rates for full year if the asset is used for more than 180 days
during the initial year. If it is used for less than 180 days, depreciation is
allowed at half the normal rates. If the same asset was purchased preceeding
to the current previous year but such asset is put into use for less than 180
days during the current previous year, then, full rate of depreciation is
allowed. Thus, if an asset is bought even on 31st March, half of the normal
rates can be claimed under income tax provided the the asset is put into use
during the previous year. Depreciation cannot be claimed for income-tax
deduction in the year of sale of the asset. Even if the asset is sold on 31st
March, the seller cannot claim depreciation. But the buyer can claim half of
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normal rate of depreciation. The date on which the asset is put to use is very
important, as depreciation can be claimed only for the period for which the
asset has been put to use.
Option of Depreciation Method:
Every Company can have its own accounting policy for depreciation.
Method should be Consistenly followed. If one chooses to claim
depreciation under the straight-line method for one class of assets and WDV
for other class of assets or under the same class of assets, too, the company
can claim one method for assets held by it and another method for assets
leased out. Well, income tax does not allow any method other than Block
Asset with WDV and that, too, only at the rates specified by it under Section
32.
Depreciation on Leased Assets:
AS 19 on leases permits the lessor to claim depreciation on assets under
operating lease and the lessee to claim on assets held under finance lease.
Under income tax, the lessor only can claim depreciation no matter whether
the lease is a finance or operating lease.
Assets Given on Lease:
It is now compulsory for companies to show assets given on lease separately
vis-a-vis the assets used by the company for itself. In respect of asset given
on lease, depending upon the internal rate of return (IRR), the company will
have to calculate lease equalisation reserve as per the guidance note on
accounting for leases issued by the ICAI. The system should be capable of
computing the lease-equalisation reserve automatically, given the various
parameters that are necessary for such computation.
Auditor and Depreciation:
AAS 20 requires the auditor to have knowledge of business. Such
knowledge of business would include the intricacies of the usage of assets
and estimated useful life of the asset. Depreciation in a routine simple
estimate (AAS 18) requires the auditor to prepare his estimate of the value
and compare it with the estimate made by the entity to satisfy him with the
value arrived at. An auditor should consider the implications of all these
factors while calculating depreciation on assets.
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Hire purchase or lease? The decision to go in for lease or hire purchase should depend on when the
asset will be put to use, the rate of depreciation available on the asset and the
cash flow position of the user, among others. In case an asset is purchased
under a hire-purchase scheme, the depreciation is available to the hirer (the
user of the asset). But if it is taken on lease, depreciation is allowed to the
lessor (the financer). Hence, acquiring an asset on hire purchase is a better
option than acquiring the same under lease, if the intention is to avail
deduction for depreciation.
However, in a lease, although a lessee (the user) loses the benefit of
depreciation, he can treat the lease rentals as an expense and reduce his
taxable income accordingly..
To claim or not to claim? Until 31 March 2001, a taxpayer had option whether or not to claim
depreciation. However, the claim of depreciation is no longer optional and
the amount of depreciation will be compulsorily treated as deduction,
irrespective of whether or not the claim has been made from 1 April 2001
onwards.
Unabsorbed depreciation: As per Income tax Act certain losses and unabsorbed depreciation can be
carried forward and set off from future profits from business. If, in a
particular year there are losses or inadequate profits, depreciation amount
may not be fully deductible. In such cases, the amount that cannot be
deducted wholly or partially can be set off against any other income. If such
‗unabsorbed depreciation‘ cannot be adjusted against the income of the same
year, it can be carried forward to next year and can be adjusted against any
income of the next year and so on. Unabsorbed depreciation can be carried
forward for any number of years without any limitation.
Special Provision for Free trade zone/Electronic hardware
technology park or Software technology park/Special economic
zone:
19
Such assessee can claim 100% of their total income for a period of
10 consecutive assessment years under section 10A of the Income
tax Act
Depreciation and Financial Implications: Method of depreciation is not a method alone. It has financial impacts that
differ from method to method. Assets that are put into use or ready to use
during the previous year can be depreciated as per the rate prescribed by
Income tax Act. Companies Act prescribe different rate as per schedule XIV.
Depreciation is to be provided on all assets except land and goodwill as per
Accounting Standard Number 6.
Before calculating depreciation we have to keep in mind that the value of
the asset is to be properly calculated. All costs that are incurred before the
asset is put into use have to be capitalized. They include purchase cost,
import duty, installation charges etc.
As I have earlier said method of depreciation makes lots of difference to the
organization with respect to finance. Observe the following tables:
Table-1: - Assumed PBDT is Rs.50, 000 and rate of depreciation is 20%
Year Beginning
value
Rs.
Depreciation
SLM
Net
income
Rate of
return on
assets
1
2
3
4
5
1,00,000
80,000
60,000
40,000
20,000
20,000
20,000
20,000
20,000
20,000
30,000
30,000
30,000
30,000
30,000
30%
37.5%
50%
75%
150%
Rate of return on assets =Income/Beginning value of asset
Table-2: - Rate of Depreciation as per WDV is 1.5 times of SLM i.e. 30%
Particulars Beginning
value
Depreciation
WDV
Net
income
Rate of return on
assets
1 1,00,000 30,000 20,000 20%
20
2
3
4
5
70,000
49,000
34,300
24,010
21,000
14,700
10,290
7,203
29,000
35,300
39,710
42,797
41.42%
72.04%
115.7%
178.25%
Important observations from the above tables:
Particulars SLM WDV
Depreciation
Net Income
Asset
Equity
ROE
ROE
Turnover Ratio
Cash Flow
Lower
Higher
Higher
Higher
Higher
Higher
Lower
Same
Higher
Lower
Lower
Lower
Lower
Lower
Higher
Same
The above table to be read from early stage of asset. It is reversed at the
latter years of the asset‘s life.
1. Cash flows are not affected directly because depreciation is a non-
cash expense. But indirectly has some impact on cash flows if such
firm comes under tax. If there is tax holiday, it does not have any
impact on cash inflow or outflow.
2. If tax is considered, then the firm, which adopts WDV, recovers its
investments much faster as tax liability under WDV at early stage is
lower. Therefore Pay back period is low and NPV is higher than the
company, which follows SLM.
3. IRR is higher if firm follows WDV
4. Firm with stable or rising capital expenditures, the early year affect
will dominate and depreciation expense on the total firm basis will be
higher.
5. If firm invests in new assets out of the cash flows generated, in such
circumstances it provides less depreciation on old asset and more
depreciation on new asset under WDV, which compensate each other.
21
6. There is a lower income under WDV, which causes a lower return on
Equity and return on Assets.
7. The turn over ratio (sales over Total Asset), the lower asset levels for
WDV method imply a higher ratio.
Depreciation and Tax PlanningU/S-32 of IT Act: In India Block Asset method is followed for tax purpose. The rate of
depreciation also prescribed as per Income Tax Act 1961. There is scope for
tax planning when an asset is sold which exceeds the block value. The
company can buy another the same nature asset having the same rate of
depreciation, which is at least equivalent to the extent of short-term capital
gain so that the block value will be zero.
When own funds used in plant and machinery -18.66% saving
When borrowed funds used –Tax savings through depreciation-
22.91%
Depreciation on intangible assets can be provided at 25% rate.
The eligible assets are: Know How, Patent Right, Copy Right,
Trade Mark, Licenses, Franchises, any other Commercial
Rights.
Carry forward and set of depreciation in the subsequent periods
Amalgamation, absorption, reconstruction and demerger-
Accumulated depreciation and set off against profits of new
company(Amalgamating company)
Purchase and put into use or ready to use a new asset at the end
of the financial year or 180 days before the end of the financial
year.
Sell old asset at the beginning of the previous year.
File your returns in the year of loss otherwise, the loss can not
be setoff.
In order to avoid Capital gain tax, the amalgamating company
should allot everything to the Amalgamated company
shareholders in shares. Cash should not be paid for settlement
of shareholders‘ claim.
22
Can a New Company(Amalgamating) which absorbs an Old Company
(Amalgamated) carry forward and set off unabsorbed losses and
depreciation?
Conditons:
(a) Sec 72 of IT Act to be fulfilled.
(b) Accumulated losses remain unabsorbed for 3 or more years.
(c) 75% of book value to be held at least for 2 years before
amalgamation.
(d) The amalgamated Co. continues to hold 3/4th of book value at
least for 5 years.
(e) New Co. should continue for another 5 years.
(f) New Co. should achieve at least 50% of installed capacity
before the end of 5 years and should continue for 5 years.
(g) The Company which acquires should be an Indian Company.
CARRY FORWARD AND SET OFF OF BUSINESS LOSSES (SECTION 72 of the Income tax Act) Where the loss under the head ‘profits and gains of business or profession’ other than loss from speculation business, could not be set off in the same assessment year because either the assessee had no income under any other head or the income was less than the loss, such loss which could not be set off in the same assessment year, can be carried forward to the following assessment years, However it is subject to following conditions. I) Business losses can be adjusted only against business income: Business income may be from the same business in which the loss was incurred, or may be any other business. II) Business in respect of which a loss is incurred may or may not be continued. III) Losses can be set off only by the assessee who has incurred loss with a few exceptions like when a partnership firm is converted into a company, amalgamation of companies, etc. IV) Period of carry forward: Each year’s loss is a separate loss and no loss shall be carried forward for more than eight assessment years immediately succeeding the assessment year for which the loss was first computed. Therefore, a loss of previous year 2002-2003, i.e. assessment year 2003-2004 can be carried 161
forward till assessment year 2011-12. Besides the above, the following can also be carried forward indefinitely, as per income tax law: i) Unabsorbed depreciation ii) Unabsorbed capital expenditure on scientific research;
23
iii) Unabsorbed expenditure on family planning.
SET OFF AND CARRY FORWARD OF SPECULATION LOSS (SECTION 73 of the Income tax). As stated earlier, the loss of a speculation business of any assessment year is allowed to be set off only against the profits and gains of another speculation business in the same assessment year. If a speculation loss could not be set off from the income of another speculation business in the same assessment year, it is allowed to be carried forward for 8 assessment years immediately succeeding the assessment year for which the loss was first computed. Also, it can only be set off against the income of only a speculation business. It may be observed that it is not necessary that the same speculation business must continue in the assessment year in which the loss is set off. Compulsory filing of loss of return (Section 80): Although the above losses are allowed to be carried forward, it is allowed only when such loss has been determined in pursuance of a return of loss submitted y the assessee on or before the due date for filing of the returns prescribed under section 139(1) .However loss under the head income from house property can be carried forward even if the return is not filed within the due date mentioned under section 139(1).
If the above conditions are fulfilled the unabsorbed depreciation and
accumulated losses can be set off against the profits of the absorbing
Company (New Company).
24
Other Tax Benefits:
1. Expenditure on amalgamation or de-merger – allowed under
Sec.35DD both revenue and capital expenditure allowed.
2. Expenditure on scientific research can be carried forward and
set off.
3. Expenditure on acquisition of patent rights, copyrights –
depreciation can be provided.
4. Expenditure for obtaining license for telecommunication
service can be written off.
5. Preliminary expenses can be written off.
6. Capital expenditure on family planning can be set off against
profits.
7. Bad debts of the absorbed Company can be written off by the
absorbing company.
Illustration 1 From the following information submitted to you, compute the taxable income in the following situation. Situation I Situation II Rs. Rs. Long term capital gain/loss (+) 2, 80,000 50,000 Short term capital gain/loss (-) 50,000 (-) 1, 20,000
25
Business income/loss (-) 1, 80,000 1, 40,000 Solution Situation I Situation II Rs. Rs. Capital gain Long term capital gain/loss (+) 2, 80,000 50,000 Short term capital gain/loss (-) 50,000 (-) 1, 20,000 Capital gain/loss after set off 2, 30,000 (-) 70,000 Set off of business income/loss (-) 1, 80,000 1, 40,000 Total income 1, 50,000 1, 40,000* *In situation II, capital loss of Rs. 70,000 will be carried forward and the total income shall be Rs.1, 40,000. Hence , we observe business loss can be set off against capital loss but vice-versa is not allowed. Illustration 2 From the following information submitted to you by Mr. X, calculate the gross total income for the A.Y 2006-07. I II Income from salary 2, 00,000 2, 00,000 Income from Bus/Prof (-) 50 ,000 (-) 50 ,000 Income from House Property _ 80,000 Solution In situation I his GTI would be 2, 00,000 and his loss from business and profession will be carried forward ( Any loss under the head Business & Profession cannot be set off against any income from Salary). In situation II business loss can be set off against income from House Property and his GTI would be Rs. 2, 30,000.
Exercise:1:Block Asset method of depreciation . Machine tools Ltd. Is considering the acquisition of a large equipment to set up its
factory in Siva Gangai District which is Mr.Chidambarm‘s constituency, the finance
Minister of India for Rs.20,00,000. The equipment is expected to have a expected useful
life of 4 years. The asset can be sold at the end of the fourth year for Rs.5,00,000. The
depreciation rate is 25% as per block asset method. The tax rate is 30%. Discounting rate
is 12% per annum.
There are two options available to you.
a) The equipment can be financed either with a 4 – year term loan at 14% interest,
repayable in equal annual instalments. or
b) Taking the property on lease paying Rs.5, 50,000 per annum.
Evaluate the method of acquiring the asset for the company
26
Calculation of Depreciation :
Year Beginning
Value
Depreciation End Value Tax benefit on
Depreciation
1 20,00,000 5, 00,000 15,00,000 1,50,000
2 15,00,000 3,75,000 11, 25,000 1, 12,500
3 11,25,000 2,81,250 8,43,750 84,375
4 8,43,750 ------------ ------------
( In the year of sale no Depreciation )
Calculation of Capital loss ( Short term )
Book value = 8,43,750
Less: Sale = 5,00,000
Short term Capital Loss 3,43,750
3) Net Cash Inflow at the end of the 4th
year
Sale of Asset 5,00,000
Tax benefit on short term capital loss 1,03,125
Cash inflow at the end of the 4th
year 6,03,125
4) Calculation of Interest and Principal
a) PVIFA = 2.914, 14%, 4 years
Equated annual investment 20,00,000
2.914
= 6,86,342
b) Calculation of Principal and Interest
Year Principal Interest Total Cash Loan
27
Repayment payment Inflow
1 4,06,342 2,80,000 6,86,342 20,00,000
2 4,63,230 2,23,112 6,86,342 15,93,658
3 5,28,032 1,58,260 6,86,342 11,30,428
4 6,02,014 84,328 6,86,342 6,02,346
c) Tax Benefit on Interest
Year Interest Tax Benefit
1 2,80,000 84,000
2 2,23,112 66,934
3 1,58,260 47,478
4 84,328 25,298
d) Cash outflows and Present Value
Year Annual
Installments
Tax Benefit
on
Depreciation
Tax
benefits on
Interest
PV factor
at
12%
Present
Value
1 6,86,342 1,50,000 84,000 0.893 4,03,941
2 6,86,342 1,12,500 66,934 0.797 4,04,006
3 6,86,342 84,375 47,478 0.712 3,94,796
4 6,86,342 ------------- 25,298 0.636 4,20,424
Total 16,23,167
Less: Net Cash Inflow on sale of asset at the end of 4
th 3,83,588
PV of Cash Outflows 12,39,580
Lease
a) Annual Lease Payment 5,50,000
Less: Tax benefit on Lease payment 1,65,000
3,85,000
Present Value of Lease Payment
3,85,000 X 3.037 = 11,69,245
Conclusion:
Select Lease
28
Exercise-2
Plant and machinery costs Rs.5,00,000 salvage value is Rs. 1,00,000
The rate of depreciation as per Companies Act is 20% whereas income tax rate
of depreciation is 25% . How do we calculate depreciation? Life is 3 years. By using calculator the value at the end of three years assuming the assets are
disposed of at the beginning of 4th
year =0.75*5,00,000= = =2,10,937.5-1,00,000
= 1,10,937(loss)
1,00,000+1,10937(.339)
=1,37,607(Inflow)
Suppose salvage value is 3,00,000
Short term capital gain= 3,00,000-2,10,937
=89,063
Tax on 89,063=89063*.339=30,192
Net cash inflow =3,00,000-30,192
=2,69,807.This should be discounted to today’s value
Example:3. Plant and machinery costs Rs.5,00,000 salvage value is Rs. 1,00,000
The rate of depreciation as per Companies Act is 20% whereas income tax rate of depreciation is
25% . Life is 3 years. Tax rate=30% surcharge 10% and 3% educational cess.
How do we calculate Capital loss? Cash Inflow at the end of the third year?.
Answer
Short term capital loss
Block value at the end of 2nd year- scrap at the end of three years
=Rs.2,81,750-Rs. 1,00,000
=Rs. 1,81,750
Cash Inflow at the end of third year
=Rs.1,00,000+(*33.90% *1,81,750)
= Rs.1,61,613
*Tax= 30%+10%(30%)+3%*33=33.99%
DDeepprreecciiaattiioonn aass ppeerr IInnccoommee ttaaxx aacctt Year
Beginning value
Depreciation
25%
End value
1
2
3
5,00,000
3,75,000
2,81,750
1,25,000
93,750
No
3,75,000
2,81,750
29
EExxeerrcciissee--44 oowwnneedd ffuunnddss VVss bboorrrroowweedd ffuunnddss
An assessee who carries on a business, acquires a plant and machinery costing
Rs.10,00,000 in a year one. This plant is used for 5 years and will be discarded at the
end of 5th year for Rs. 2,00,000.
Tax rate is 30%, surcharge is 10% and educational cess is 3%.Assume the plant is
sold at the end of the 5th year. Cost of Capital is 10% and rate of depreciation is
15%.
Required:
1. Evaluate when owned funds are invested
2. When 75% cost of plant is financed by deposit taken from public at the rate of
9%pa.
Present value of scrap =*3,09,158*.620=1,91,678
*Scrap value=2,00,000
*Calculation of short term capital gain as the asset is depreciated
Book value at the end of 4th year-scrap value=5,22,000-2,00,000
=3,22,000
Tax savings on STCG=3,22,000*.339
=*1,09,158
Present value on tax saving on STCG= 1,09,158*0.620=37,004=67,678
Net present cash out flow value
Initial cash out flow-Present value of tax savings on depreciation-present value of cash inflow on
scrap
Rs.10,00,000-Rs.1,35,420-Rs.1,91,678=Rs.6,72,902
30
EExxeerrcciissee--55 LLeeaassee vvss PPuurrcchhaassee An assessee who carries on a business, acquires a plant and machinery costing Rs.10,00,000 in a
year one. This plant is used for ten years and will be discarded at the end of ten years for Rs.
2,00,000.
Tax rate is 30%, surcharge is 10% and educational cess is 3%.Assume the plant is sold at the end of
the 10th year. Discounting rate is 10% and rate of depreciation is 15%.
Required:
1. Evaluate when plant taken on lease by paying lease rental of Rs. 3,50,000 for the first five years in
the beginning and 50,000 thereafter for the remaining years.
2. When 75% cost of plant is financed by deposit taken from public at the rate of 9%p.a.
Exercise-6
21. Machine tools Ltd. is considering the acquisition of a large equipment to set
up its factory in Siva Gangai District which is Mr.Chidambarm ,Finance Minister‘s
constituency, for Rs.20,00,000. The equipment is expected to have a useful life of 4
years.. The asset can be sold at the end of the fourth year is Rs.5,00,000.The depreciation
rate is 25% as per block asset method as per Income tax Act 1961. There are two options
available to you
a) The equipment can be financed either with a 4 –year term loan at 14% interest,
repayable in equal annual instalments.
b) Taking the property on lease paying Rs.5,50,000 per annum.
The tax rate is 30%.
Some shortcut techniques in finance:
11..NNPPVV wwiitthh tthhee HHPP1100BB:: -276,400 CFj
83,000 CFj
4 shift Nj
116,000 CFj
15 I/YR
shift NPV
You should get NPV = 18,235.71.
Somss
22..NNPPVV wwiitthh tthhee HHPP1177BBIIII::
Select CFLO mode.
FLOW(0)=? -276,400 INPUT
31
FLOW(1)=? 83,000 INPUT
#TIMES(1)=1 4 INPUT
FLOW(2)=? 116,000 INPUT
#TIMES(2)=1 INPUT EXIT
CALC 15 I% NPV
You should get NPV = 18,235.71
33..NNPPVV wwiitthh tthhee TTII BBAAIIII PPlluuss::
Select CF mode.
CFo=? -276,400 ENTER
C01=? 83,000 ENTER
F01= 1 4 ENTER
C02=? 116,000 ENTER
F02= 1 ENTER
NPV I= 15 ENTER CPT
You should get NPV = 18,235.71
44..PPII wwiitthh tthhee HHPP1100BB::-276,400CFj
83,000 CFj
4 shift Nj
116,000 CFj
15 I/YR
shift NPV
You should get NPV = 18,235.71.
Add back IO: + 276,400
Divide by IO: / 276,400 =
You should get PI = 1.066
32
55..SShhoorrtt ccuutt tteecchhnniiqquueess bbyy uussiinngg aann oorrddiinnaarryy
ccaallccuullaattoorr.. Future value at 10%
year 1. 1.1
Year 2. 1.1*=
Year 3. 1.1*= =
Year 5. 1.1*= = = =
66..SScciieennttiiffiicc ccaallccuullaattoorr Amount*1.1= for the first year
Amount *1.1*1.1= for the second year
Amount *1.1*1.1= = = = 6th year value
77
7
77..PPrreesseenntt vvaalluuee bbyy oorrddiinnaarryy ccaallccuullaattoorr 1st year 1.1/=
2nd year 1.1/= =
6rd year 1.1/= = = = = =
88..WWDDVV vvaalluuee 15% depreciation as per WDV
value at the end of 1st year= 0.85*asset value=
Value at the end of 2nd year =0 .85*asset value= =
Value at the end of 6th year=0.85*asset value= = = = = =
Threat is an Opportunity:: Strengthen Your Weakness
CHAPTER - 1
CAPITAL STRUCTURE
33
isk and Return is the base for Capital Structure. Firm with low debt
with less risk receives fewer returns. High risky debt capital (Cost of
acquisition per year) reduces the shareholders‘ value due to high
expectations of the shareholders as they discount the cash inflows at a higher
cost of capital. The optimal capital structure finds the balance between the
use of debt and equity in order to maximize stock price.
The Target Capital Structure: Every firm tries to maintain debt equity ratio over time. If the debt ratio is
less than the target level the firm will raise new capital by using more debt.
If the debt ratio is more than the target level, the firm will raise new capital
by retained earnings or issuing new equity or capitalizing existing reserves
by issue of bonus shares. Every firm has to weigh the trade off between risks
and return associated with the use of debt. Increase in debt increases the risk
of shareholders. Thus, the firm‘s optimal capital structure is the one that
balances the influence of risk and return that maximize the firm‘s stock
price. The optimal debt ratio will be the firm‘s target capital structure.
Factors influence the firm’s capital structure: There are many factors which influence the firm‘s capital structure
decisions. They are:
Existing debt position
Management‘s perception towards risk
Business risk
Cost of debt
Cost of Equity
WACC
The firm‘s Tax position
Financial flexibility
Leverages
Explanations 1. Business Risk:
This is the risk inherent in the firm‘s operations assuming no debt capital.
The greater the firm‘s business risk, the lower its optimal debt ratio. The
uncertainty inherent in a firm‘s return on assets (ROA) is considered as
business risk. They are as follows:
Uncertainty on demand (units)
Sales volume and price variability
R
34
Uncertainty with respect to input cost
Ability to adjust output prices for changes in input prices
High/low fixed costs which are reflected on operating
leverage.
Business risks could be measured as follows:
2. The Firm’s Tax Position: As far as India is concern, the tax rates were brought from 67% before 1991
to 34% in 2008, which has an impact on capital structure of Indian firms.
Tax holidays are given to some of the industries may not realize benefits
much from debt capital comparing to the companies, which comes under tax.
Additional debt or equity or capitalization of reserves depends on tax
benefits to the firm in the form of reduction from operating profit for tax
purpose.
In India the higher the income tax the higher the debt/Equity ratio.
3. Financial Flexibility:
This is the firm‘s ability to raise capital with reasonable terms under adverse
conditions.
4. Leverages: Firm incurs variable and fixed costs. If fixed costs are high percentage, the
firm is said to be in high operating leverage. In business terms, higher
operating leverage produces a higher expected rate of return. It means
relatively small change in sales will result in a large change in operating
income.
Degree of operating leverage is defined as the percentage change in
operating income (EBIT) that results from a given percentage change in
sales.
Standard Deviation of Operating Income
Business Risk = ----------------------------------------------------
Average of Operating Income
35
Financial leverage refers to the use of fixed income securities (debt and
preference shares). It magnifies the variability of earning per share due to the
existence of the required interest payments. The degree of financial leverage
(DFL) is defined as the percentage change in earnings before interest and
taxes.
The % change in EPS = DFL(% change in EBIT)
How to determine the Optimal Capital structure?
If risk is increased due to rising of debt it should be compensated by high-
expected rate of return. If the issuance of debt increases the value of the
firm, then debt should be used and the debt ratio that maximizes the firm‘s
value is the optimal capital structure.
We can use EBIT/EPS analysis in order to understand the concept.
Example: 1
Debt/Asset
Ratio
Amount
Borrowed
(Rs.)
Rate of Interest
10%
20%
30%
40%
2,00,000
4,00,000
6,00,000
8,00,000
8%
9%
11%
12%
Assume tax rate is 34% including educational cess, contribution ratio is
40%. Fixed cost Rs.4,00,000/- Number of shares outstanding before
borrowing is 1,00,000. The firm expects that the sales will be Rs.
20,00,000/- How does different levels of debt/Asset ratio affect the EPS?
Answer:
Contribution = 40% of 20,00,000/-
= Rs.8,00,000/-
Less: Fixed cost = Rs. 4,00,000/-
PBIT = Rs.4,00,000/-
Particulars 0 debt 10% debt 20% debt 30% debt 40% debt
PBIT
Less: Interest
4,00,000
NIL
4,00,000
16,000
4,00,000
36,000
4,00,000
66,000
4,00,000
96,000
36
PBT
Less: Tax (34%)
PAT
No. of shares
EPS
4,00,000
1,36,000
2,64,000
1,00,000
2.64
3,84,000
1,30,560
2,53,440
90,000
2.816
3,64,000
1,23,760
2,40,240
80,000
3.003
3,34,000
1,13,560
2,20,440
70,000
3.149
3,04,000
1,03,360
2,00,640
60,000
3.344
We can understand from calculations shown above that issuing debt to
finance assets definitely increases EPS. Since EPS increases does it mean
that we can increase the debt to 100%? The answer is no. The optimal
capital structure is the one that maximizes the firm‘s stock price and not the
one that maximizes the firm‘s EPS.
The following discussion explains the impact on stock price: Debt/Asset ratio Kd(Cost of debt Expected
EPS=DPS
Estimated Beta
0%
10%
20%
30%
40%
-
8%
9%
11%
12%
2.64
2.816
3.003
3.149
3.344
1.5
1.55
1.8
2.3
2.5
Assume tax rate is 34%, risk free return(Krf) is 6% and the market
expectations Km=10%.
By using CAPM model to estimate the company‘s stock required rate f
return will be:-
Ks = Risk free return + beta(Km-Krf)
Where Ks = Required rate of return on Company‘s stock
Krf = Risk free return(Normal return under any circumstances
Km = Market return on portfolio
Beta = Relative volatility (risk) compared to the stock market
portfolio.
Let us analyse under different debt/asset ratio the price of stock and WACC.
Zero debt:
Ks = 6%+ 1.5(10-6)=12%
37
Po = dividend per share/Ks=2.64/.12=Rs.22
WACC=Cost of Equity= 12%
10% debt:
Ks = 6%+ 1.55(10-6)=12.2%
Po = 2.86/0.122=Rs.23.08
WACC= 0.1(8)(1-0.34) + 0.9(12.2)=11.508%
20% debt:
Ks = 6%+ 1.8(10-6)=13.2
Po = 3.003/0.132= Rs.22.75
WACC= 0.2(9)(0.66) +0.8(13.2)=11.748%
In the same way level 30% and 40% debts can be calculated. The summary
is given below.
Particulars 0 debt 10% debt 20% debt 30% debt 40% debt
Cost of debt
EPS
Cost of Equity
Stock Price
WACC
-
2.64
12%
22
12%
8%
2.816
12.2%
23.08
11.508%
9%
3.003
13.2%
22.75
11.74%
11%
3.149
15.2%
20.717
12.818%
12%
3.344
16%
20.9
12.768%
The above table explains that at 10% debt the WACC is minimum and the
stock price is maximum. It also indicates that beyond certain % of debt the
cost of equity is high as the expectation of shareholders are high when risk
is high which brings down the stock price
Important ratios to study Capital Structure:
1. Business Risk = S.D of operating Income/Average of Operating Income.
2. Sales Variability= S.D of Sales/Average of Sales.
3. Operating Leverage = Average change in operating earning/Average
change in sales.
4. Debt Equity Ratio = Debt/Equity.
5. Asset to Equity Ratio= Total assets/Equity.
6. Earning or Cash Flow Ratios.
7. Interest coverage ratio= EBIT/Interest expenses
8. Fixed Charge Coverage Ratio = (EBIT+ Lease payment)/ (Interest
payment+ Lease payment+ Preference dividend/(1-t)
38
Basic Terms used in Capital Structure:
1. Definitions:
Capital structure is the mixture of sources of funds a firm uses (debt,
preferred stock, common stock). The amount of debt that a firm uses to
finance its assets is called leverage. A firm with a lot of debt in its capital
structure is said to be highly levered. A firm with no debt is said to be
unlevered.
Capital structure can be viewed as the permanent financing the firm
represented primarily by long-term debt, preferred stock, and common
equity but excluding all short term credit.
2. Financial Risk The increased financial risk that comes with increased use of debt tends to
moderate the use of debt in the firm's capital structure.
3. Cost of Capital:
Interest rate on borrowings after tax or opportunity cost on equity or reserves
and surplus.
4. WACC:
Overall cost of firm which includes cost of debt, preferred stock, equity and
reserves and surplus.
5. EPS= Earning Per Share: Profit after tax and preference dividend / number of equity shares.
6. Diluted EPS: It is due to future income which will be derived after redemption of
preference shares/debt/buy back or fresh issue of shares/all shares that will
be obtained after converted preference shares, convertible debentures and
bonus issues.
7.Working capital loan criteria by IDBI •Eligibility criteria-financially sound companies
39
•Net worth:- Not less than Rs.15 Cr.
•Debt/Equity ratio:-3:1
•Current ratio:1.25:1
•Interest Coverage ratio:2:1
•Extent of Asistance:Upto 80% of Working capital gap. Min. Rs.2 Crore or US$ .50mn
•Rupee loan Interest-Minimum term lending rate plus Risk Spread
Exercise: 1.
•
Current liabilities
Creditors for purchase 200
Other current liabi-80
Bank borrowing-400
•Current Assets
Raw materials-300
Stock in progress-100
Finished goods-150
Receivables-100
Other current assets-50 What is the Maximum permissible bank finance(MPBF) as per Narasiman committee? Answer: Method -1
Total current assets 700
Less: other current liabilities 280
(excluding borrowing)
Working capital gap 420
25%of working capital margin 105
Maximum permissible bank finance(MPBF)-315
Excess borrowings-85
NO WORKING CAPITAL FINANCE PERMISSABLE
Method-2
Total current assets 700
Less:25% of above as margin
40
From long term source 175
Eligible current assets 525
Less:other current liabilities 280
MPBF 155
(Maximum Permissible Bank Finance) Notes:
•
II method ensures a minimum current ratio of 1.33:1
•Chore committee recommends the II method of lending.
•Repayment of loan can not be more than 5 years.
CCaasshh FFllooww SSttaatteemmeenntt aanndd ootthheerr ffiinnaanncciiaall aannaallyyssiiss
Companies obtain different types of capital. We can broadly categories into Long term
funds and Short term funds. We know that whenever long term funds such as issue of
shares, preference shares, debentures and public deposits are issued they are expected to
be used for long term profit generating assets such as purchase of plant and machinery,
building etc. If short term funds such as over drafts, cash credit are generated, it is
expected such funds should be used for short term purpose such as purchase of stock,
payment to creditors etc. All long term funds are not fully utilized for long term or all
short term funds are utilized for short term. Invariably, there are movements of funds
which take place from long term to short term or short term to long term.
Funds are also generated from profit by doing basic functions of the organization by
buying and selling of goods and services or lost when company incurs trade losses. The
funds that are generated/lost from trade activity is called fund from operation/loss from
operation. These funds may be utilized for long term or for short term.
All funds that are generated in cash forms are studied and see the flow of cash from long
term to short term or vice versa are creating any cash crunch problem to the organization.
If problem arises the organization should know which funds has to be brought whether
short term or long term funds. The cash flow statement is prepared to know the flow of
funds and their financial impact on long term or short term.
Each type of fund has some impact on the overall performance of the company. Debt
Equity ratio, current ratio, liquid ratio, return on capital employed, WACC, profitability,
liquidity, flexibility are affected. We use CFS as the means to study the impact and
required adjustments required by forecasting these changes. Balance sheets and income
statements are forecasted for three to five years and study the flow of cash whether they
are conducive to the firm.
41
(A) Relevance of Cash Flows:
Explain the relevance of cash flows to analyzing business activities.
Cash is the most liquid of assets and offers a firm liquidity and flexibility. The term cash
includes cash and cash equivalents, which are short-term highly liquid investments.
The Statement of cash flows helps in assessing:
Liquidity, which represents how near assets and liabilities are to being cash.
Solvency, which represents the firm‘s ability to pay liabilities when due.
Financial flexibility, which represents the firm‘s ability to react and adjust to
opportunities and difficulties.
The statement of cash flows provides information to answer questions such as:
How much cash was generated from operations?
What was the cash used for?
What was the source of the cash invested in Property Plant & Equipment
(PP&E)?
How was the cash received from a bond issue used?
How was the firm able to pay dividends when the company experienced an
operating loss?
How was the firm able to retire its long-term debt?
How were investments financed?
Why did cash decrease when the firm experienced record profits?
(B) The Statement of Cash Flows:
Statement of Financial Accounting Standards (SFAS) 95 and Indian Accounting
Standard 3 require that a Statement of Cash Flows (SCF), accompany the
income statement and balance sheet.
The SCF explains the change in cash and cash equivalents during the year,
classified by operating (i.e., earning) activities, financing activities, and investing
activities.
42
SFAS 95 encourages the use of direct or inflow-outflow method, which makes
adjustments for balance sheet changes directly to revenue and expense
components of income statement, rather than to net income.
Operating Cash Flows:
Describe the elements of operating cash flows.
1. Cash flows from operations (CFO) reflect flows related to the normal operating
activities of the business.
2. These items essentially flow through the firm‘s income statement and working
capital accounts. Working capital accounts are current assets and current
liabilities.
3. Cash flow from operations includes cash collection from customers and cash
payments to merchandise suppliers, for salaries, and for interest.
4. Under SFAS 95, interest and dividend revenue and interest expense are
considered
operating activities, but dividends paid are considered financing activities.
5. All income taxes arc considered operating activities, even if some arise from
financing or investing.
Investing Cash Flows:
Describe elements of investing cash
1. Cash flows from investing (CF1) reflect investing activities. These are the
acquisition of noncurrent assets (outflows) and the retirement of these assets
(inflows).
2. These items are found in the noncurrent portion of the asset section of the halance
sheet. Cash How from investing includes cash received from the sale of properly
plain & equipment and long-term investments in addition to the cash paid out to
purchase these noncurrent assets.
3. Investing cash flows also include cash flows from investments in joint ventures
and affiliates, long-term investment in securities.
Financing cash flows:
Describe the elements of Financing cash flows.
43
1. Cash flows from financing (CFF) reflect cash received from issuing or cash paid out
retiring long-tenrm debt (including the current portion of long-term debt), stock
(common and preferred), or in paying dividends.
2. These items are found in the long-term capital section of the balance sheet and the
statement of retained earnings (RE).
3. CFF includes dividends paid to stockholders but not interest paid to creditors. The
interest payments are run through CFO. Excluding interest payments from CFO
would make cash flow from operations independent of the firm‘s leverage decisions.
Thus for analytical purposes you might prefer to reclassify interest payments as CFF
rather than CFO.
Classify a particular item as an operating cash flow, an investing cash flow, or a
financing cash flow.
The following is the format of the basic statement of cash flows:
Example:
Using the following income statement (I/S) and balance statement (B/S) items for 2009,
calculate the firm‘s SCF:
(Rs.)
Sale of land 20,000
Collections from customers 70,000
Payment of interest 1,000
Cash payment of dividends 6,000
Cash received from issue of long term debt 40,000
Payment of wages 10,000
Purchase of equipment 90,000
Payment to suppliers 5,000
Cash balance on 31st march 2008 25,000
STATEMENT OR CASH FLOWS (SCF)
FOR THE PERIOD 31/12/2008 TO 31/12/2009
Cash Flow from Operations (CFO)
+ Cash Flow from Investing (CFI)
+ Cash Flow from Financing (CFF)
= Change in the cash account
+ Beginning of period cash
= Ending cash balance
44
The Statement of Cash Flow for the Year ending 31/03/09 is:
Cash Flow from Operations (CFO):
Collections from customers Rs.70,000
Payment of wages (10,000)
Payment to suppliers ( 5,000)
Payment of interest ( 1.000)
CFO Rs.54,000
Cash Flow from Investing (CFI):
Sale of land Rs.20,000
Purchase of Equipment (90.000)
CFI (Rs.70,000)
Cash Flow from Financing (CFF):
Issuance of long-term debt Rs.40,000
Payment of dividends ( 6.Q00)
CFF Rs.34.000
Net Increase in cash: Rs.18,000
Cash balance on 31/03/2008 25.000
Cash balance on 31/03/2009 Rs.43,100
The ending balance of the cash account is a managerial finance decision and thus has
little analytical significance. The cash flow tells us that the investing significantly in
equipment financed by cash thrown-off from operating and by issuing long-term debt.
For analytic purposes the cash payment of interest can be reclassified as a cash flow from
financing thereby increasing CFO to Rs.55,000 and decreasing CFF to Rs.33,000.
[c] Direct and Indirect Methods
When using the indirect method, start at the bottom of the income statement with net
income and back into cash flow from operations by adjusting reported net income.
When using the direct method, start at the top of the income statement with sales then
work with the individual components of net income directly related to cash flows (e.g.
revenue, cost of goods sold, salary expense, and interest expense).
Note: These methods are equivalent since they both yield the same cash flow from
operations. These two methods differ only in the detail of presentation.
Calculating Operating Cash Flows Using the Indirect Method
Start with net income and adjust for all non-cash expenses and non-cash gains and
losses.
45
[Net income + non-cash expenses — non-cash gains + non-cash losses]
↓
Calculate the change in all other operating account items
[Increases in operating asset accounts are negative adjustments and increases in operating
liability accounts are positive adjustments]
↓
Put it all together
[CFO = net income +/- non-cash items - change in operating assets accounts + change in
operating liability accounts]
Calculating Operating Cash Flows Using the Direct Method
Calculate cash collections
[Net sales - change in accounts receivable + other cash collections]
Calculate direct cash inputs^
[Cost of" goods sold"- change in inventory + change in accounts payable]
↓
Calculate other cash outflows
[Cash expenses + cash taxes paid + cash interest paid]
↓
Put it all together
[CFO = cash collections + direct cash inputs + other cash out flows]
Observe that the direct method just looks at the cash received from customers and other
operating sources and cash paid out in operating expenses. However, the indirect method
does not communicate cash inflows and outflows with the particular revenues and
expenses as is done under the direct method. Because most companies use the indirect
method, it is often necessary to convert an indirect CFO statement into a direct CFO
statement.
(D) Preparation of a Statement of Cash Flows
1. Transactional analysis reconciles changes in the balance sheet accounts with the
related income statement components in the derivation of cash flows.
This method involves looking at change in balance sheet items and comparing them
to the corresponding income statement components.
Steps:-
Start with sales, and adjust for cash effect of changes in balance sheet items.
a. Changes in accounts result in effects on cash flows.
An increase in an asset is a decrease in cash flow.
A decrease in an asset is an increase in cash flow
An increase in a liability or equity account is an increase in cash flow.
A decrease in a liability or equity account is a decrease in cash flow.
Depreciation / 46
2. The direct and indirect methods must adjust cash for changes in the working capital
balances.
a. For example, if sales grow (or fall) but the collections of receivables proceed at a
pace different from the change in sales, there will be a change in the accounts
receivable balance. This could represent either a source or use of the firm‘s cash.
To determine which, subtract for increases in accounts receivable (a use of cash)
or add for decreases in accounts receivable (a source of cash) to adjust for
changes in sales and collection.
b. Similar adjustments must also be made for changes into the inventory account and
the accounts payable account. Remember, this is the flow of cash and not
accruals based income, so adjustments must be for changes in these accounts.
The following charts should help determine whether to add or subtract for
changes in working capital accounts.
Increase Decrease
Current Assets:
Accounts Receivable and Inventory
- +
Current liabilities:
Accounts Payable, Wages Payable, and Taxes and
Deferred Taxes.
+ -
Example:
Calculate cash collected from customers from the following chart that discloses sales, bad
debt expense, and year-end net receivables.
1999 2008 2009
Sales Rs.100 Rs.200 Rs.300
Bad Debts Expenses 5 5 6
Net Receivables (1998=20) 30 70 120
Cash Collected = Sales – increase or + decrease in net receivables – bad debts expense.
1999 Cash collected = Rs.100 – 10 – 5 = Rs. 85
2008 Cash collected = Rs.200 – 40 – 5 = Rs. 155
2009 Cash collected = Rs.300 – 50 – 6 = Rs. 244
During the 3-year period sales have tripled, net receivables have increased four fold, and
bad debts expenses increased only by 20%. The analysis indicates that the bad debts
expense is probably not adequate. See problem 4.
Depreciation / 47
3. Some things to remember:
Accounts receivable and advances from customers relate to cash received from
customers.
Inventories and accounts payable to cash paid out for inputs.
Prepaid expenses and rent payable related to cash expenses, interest payable to
cash paid for interest.
Income tax payable and deferred income taxes relate to cash paid for income
taxes.
Changes in property, plant & requirement relate to capital expenditures and
purchases.
Changes in short-and long-term debt, notes payable, and bonds payable relate to
cash received or used in changes in debt.
Common stock changes relate cash received or used in changes in equity
financing and retained earnings to dividends paid.
Compute, explain, and interpret a statement of cash flows using the direct method and the
indirect method.
4. Cash flow from operations using the direct and indirect methods: The following is an
example of calculating the Cash Flow Statement using the direct and indirect methods for
deriving cash flow from operations. Given the 2009 Income Statement and December
31, 2008, and 2009 balance sheets, you can calculate the Statement of Cash Flows.
Income Statement for the year 2009
Sales Revenue Rs. 100,000
Expenses:
Cost of goods sold Rs.40,000
Wages 5,000
Depreciation 6,000
Godwill amortization 1,000
Interest 500
Total Expenses 52,500
Income from Continuing operations Rs.47,500
Gain from sale of land 10,000
Pre-tax income Rs.57,500
Provision for taxes 20,000
Net income 37,500
Common dividends declared: 8,500
BALANCE SHEET
2008
(Rs.)
2009
(Rs.)
Change
(Rs.)
Current Assets:
Depreciation / 48
Cash 9,000 33,000 +24,000
Accounts receivable 9,000 10,000 +1,000
Inventory 7,000 5,000 -2,000
Noncurrent Assets:
Land 40,000 35,000 - 5,000
Plant and equipment 60,000 85,000 + 25,000
Less: Accumulated depreciation (9,000) (15,000) + 6,000
Goodwill 10,000 9,000 - 1,000
Current Liabilities:
Accounts payable 5,000 9,000 4,000
Wages payable 8,000 4,500 - 3,500
Interest payable 3,000 3,500 - 500
Taxes payable 4,000 5,000 + 1,000
Dividends payable 1,000 6,000 + 5,000
Non-current Liabilities:
Bonds 10,000 15,000 + 5,000
Deferred Taxes 15,000 20,000 + 5,000
Stockholders’ Equity:
Common Stock 50,000 40,000 - 10,000
Retained Earnings 30,000 59,000 + 29,000
Total Liabilities & Stockholders‘ Equity 126,000 162,000
Begin by calculating the net change between the start of the period and end of the period
values for all the accounts. In the preceding balance sheet, the change has been
calculated (year to year) and put in the last column. Note that the change of +Rs.24, 000
in cash is what the statement of cash flows explains.
a. Calculating cash flows from operations using the direct method.
In the direct method, revenue and expense components of the income statement
are used separately to calculate the cash received from customers and cash paid
for the various expenses.
Depreciation, amortization, gains, and losses are not considered since they do not
directly flow thought he cash account.
The same rules for changes in current assets (subtract increases and add
decreases), current liabilities (add increases and subtract decreases0, and deferred
taxes, given on the preceding page, are used to convert cash flows from accrual
accounting revenues and expenses to a cash basis. Using the data from the
income statement above, you can develop the CFO.
Cash flow from operations using the direct method:
Depreciation / 49
Cash collections:
Cash receipts from customers
Revenues Rs.100,000
Less increase in A/R - 1,000
Cash collected from customers Rs.99,000
Direct Cash inputs:
Cash paid to suppliers of inventory (associates cost of goods sold with changes in
inventory and accounts payable).
Cost of goods sold - Rs. 40,000
Add decrease in inventory + 2,000
Add increase in acct. payable + 4,000
Cash paid to suppliers - Rs.34,000
Cash paid to employees (associates wage expense with change in wages payable)
Interest expense - Rs. 500
Add increase in interest payable + 500
Cash paid for interest Rs. 0
Cash paid for taxes (associates provision for income taxes with taxes payable and
deferred taxes).
Tax expense - Rs.20,000
Add increase in taxes payable + 1,000
Add increase in deferred tax + 5,000
Cash paid for income taxes -Rs.14,000
Cash flow from operations Rs.42,500
b. Calculating cash flow from operations using the indirect method:
Start with reported net income.
Adjust for non-cash expenses and losses. (i.e., depreciation,
amortization, and losses).
Adjust for non-cash revenues and gains. (Profit from sale of
assets).
Adjust for changes in current assets and current liabilities, and
Adjust for deferred taxes.
Cash flow from operations using the indirect method:
Depreciation / 50
Net income Rs.37,500
+ 6,000
Add depreciation expense + 1,000
Add goodwill amortization - 10,000
Subtract gain from sale of land Rs.34,000
Current Asset adjustments
Increase in accounts receivable - 1,000
Decrease in inventory + 2,000
+ 1,000
Current Liability adjustments
Increase in accounts payable + 4,000
Decrease in wages payable - 3,500
Increase in interest payable + 500
Increase in taxes payable +1,000
+ 2,000
Deferred Taxes Change
Increase in deferred taxes + 5,000
Cash flow from operations Rs. 42,500
Keep track of the balance sheet items used by marking them off the balance sheet. They
will not be needed again when determining CFI and CPF.
Depreciation / 51
C. Cash flow from investment activities for both the direct and indirect methods:
Purchase or sale of equipment: To determine how much was actually spent on
assets or received from the sale of assets, depreciation expense and goodwill
amortization reported on the income statement must be matched to the
accumulated depreciation and goodwill reported on the balance sheet. If the
increase in the accumulated depreciation account matches the depreciation
expense listed on the income statement and the decrease in goodwill matches the
amortization of goodwill listed on the income statement, as in this example, then
nothing more needs to be done. If, however, they were not the same, then
equipment must have been sold. Look in the footnotes to learn what was sold.
Sale of land: Compare the Rs.10,000 gain from the sale of land to the change in
the land account. Land decreased by Rs.5,000. 1 low much cash was actually
received from the sale of the land must be determined. Review the following
math:
Decrease in land (land sold) Rs. 5,000
Plus for a gain (or - for a loss) + 10,000
Cash received from land sale Rs. 15,000
Review other non-current assets. An increase in these items uses cash, while a
decrease provides cash. Plant & equipment increased by Rs.25,000; thus, cash
used to purchase PP&E was Rs.25,000.
Cash Flow from Investing Activities:
Sale of land Rs. 15,000
Purchase of PP&E - 25,000
Cash flow from investing Rs. 10,000
d. Cash flow from financing.activities for the direct and indirect methods
This involves the analysis of changes in liabilities and stockholders' equity. All
events that could have increased or decreased cash must be reconstructed.
These are:
Issuance or retirement of bonds
Issuance or retirement, of common and preferred stock
Payment of dividends
Review long-term debt and stock: increases supply cash; decreases use cash.
Bonds payable increased by Rs.5,000; thus, cash was increased by
Rs.5,000.
Common stock decreased by Rs.10,000; thus, cash was decreased by
Rs.10,000.
Review retained earnings to determine or verify if dividends were declared and paid:
Depreciation / 52
Beginning
retained earnings
+
Net
Income
-
Dividends
Declared
=
Ending
retained earnings
so:
Beginning
retained earnings
+ Net
Income
- Dividends
Declared
- Ending
retained earnings
=0
Rs.30,000 + Rs.37,500 - dividends declared - Rs.59,000 = 0
Solving for dividends,
Dividends declared = Rs.30,000 + Rs.37,500 - Rs.59,000 = Rs.8,500
Use the change in dividends payable to derive the amount of dividends actually paid.
Treat dividends as a negative (they use up cash). The same treatment would apply to any
liabilities paid off or retired.
Dividends declared - Rs.8,500
Plus increase in Dividend payable + 5,000
-----------
Dividends paid - Rs.3,500
Cash Flow from Financing Activities:
Issue of debt Rs. 5,000
Purchase of stock - 10,000
Payment of dividends - 3,500
Cash Flow from Financing - Rs. 8,500
e. The completed statement of cash flows (indirect method) is:
Cash Flow from Operations:
Net income Rs.37,500
Add depreciation expense + 6,000
Add goodwill amortization + 1,000
Add loss (none in this example)
Subtract gain from sale of land -10,000
Current Asset change
Increase in A/R - 1,000
Decrease in inventory + 2,000
Current Liabilities change
Increase in A/P + 4,000
Decrease in wages payable - 3,500
Depreciation / 53
Increase in interest payable + 500
Increase in taxes payable + 1,000
Deferred Taxes change
Increase in deferred taxes + 5.000
Cash Flow from Operations: Rs. 42,500
Cash Flow from Investing Activities:
Sale of land Rs.15,000
Purchase of property and equipment -25.000
Cash Flow from Investing: - 10,000
Cash Flow from Financing Activities:
Issue of debt Rs. 5,000
Purchase of stock - 10,000
Payment of dividends - 3,500
Cash Flow from Financing: - 8,500
Net increase in cash Rs. 24,000
Beginning cash, 1/1/01 9,000
Ending cash, 12/31/01 Rs. 33,000
Although there are none in this example, there may be notes attached to the
statement of cash flows listing investing and financing activities that did not affect
cash. Knowing how to handle non-cash transactions is important. Assume there
was a non-cash transaction where the firm acquired some PP&E assets by issuing
mortgage debt. When analyzing the balance sheet to do the statement of cash
flows, an increase in debt and increase in fixed assets should have been noted.
Since no cash flow was involved in these transactions, they should not appear on
the SCF. However, the change-in PP&E and mortgage must be accounted for. Do
this by mentioning it in the SCF notes.
Also, cash paid for interest (Rs.0) and cash paid for income taxes (S 14,000) must
be disclosed at the bottom of the cash flow statement. This information will
enable the analyst to convert CFO from the indirect method to the direct method.
(E) Analysis of Cash Flow Information
1. The cash flow statement helps predict the firm‘s ability to sustain or increase cash
flow from operations by providing objective information about:
The firm‘s ability to generate cash from operating activities.
Trends in the cash flow components and the cash consequences of the firm‘s
investing and financing activities.
Depreciation / 54
The cash flow consequences of managerial decisions such as: financial policy
(leverage) decisions, investment for growth, and dividend policy.
2. Information in the cash flow statement:
Cash flow from operations clearly identifies non-cash expenses (depreciation and
amortization), non-operating cash flows (gains and losses and interest expense), and
changes in operating (current) assets and liabilities.
Investing cash flows separate those flows related to the purchase and sale of
PP&E from the purchase and sale of investments in affiliates and net investment in
short-term financial instruments.
Financing cash flows separate the flows between the firm and its suppliers of debt and
equity capital. Although net changes in short-term debt is communicated, cash
received or paid from issuance or retirement of long-term debt is disclosed separately.
Dividends paid and cash received from sale of stock are included in CFF. The effect
of changes in exchange rates of cash denominated in a foreign currency is a
component of CFF.
3. Income, cashflow, and the going concern assumption:
Accrual accounting concepts (e.g., revenue recognized when earned) and asset
valuations assume that the firm is an ongoing enterprise. When the going concern
assumption is subject to question, then accounting income predictive ability of future
cash flows and valuation of assets {accounts receivable, inventory, PP&E, and
goodwill) deteriorates. Under this situation cash flow from operations is more useful
than, and serves as a check to, the inherent assumptions underlying the income
statement.
1. Income, cash flow, and choice of accounting policies: Management has some
latitude in choosing accounting methods of revenue recognition. Under such
circumstances, the cash flow statement allows the analyst to distinguish between
actual events and the accounting choices used to report these events.
For example, if a firm uses the percentage of completion method, then it will
report income sooner than a similar firm that uses the completed contract method
of revenue recognition. However, the cash flow from operations will be identical
or similar. This allows the analyst to compare the two firms without reliance on
the otherwise misleading differences in income.
2. Income, cash flow, and liquidity: A company (usually new and perhaps
undercapitalized) can grow too fast and, therefore, have liquidity problems. The
cash flow statement would reveal this situation. Cash flow from operations would
not be impressive because of necessary increases in inventories and significant
increases in accounts receivable.
Depreciation / 55
Typically, accounts payable cannot be increased and cash required for investment
to support growing sales is required. The cash flow statement would disclose
information about the firm's liquidity challenge and its (in) ability to finance
future growth.
(F) Preparing a Statement of Cash Flows using the Three Box Method:
The exam will probably include preparing a statement of cash flows from a list of items.
The following steps are used in the three-box method:
Three-Box Method of Preparing a Statement of Cash Flows
Draw three boxes and three lines on a piece of paper
Label the boxes: CFO, CFI and CFF
Label the lines; Change in Cash, Beginning Cash and Ending Cash.
↓
Review each of the items, deciding if it is + or -
Write it in a box or line.
If the item has to do with a change in the capital structure (debt or equity) or a
dividend payment put the item in the CFF box.
If the item has to do with buying or selling assets put it in the CFI box.
Put every thing else in the CFO box.
↓
Add everything up to prepare a statement of cash flows
The only error that can be made is to put a miscellaneous or noncash flow item in the
CFO box or assign the wrong signs to the items in the box.
Using the following information, try the Three-box method
1) Cash payment of dividends Rs.25
2) Profit on sale of equipment 10
3) Sale of equipment 30
4) Paid for used equipment
5)
Depreciation / 56
Using the following, try the three-box method:
Cash payment of Dividends Rs.25
Profit on sale of equipment 10
Sale of Equipment 30
Paid for used Equipment 45
Depreciation and Amortization 80
Increase in accounts payable 25
Beginning Cash 150
Dividend declared but not yet paid 15
Purchase of land 15
Net Income 35
Decrease in accounts receivable 20
Sale of preferred stock 50
Assets acquired for debit issue 200
Increase in deferred taxes 05
Repurchase of common stock 40
A three for one stock split was declared
Depreciation / 57
Beginning Cash --------------------------------------
Change in Cash --------------------------------------
Ending Cash ---------------------------------------
Solution:
Item Amount Adjustment
to arrive at
Amount
and
Direction
Cash payment of Dividends Rs.25 CFF Rs.-25
Profit on sale of equipment 10 CFO -10
Sale of Equipment 30 CFI +30
Paid for used Equipment 45 CFI -45
Depreciation and Amortization 80 CFO +80
Increase in accounts payable 25 CFO +25
Beginning Cash 150
CFO
CFO
CFI
CFI
CFF
CFF
Depreciation / 58
Dividend declared but not yet paid 15
Purchase of land 15 CFI -15
Net Income 35 CFO +35
Decrease in accounts receivable 20 CFO +20
Sale of preferred stock 50 CFF +50
Assets acquired for debit issue 200
Increase in deferred taxes 05 CFO +05
Repurchase of common stock 40 CFF -40
A three for one stock split was declared
CCaasshh ffllooww ffrroomm ooppeerraattiioonnss
Net Income Rs.35
Add depreciation and Amortization 80
Less profit on sale of equipment -10
Add the increase in accounts payable 25
Add the decrease in accounts receivable 20
Add the increase in deferred taxes 05
CFO Rs.155
CCaasshh ffllooww ffrroomm ffiinnaanncciinngg Sale of preferred stock Rs.50
Repurchase of common stock -40
Cash dividends paid -25
CFF -15
Cash Flow from investing
Purchase of land Rs.15
SSttaatteemmeenntt ooff
CCaasshh FFlloowwss
Depreciation / 59
Beginning Cash Rs.150
Change in Cash 110
Ending Cash Rs.260 (plug figure)
CCaasshh FFllooww CCllaassssiiffiiccaattiioonn IIssssuueess
1. Cash flows for property, plant, and equipment: Adding depreciation and decreases
in inventory back to net income to calculate cask flows from operations via the
indirect method reflects that cash was paid out earlier when the equipment or
inventory was purchased but expensed later when it is used. Here are some
inconsistencies found in cash flow from operations.
a) When cash is paid for inventories, it is classified as a cash outflow from
operations, but when cash was paid for depreciable asset it is classified as a
cash outflow from investing activities. Yet, both are investments in productive
assets.
b) Cash flow from operations is not charged for the use of operating capacity
(assets), so a firm might have a positive CFO but fail because it cannot replace
the productive capacity used to operate the business
c) Two identical firms: Firm A buys asset ; the cash paid is charged to investing.
Firm B rents (with an operating lease) the identical asset; the cash paid is
charged to operations
d) Two identical firms: Firm A buys inventory; the cash paid is charged to
operations. Firm B purchases a company with inventory; the part of the
purchase price related to that inventory is charged to investing activities
The change in cash must
equal the sum of CFO,
CFF and CFI
Depreciation / 60
e) Investments can be poorly defined. For example, rental car companies calling
their car fleets inventory (CFO) rather than fixed assets (CFI)
2. Differences in accounting methods: Differences in accounting methods can affect
the classification of cash payments as either operating or investing activities.
If a firm capitalizes expenditures and then later amortizes or depreciates them,
(e.g., capitalizing computer software rather than expensing it or treating a lease as
a capital lease rather than an operating lease) costs are run through cash flow from
investing rather than cash flow from operations.
3. Interest and dividends received are run through cash flow from operations.
However, when the firm buys or retires the investment, the funds are run through
cash flow from investing. So, the return on capital is separated from the
expenditure or return of capital.
4. Interest paid decreases cash flow operations while dividends paid causes a
Decrease in cash inflow from financing. Both interest and dividend payments
reflect leverage or capital structure choices, not operating decisions. If payments
for equity capital (dividends) were included in CFF, should not pay for debt
(interest) also is classified as financing? If interest were a component of CFF, then
the comparison of operating cash flows of firms with different capital structures
would be facilitated.
5. Non-cash transactions are financing and investing activities that do not directly
Require cash. The purchase of building by issuing a mortgage payable is an
example of a non-cash transaction. Non-cash transactions are disclosed on the
cash flow statement using footnotes. If these non-cash events were re-classified as
using cash from investing and providing cash to financing activities, then the user
would have superior information on investing and financing activities of a firm.
(H) Free Cash Flow
1. Free cash flow (FCF) is the cash generated during a period in excess
of that needed to maintain the firm‘s present productive capacity:
Free cash flow = Cash flow – (Capital expenditures needed
to maintain productive capacity)
2. The larger a firm‘s free cash flow; the better able the firm is to meet
Financial obligations and to grow in the future.
3. Because it is not possible for an analyst to determine the amount of a
Period‘s capital expenditures that is needed for maintaining productive
capacity, many analysts simply subtract all capex cash flows from cash
flow from operations.
Depreciation / 61
Free cash flow = (Cash flow from operations) + (Capital expenditures)
4. There are variations in the definition of free cash flow in actual practice:
whether this is cash flow available to the firm (use cash flow from
operations). There are also variations that subtract cash dividends.
Important note: You will see different definitions of free cash flow within
the CFA curriculum. The most popular definition is CFO – Capex.
Example:
Consider the last example (in which the change in cash is $110). What is
the firm‘s free cash flow? The CFO is the starting place and then the cash
flows for acquiring and from selling property, plant and equipment, are
used to adjust CFO.
Free cash flow available to equity shareholders is:
FCF = Rs.155 45 + 30 = Rs.140
Calculating free cash flow available to all providers of capital (that is, both
debt and equity), requires adjusting for interest on debt (adding it back on a tax-adjusted
basis to CFO).
Conceptual Overview:
1. Depreciation is added back to net income since it is an expense not requiring cash.
2. An increase in accounts receivable means some of the current income was not
collected in the form of cash. In a sources and uses framework, an increase in
accounts receivable is a use of cash (-). A decrease in accounts receivable is a
source of cash (+).
3. An increase in accounts payable is a source of funds (+), and decrease in accounts
payable is a use of funds (-).
4. The indirect method starts with net income. Extraordinary items are listed above
net income so they are already in cash flow from operation. No adjustment is
needed.
5. The CFO includes cash flow from discontinued operations.
6. Taxes paid are a cash outflow and are in net income. No adjustment is needed.
7. When you sell plant & equipment for more than book value (that is you receive a
taxable gain), you must subtract the gain from net income. The cash received
from the sale of assets belong in the investment section of the SCF. Assume you
have assets with an original value of Rs.75, 000 with Rs.50, 000 in accumulated
depreciation. These were sold for Rs.30, 000. The closing entry would be:
CFO Purchase of
equipment
Sale of equipment
Depreciation / 62
Cash Rs.30, 000
Accumulated Depreciation Rs.50, 000
Plant & Equipment Rs.75, 000
Gain Rs.5, 000
You need to back the Rs.5, 000 gain out of income because the full Rs.30, 000 is
listed under Cash Flow from Investing.
8. What do you when a firm issues securities for assets? For example, the firm
bought a Rs.60, 000 building for Rs.100, 000 in cash, Rs.200, 000 in un-issued
common stock, and a Rs.300, 000 mortgage note.
Only the Rs.100, 000 cash paid is listed as cash flow from investing. The
remaining Rs.500, 000 of stock and debt is disclosed in the notes to the SCF as
investing or financing activities that did not affect cash.
9. When a company retires a debt issue through the issuance of stock, the firm
converts bonds into common stock. Since no cash was used in the conversion of
debt into common stock, it would not be in the financing section but would be
disclosed on the SCF as investing or financing activities that did not affect cash.
10. Declared dividends do not affect cash and are not listed on the SCF until paid.
For example, if a company declares cash divided in October, payable in January
to December holders of record.
11. A stock split is a non-cash event and is never reported on the SCF.
RECAP: Calculation of Cash flows from operations using the direct method
Step 1: Net Sales
+/- Changes in A/R
+ Other cash collections
= Cash collections and other receipts
Step 2: Cost of goods sold
+/-Changes in inventory
+/-Changes in A/P
= Direct cash inputs
Step 3: Cash expenses (other cash outflows)
+ Cash taxes paid
+ Cash interest paid
RECAP: Calculation of cash flows from operations using the indirect method
Net Income
Adjustment for non-cash or non-operating items in net income:
+ Non- cash expenses or losses
Non-cash revenues or gains
+/ Changes in operating asset accounts (accounts receivable and inventory)
+/- Changes in operating liability accounts ( accounts payable and wages payable) Cash flows from operations
Depreciation / 63
PROBLEM SET: WHITE, SONDHI & FRIED, CHAPTER 3
1. Using the following information, what is the firm‘s cash flow from operations?
Statement of Cash Flows
FFoorr tthhee ppeerriioodd 11//11//0011 ttoo 3311//1122//0011
Cash flow from operations (CFO) + Cash flow from investing (CFI) + Cash flow from financing (CFF) = Net cash flow (the change in the cash account) + Beginning of period cash = Ending cash balance
Depreciation / 64
Net Income Rs.120
Decrease in accounts receivable +20
Depreciation +25
Increase in inventory - 10
Increase in accounts payable +7
Decrease in wages payable - 5
Increase in deferred taxes +15
Profit from the sale of fixed assets +2
A. Rs.142
B. Rs.158
C. Rs.170
D. Rs.185
Use the following information to answer 2 to 4
Net Income Rs.45
Depreciation +75
Taxes paid - 25
Dividends paid 10
Cash received from sale of company building 40
Sale of preferred stock 35
Re-purchase of common stock 30
Purchase of machinery 20
Issuance of Bonds 50
Debt retired through issuance of common stock 45
Paid of long term bank borrowings 15
Profit on sale of building 20
2. The cash flow from operations is
A. Rs.75
B. Rs.100
C. Rs.120
D. Rs.185
3. The cash flow from investing activities is
A. Rs.30
B. Rs.20
C. Rs.70
D. Rs.50
4. The cash flow from financing activities is
A. Rs.75
B. Rs.55
C. Rs.85
Depreciation / 65
D. Rs.30
5. Given the following
Sales Rs.1, 500
Increase in inventory Rs.100
Depreciation Rs.150
Increase in accounts receivable Rs.50
Decrease in accounts payable Rs.70
After tax profit margin 25%
Gain of sale of machinery Rs.30
The cash flow from operation is
A. Rs.25
B. Rs.115
C. Rs.275
D. Rs.375
CHAPTER -3
Different Approaches to Costing
Decision Making Approaches
Deals in details the following
Marginal Costing, Linear Programming, Learning Curve, Statistical
Investigation, Differentiation, Probability, Capital Budgeting and Economic
Applications for Decisions.
AApppplliiccaattiioonnss
1. Special Selling price decision
Depreciation / 66
2. Product –Mix decisions when capacity constraints exit
3. Decision on replacement of equipment
4. Outsourcing (make or buy)
5. Discontinuation decision
6. Export or local sales if local sales are affected/when local sales are not
affected
7. Relevance of variable cost and irrelevance of variable costs
8. Irrelevance of fixed cost and relevance of fixed cost
9. Cost–volume –Profit analysis in hospital, hotel industry
10. Changes in product
11. Graphical representation mix
12. Product abandonment
13. Limiting factor
14. BE chart and expected value
15. Changes in sales mix
16. Break even graph
17. P/V Ratio
18. Mathematical application of Break Even
19. Multi product Cost volume profit analysis
20. P/V Graph
21. Further processing
22. Investigation of variances
23. Determining Probabilities in Investigation of variances
24. Statistical control chart
25. Optimum selling prices using differential calculus
26. Cost volume profit analysis under conditions of uncertainty
Depreciation / 67
Find the difference between Absorption Costing and Variable/ Marginal
Costing.
ABSORPTION COSTING
LabourMaterial
Manufacturing
Cost
Cost
Non-
Manufacturing cost
Profit & Loss
A/C
Finished
goodsWIP
Overheads
The entire fixed manufacturing overheads are absorbed to manufacturing cost
which increases cost per unit.
VARIABLE COSTING
LabourMaterial
Manufacturing
cost
Cost
Non-
Manufacturing cost
Profit
and loss A/CFinished goodsWIP
Overheads
Variable
overheads
Fixed
Overheads
The fixed manufacturing overheads are transferred to profit and loss account
and treated as period cost.
Depreciation / 68
Example:
Absorption Costing vs. Variable
Costing Income Statements
Absorption Costing Variable /costing
Sales
Cost of Sales
Gross Profit
60,000
30,000
30,000
Sales 60,000
Operating Expenses
Variable
Fixed
Total Operating Expenses
6,000
20,000
26,000
Variable Costs
Cost of Sales
Operating Expenses
Total Variable Costs
30,000
6,000
36,000
Income 4,000 Contribution Margin
Fixed cost 24,000
20,000
44,000
Income 4,000
Depreciation / 69
Break Even Analysis
Costs/Revenue
Output/Sales
Initially a firm will incur fixed costs, these do not depend on output or sales.
FC
As output is generated, the firm will incur variable costs –these vary directly with the amount produced.
VC The total costs therefore (assuming accurate forecasts!) is the sum of FC+VC
TC Total revenue is determined by the price charged and the quantity sold – again this will be determined by expected forecast sales initially.
TR The lower the price, the less steep the total revenue curve.
TR
Q1
The break even point occurs where total revenue equals total costs –the firm, in this example, would have to sell Q1 to generate sufficient revenue to cover its costs.
Break Even AnalysisCosts/Revenue
Output/Sales
FC
VCTCTR (p = £2)
Q1
If the firm chose to set price higher than £2 (say £3) the TR curve would be steeper –they would not have to sell as many units to break even
TR (p = £3)
Q2
Depreciation / 70
Break Even AnalysisCosts/Revenue
Output/Sales
FC
VCTC
TR (p = £2)
Q1
If the firm chose to set prices lower (say £1) it would need to sell more units before covering its costs.
TR (p = £1)
Q3
Break Even AnalysisCosts/Revenue
Output/Sales
FC
VC
TCTR (p = £2)
Q1
Loss
Profit
Costs/Revenue
Output/Sales
FC
VC
TR
High initial FC. Interest on debt rises each year – FC
rise therefore.
FC 1
Losses get bigger!
Depreciation / 71
Break Even Analysis
Remember:
A higher price or lower price does not mean that break even will
never be reached!
The break even point depends on the number of sales needed to
generate revenue to cover costs – the break even chart is NOT time
related!
Importance of Price Elasticity of Demand:
Higher prices might mean fewer sales to break even but those sales
may take a longer time to achieve.
Lower prices might encourage more customers but higher volume
needed before sufficient revenue generated to break even.
Break Even Analysis
Links of break even to pricing strategies and elasticity.
Penetration pricing – ‗high‘ volume, ‗low‘ price – more sales to
break even.
Market Skimming – ‗high‘ price ‗low‘ volumes – fewer sales to
break even.
Elasticity – what is likely to happen to sales when prices are
increased
or decreased?
Objective of CVP Analysis:
The objective of CVP analysis is to establish what will happen to the
financial results if a specified level of activity or volume fluctuate.
Volume plays a vital role in management decision because
management is interested in critical output level ie Break even point
where there is no loss or no profit.
CVP -Short Run:
CVP is based on the relationship between volume and sales revenue,
costs and profit in the short run.
Short run-one year or less.
In short run some input can be increased but others not.
Depreciation / 72
Example:
Additional supply of materials or unskilled labour can be obtained in the short run
but it takes time to expand the capacity of plant and machinery.
Out put is limited in the short run
Major constraints is sales which is uncertain
Short run profitabilities are sensitivity to sales volume.
CVP- Long Run:
Expansion of output beyond certain points may requirements of fixed costs,
such as additional supervision and machinery, appointment of additional
sales persons and expansion of distribution facilities.
In the long run other factors besides volume are likely to be important.
CVP analysis is only appropriate if all variables other than volume, remain
unchanged.
Increase in fixed cost and
Break Even Analysis
Costs/Revenue
Output/Sales
TC
TR
Q1
Profit
Q2 Q3
C
A Mathematical Approach to CVP
It is more flexible and quicker method with financial calculators.
Depreciation / 73
Assumptions:
a. Selling price and costs remain constant per unit of output.
b. In the short run fixed costs are constant total amount whereas unit cost
changes with output level.
Mathematical formula-CVP:
Net profit = (Units sold x Unit selling price) –
[(Unit sold x Unit variable cost) + Total
fixed cost]
NP = Px - (a+bx)
Where NP=Net Profit
x= Units sold
P=selling price
b=unit variable cost
a=total cost
BE Point
A + bx = Px - NP
BEP = Fixed Cost/Contribution per unit
(FC + target profit)
Units sold for target profit = -------------------------------
Contribution per unit
Contribution x 100
Profit volume ratio(P/V ratio) = --------------------------
Sales
or
NP = Sales revenue x P/V ratio – Fixed Costs
BEP = FC / P / V Ratio
Margin of Safety = Expected sales – Breakeven Sales
Student’s Exercise on BEP and application of LP:
Depreciation / 74
Tim Enterprises promotes concerts in Bangalore. The Company wants to examine
the viability of concerts In Bangalore on 31st December 2007.
Estimated costs:
Stage Costs Rs. 2,00,000/- on the first day and Rs. 50,000/- extra for
the second day.
Music party fees Rs. 2,50,000/- for the first day and Rs.1,00,000/-
for the second day.
Audios and videos Rs.1,50,000/- for the first day and Rs.25,000/-
only for the second day.
The pre-packed buffet per head is Rs.300/- for the first day and
Rs.50/- per children on the second day.
The tickets are sold @ Rs.790/- per head for the first night show.
The Management of Tim Enterprises requested the following information:
(i). The number of tickets that must be sold to break even for the first day.
(ii). How many tickets should be sold to earn Rs.5,00,000/- as profit on the first
day?
(iii). What profit would result if 3000 tickets are sold on the first day?
(iv). If 3,200 tickets are sold, and the expected profit is Rs.6,00,000/- how much
price per ticket the company can charge minimum for the first day?
(v). They want to have a separate program on the second day for children which
is fully sponsored by the Fly king Freshers Ltd. This show is meant for
Children at free of cost, and the expected number of children is 1000.
Calculate the sponsorship amount.
Answer for the Problem: Tim Enterprises
1. Mathematical & Linear Programming Approach:
Answer to question no-(i):
NP = Px-(a+bx)
a + bx = Px- NP the break even point
Depreciation / 75
a = fixed cost = 6,00,000
b = 300
X =number of tickets
P = ticket price = 790
BE Tickets = 6,00,000 + 300x = 790x – 0
x = 6,00,000/490
x =1224.48
1225 tickets to be sold to break even.
Answer to question no-(ii):
Tickets to be sold to get profit of Rs.5,00,000/-
Np = Px - (a+bx)
5,00,000 = 790x-(6,00,000+300x)
490x = 11,00,000
x = 11,00,000/490
= 2244.89
= 2245 tickets
Using Contribution Approach:
Units sold at the required profit = FC+Target profit)/ contribution per unit
= 6,00,000+5,00,000)/490
= 2245 tickets
Answer to question no-(iii):
If 3000 tickets are sold profit will be
Np = Px - (a+bx) = 3000 x 790 - (6,00,000+3000 x 300)
= 8,70,000
Answer to question No (iv):
If 3200 tickets are sold and profit should be 6,00,000 the minimum selling price
will be
6,00,000 = 3200(x) – (6,00,000+3200 x 300)
X = 21,60,000/3200
= 675
Depreciation / 76
Answer to question No (iv):
1,75,000 + 1000 x 50 = 2,25,000 no of tickets
Practical Applications of Marginal Costing:
1. Evaluation of Performance:
Evaluation of performance of department or product or individual worker a
branch.
Criteria:
Use contribution generating capacity of the segments or individual worker
2. Profit Planning:
Planning of Profits:
Due to competition company would like to reduce selling price but to increase
volume and have to maintain the same profit as before.
Step-1: Calculate current profit
Step-2: Calculate new contribution and new P/V ratio.
Step-3: Break even at the required profit= (FC+ Required profit)/ P/V ratio.
Step-4: Fixation of Selling Price:
Fixed costs are stagnant; it can be ignored in the short run.
In the long run fixed costs can not be ignored.
Fixing price above variable cost brings some contribution, which can be used
to recover fixed cost.
During the phase of depression, serious competition in the market introduces a
new product fixing selling price below variable cost or to dispose of the
product which may deteriorate in quality.
Export price above variable cost will increase the contribution when inland
sales can take care of the fixed cost.
If local sales are disturbed for export the contribution lost should be recovered
or fixed costs, which are not recovered, should be recovered from export.
Therefore selling price for export
= (Variable cost+ fixed costs not recovered inland)/expected number of units sale.
Depreciation / 77
If fixed and variable costs are incurred exclusively for export has to be
recovered.
4. Make or Buy Decision:
Produced in house or out sourced.
Accounting operations to be done in the USA or out sourced to India or
Brazil or China or Philippines?
Criteria: View total cost without considering the classification of cost like
fixed or variable.
Decision Criteria:
If Purchase price < variable cost, go for purchase proposition.
If Purchase price > variable cost, go for manufacturing proposition.
If one production capacity used for same component or product may be diverted to
manufacture another component or product how do you take decisions?
Loss of contribution due to diversion of facility should be considered while fixed
price of alternative product.
Variable cost+ loss of contribution+ additional fixed cost to be considered.
5. Optimizing Product Mix:
Proportion in which various products of a company can be sold (Mix)
Criteria:
Study contributions generated by various products individually and by selecting
that mix generates the maximum contribution
6. Key factor/Scarce factor/Limiting factors:
Raw materials are constraints or Labour hours are constraints or machine
hours are constraints
Do not Use Maximum contribution or Maximum P/V Ratio are treated as
the maximum profitable products.
What criteria to be followed?
Limiting factor:
Criteria:
Contribution per limiting factor to be used
7. Multiplicity of the key Factors:
1. If there are two limiting factors- use graphical solution.
Depreciation / 78
2. If more than two limiting factors use Linear programming such as Simplex
method.
8.How the optimum output and selling price is determined? •Demand and costs can be estimated at each potential demand level.
•The Optimum output is determined where marginal cost equals to marginal revenue.
•The selling price at which the optimum output can be sold determines the optimum price
Example:
Different price levels
Price unit of demand total revenue Marginal Revenue.
•40 10 400 ---
•38 11 418 18
•36 12 432 14
•34 13 442 10
•32 14 448 06
•30 15 450 02
•28 16 448 -02
Estimated profit at different out put levels
•Price unit of demand Total Rev. total cost profit
•40 10 360 400 40
•38 11 364 364 54
•36 12 370 370 62
•34 13 378 378 64
•32 14 388 388 60
•30 15 400 400 50
•28 16 414 414 34
When price is Rs. 34 profit is maximum
9. Differential calculus to decide optimum selling price Marginal revenue is equal to Marginal cost to decide the optimum selling
price.
Tc= Rs.7,00,000+70 X where X is the annual level of demand and output
SP=Rs. 200-Rs.0.004X :
Total revenue(TR)= Rs.200X-Rs.0.004X
Marginal cost(MC) =dTC/dx =Rs.70
Marginal Revenue(MR)=dTR/dx=Rs.200-Rs..008X
Optimum output level dTC/dx=dTR/dx
X=16,250units; SP=Rs.135
Depreciation / 79
Target Costing approach to pricing
•
It is a reverse of cost plus pricing
•Decide the target selling price- customer is willing to pay for the product.
•Target profit margin is deducted to find target cost
•Predicted actual costs are compared with the target cost
•If predicted cost exceed target cost intensive effort made through value engineering
methods.
•
Cost-plus pricing •
Direct variable cost+total direct costs+Indirect costs+share of
organisational cost+% of Profit margin
Relevant cost and relevant benefit required for decision making:
Costs that are affected by the decision.
Costs and benefits that are independent of a decision are not relevant and need
not be considered.
Future cash inflows and future outflows are relevant.
Sunk costs are irrelevant.
Allocated common costs are irrelevant
Opportunity costs are relevant (shadow price)
Incremental costs and incremental benefits are relevant.
Avoidable costs are relevant and unavoidable costs are irrelevant for decision
making.
Problems related to relevant and irrelevant cost:
Five engineers are already employed on monthly salary basis but will not be sent
out if not employed in an another project.
(i). Are the salary paid to those engineers relevant or irrelevant to estimate the
price for a new project which will be completed within a month?
(ii). Two more engineers are selected exclusively to the new project. Are the costs
relevant to take decision for new project?
Depreciation / 80
(The students are expected to solve the above problem)
Example for Relevant Cost and relevant benefits:
Survey conducted by incurring Rs.10,00,000 product P can be produced and
marketed. If P is produced it was found that 1,00,000 units per annum can be
produced at a selling price of Rs.100/- per unit. It requires a machine costs Rs.1.5
crores .The material, manufacturing variable cost is Rs.65/- per unit.
What are the relevant costs to take decision whether to go for the project or not?
(The students are expected to solve the above problem)
Example-1:
Machine just purchased a few days ago by spending Rs.20,00,000/- Cost of
running this machine per hour is Rs 100/- It is about to be installed but we come
across an another efficient machine available in the market for Rs. 35,00,000/- The
cost of running this machine is Rs 70/- per hour. If new machine is purchased, the
machine just bought could be disposed for Rs 12,00,000/- Question-1: What are
relevant costs in this problem?
1. If so, how many hours should we run minimum so that it is beneficial to the
company.
2. If company wants to run maximum 60000 hours which machine is beneficial?
3. What is the Break even hours between these two machines?
Example - 2:
We have manufactured 20,000 units of shirts which are meant for export by
spending Rs.150/- per shirt. We can sell this product in the market for Rs.120/- per
shirt because of defects. We can further process them to rectify the defect by
spending Rs.30/- and we can export and sell for Rs.160/- Other good units are sold
for Rs.200 per shirt.
Questions:
1. What are the relevant cost and relevant benefits?
2. Should we rectify them or not?
3. How much gain or loss if not rectified?
4. How much gain or loss if rectified?
Example-3:
You have joined a course by spending Rs.50,000/- The course is for three years.
The cost of the course is Rs 50,000/- per year. In the mean time you come across a
Depreciation / 81
new innovative course which will be available for Rs.1,75,000/- Question-1: What
are relevant costs for current decision?
Example-4:
Mr.Kumar purchased a car for Rs.4,00,000/-; insurance Rs.15.000/- Registration
Rs.30,000/- After spending so much he heard that Metro Train will be ready with
in another two weeks.
Every kilometer if he uses the car the running cost per Kilometer = Rs.4/- The
season ticket available for metro is Rs 2000/- per month. His office is 15
kilometers away.
Questions:
(a) What are the relevant costs to take decision?
(b) What are the other factors to be considered before taking decision?
Example-5:
Examination fees had been paid for the final semester. This is the last semester.
The student has already been recruited by the IBM at the campus recruitment. It‘s
so happened that the exam falls on the 30th
day student‘s father‘s death.
What is relevant to take decision i.e. should he go for the exam or attend the death
ceremony? (Assume both are held in the same city and at the same time).
Example-5:
Component
“X”
Component
“Y”
Component
“Z”
Contribution per unit 12 10 6
Machine hour required per unit 6 hours 2 hours 1 hour
Estimated sales in demand 2000 units 2000 units 2000 units
Required machine hours for the
quarter
12,000
hours
4000 hours 2000 hours
One of the machines breakdown the total machine hours available =12000 hours
for the period.
Question-1: Advice the mix of the product.
Example-7:
Depreciation / 82
X Ltd has a Machine-001 produces product H. The selling price of H is Rs.100/-
and marginal cost is Rs.60/- It takes 20 hours to produce one H. The company has
alternative to produce product ‗S‘ which takes 3 hours per unit of S. The marginal
cost of S=5. S can be purchased from market at a price of Rs.10/-
Question: Should product ‘S’ be produced on the same Machine-001?
Answer-7:
Present contribution = 100 – 60 = 40
Contribution per hour = 40/20 = Rs.2 per hour
S requires 3 hours. The loss of contribution in place of H is 3 x 2 = 6
Full cost of producing component S=MC + loss contribution = 5+6 = 11.
As the supplier‘s price is cheaper buy from market.
Example-7:
A BPO Company based in Bangaloru had capacity to process 2,00,000 accounts in
a month. The Sales division reports that the following schedule of sales price is
possible.
Capacity Utilization Sales per account
(Rs.)
60% 90
70% 80
80% 75
90% 67
100% 61
The variable cost per account in Rs 15/-
Fixed cost is Rs 40,00,000/-
Questions:
(i). What capacity is the utilization most profitable proposition?
(ii). Which marginal costing technique do you follow?
Depreciation / 83
Answer-8• Technique is Incremental cost and incremental revenue
-
3
3
3
3
58
61
64
67
70
40
40
40
40
40
18
21
24
27
30
-
.04=4lak
8
.006
.014
1.08
1.12
1.2
1.206
1.22
1.2
1.4
1.6
1.8
2.0
60%
70%
80%
90%
100%
Differe
ntialco
st
(Rs.
Lakhs)
Total
cost
(Rs.
Lakhs)
Fixed
cost
(Rs.
Lakhs)
Variabl
e cost
(Rs.
Lakhs)
Increm
ental
revenu
e(In
Crores
)
Sales
Value(
Rs.in
crores)
Units(l
akhs)
Capac
ity
Incremental benefit/Incremental cost
Conclusion-8:
Incremental revenue is higher than differential cost up to the output level of
80% of capacity. Therefore operate at 80% level.
At 90% level of activity differential cost exceeds incremental revenue.
Is there any difference between differential cost and marginal cost?
Differential cost can include items of fixed cost if fixed cost is affected by
the decision.
Depreciation / 84
Example-9
Information-2008
Fixed costs increases by 6%
Direct material cost increases by 5%
Labour cost increases by 10%
Due to market pressure selling price
and quantity will remain unchanged
in 2008.
An enquiry for the supply of 10,000
dozens to a customer. What could
be the lowest quotation if business
wants to make a minimum profit of
Rs. 8,00,000?
If 80% learning effect what would be
the impact?
Information-2007
Product- fountain pen
Selling price 100 per dozen
Average net profit is 20% on sale of
50,000 dozen
Capacity-75,000 dozen
Cost sheet: cost per dozen
Direct materials- 36
Direct labour 30
Works over heads 10
(50% variable)
Sales overheads 4
(25% is variable)
Depreciation / 85
Answer -9
50,00,000
37.8(36*1.05)
33.0(30*1.1)
5.0
1.0
76.8
38,40,000
4,24,000
(4,00,000*1.06)
42,64,000
7,36,000.
50,00,000
36
30
5
1
72
36,00,000
5
3
8
4,00,000
40,00,000
10,00,000
Sales(50,000*100)other than special order (A)
Variable cost:
Direct material
Direct labour
Works Overheads
Selling overheads
Total variable overhead per unit
Total variable cost (B)
Fixed cost per unit at 50,000 dozens:
Works over heads
Selling over heads
Fixed overheads per unit at 50000 dozens
Total fixed cost (C)
Total cost D= B+C
Profit A-D
2008
Rs.
2007
Rs.
particulars
Answer:
Management wants to get minimum Rs.8,00,000/-
The profit from regular sales is Rs.7,36,000/-
There is a need for additional profit of Rs. 64,000/-
Minimum price per unit = Variable cost + Expected cost +
Additional fixed cost =76.80+(64,000/10,000)+0= Rs 83.20 per unit
Additional fixed costs are covered by the existing sale of 50,000
units.
If 80% learning effect then labour cost=Rs.30*.8*2*1.1=Rs.19.8
Exercise-10:
Bangaluru based BPO has the capacity to process 50,000 accounts per month.
Because of liquidation of one of the European clients the company has excess
capacity. For the next quarter current monthly accounts processed is expected to
be 35,000 accounts at a selling price of 4 pounds per account. The expected costs
Depreciation / 86
and revenues for the next month at an activity level of 35,000 accounts are as
follows:
Particulars Pounds
Pounds Per account
Direct labour Variable processing overheads Processing non-variable overheads Marketing costs Total cost Sales ( Collection) Profit
42,000 35,000 28,000 10,500
1,15,500 1,40,000
24,500
1.2 1.0 0.8 0.3 3.3 4.0 0.7
Questions:
(i). Another European client has asked his 3000 accounts to be processed each
month for three months at a price of 2.3 pounds per accounts. Do you
advise the company to go for this proposal?
(ii). If the existing labour force is not reduced but as per labour agreement
minimum three months notice to be given. The company feels that the jerk
is a temporary phenomenon. Do you advise the company to go for the
proposal for 2 pounds?
(iii). If upsurge is going to be permanent. The future sales will be 35,000
accounts for next one year. How much price is advisable to accept the
offer?
(iv). If demand will remain 35000 accounts for next one year and the permanent
employees will be sent out after three months what would be the best price
to accept?
(v). If the laborers are contract labourers and do you accept to process at 2
pounds per accounts?
Exercise-11:
A division of Shanthi Ltd. has received an enquiry from one of its major
customers for a special order for a component that will require 1000 skilled labour
hours and that will incur other variable costs of Rs.8000/- Skilled labour is in
short supply and if company accepts the order then it will be necessary to reduce
production of component P.
The details of the cost per unit and the selling price of component P are as follows:
Selling price=Rs.88; Direct labour(4 hours atRs.10 per hour) =40; other variable
costs =12.
Allocated fixed cost based on labour hours=8.
Question:
What is the minimum selling price the company should accept for the special
order?
Depreciation / 87
Relevant cost
Labour cost +contribution lost per labour hour= 10+9=19
19000+8000=27,000
27000/1000=Rs.27 per unit
Example-12: (EOQ Stock with probability)
A dress dealer specializing in seasonal fashion dresses has to decide on the
number of units of a particular dress type to order prior to Diwali. The order has to
be placed in advance only once. The cost of the dress is Rs. 6000, which can be
sold at a price of Rs.9000 per unit. Unsold units after Diwali will be sold at a price
of Rs. 3000 per unit. Demand that can not be fulfilled due to stock shortage incur a
goodwill loss estimated at Rs. 4000 per unit inventory carrying cost is 15% of the
cost incurred. The demand is subject to random fluctuation as per pattern indicated
below:
Determine the optimal number of units that the dealer should order in advance.
Demand units: 3 4 5 6 7 8
Probability: 0.1 0.2 0.3 0.2 0.1 0.1
Answer: 12
Selling Price=Rs.9000
Cost per unit=Rs.6000
Inventory carrying cost=.15* 6000/2=Rs.450
Stock out cost (loss of goodwill)=Rs.4000
Salvage per unit=RS.3000.
Unit cost of not stocking= 9000-6000-450+4000=Rs.6550.
Cost of over stocking=6000+450-3000=Rs.3450
Demand units: 3 4 5 6 7 8
Probability: 0.1 0.2 0.3 0.2 0.1 0.1
Cum.probability: 1.0 0.9 0.7 0.4 0.2 0.1
(Demand>)
P(D)>= 3450/6550+3450=0.345
From the above table it is clear that lowest cumulative probability >0.345 i.e. at
demand 6. Therefore optimal order is 6.
Depreciation / 88
Exercise 13(Transfer Price-
Marginal costing)• A company is organised into two divisions namely A and B produces
three products, K,L,M. Data per unit are:
• Division B has a demand for 600 units of product L for its use. If division A can not supply the requirement, Division B can buy a similar product from market at Rs.112 per unit.
• Question: What should be the transfer price of 600 units of L for Division B, if the total direct labour hours available in Division A are restricted to 15,000?
100
70
3
600
115
60
5
1000
120
84
4
1600
Market price
Variable costs
Direct labour hours
Maximum sales
potential(Units)
M
RS./unit
L
Rs./unit
K
Rs./unit
Answer-13• M
RS./unit
L
Rs./unit
K
Rs./unit
100
70
30
3
10
II
600 units
1800
hrs.
115
60
55
5
11
I
1000 units
5000 hrs.
120
84
36
4
9
III
1600 units
6400 hrs.
Market price
Variable costs
Contribution
Direct labour hours
Contribution per labour hour
Ranking
Maximum sales (Balance to K
6800/4=1700 units but limited to
1600 only)
Hours allotted based on ranking
Total hours = 15000
No of hours used = 13,200 (all three products)
Number of hours unutilized=1800 hours
Depreciation / 89
Number of units can be produced without disturbing any
product =1800/5= 360 units of L
Remaining number of units of L to be supplied by disturbing
product K=600-360=240
Number hours required to produce 240 units of
L=240*5=1200 hours.
We will disturb only product K. Product K contributes Rs.9 per
labour hour.
Therefore Price of 240 units of L per unit
Variable cost 60
Opportunity cost(9*5) 45
Total cost for 240 units of L 105
Price of 360 units per unit
Variable cost 60
Total cost=(240*105)+(360*60)= 25200+21600=46,800
Average cost per unit=Rs.78.
Depreciation / 90
Answer-14 make or buy
5625
6750
1350
1.5
1
2025
1350
900
2
3
1800
2700
900
2
3
1800
2700
Demand
Hours per unit in Dep.P
Hours per unit in Dep.Q
Total hours required in
Dep.P to produce compo
Total hours required in
Dep.Q to produce compo
TotalCBAparticulars
Statement showing number of hours required in Department P and Q to meet
The monthly demand of components
Department P is under utilised and department Q over utilised by 750 hours
Prob.14.Statement showing the units of
components to be purchased to minimise
the cost
50
70
20
1
20
114
-
-
-
-
99
129
30
3
10
Variable cost to make
Variable cost to buy
Extra cost to buy
Hours required to Dept.Q
Extra cost per hour
required on buying
CBAcomponents
Since the extra cost incurred per hour on buying component A is minimum, 250 units
Of component A(750 hrs/3 hours) should be purchased from outside.
Exercise-15: Optimum Selling Price Using Calculus
A company sells one of its products in the domestic market as well as in the export
market. The relationship between price and demand in the two different markets
are represented as under:
Depreciation / 91
Domestic Market: 136-8Q1
Export market : 228-20 Q2
Q1 and Q2 represent the quantity of demand in thousand units in the domestic and
export markets respectively.
The variable cost is represented by 38 Q where Q= Q1+ Q2
Calculate the optimum selling price and the total contribution for the sale in the
(i). Domestic market
(ii). Export market
Answer for 15:
Variable cost=38-Q
Total variable cost=38Q-Q2
Marginal cost(MC)= 38-2Q
Selling price= 136-8Q
Total sales=136Q-8Q2
Marginal revenue=136-16Q
We know that profit is maximum when MR=MC
136-16Q= 38-2Q
Q=7
Optimum selling price=136-8*7=Rs.80
Variable cost per unit=38-Q=38-7=31
Contribution per unit=80-31=49
Total contribution=7*49=343
Export:
Selling price=228-20Q
Total revenue 228Q-20Q2
Marginal revenue= 228-40Q
Marginal cost remains the same=38-2Q
Profit is maximized when MR=MC
228-40Q=38-2Q
Q=5
Optimum selling price=228-20*5=128
Variable cost per unit=38-Q=38-5=33
Contribution per unit=128-33=95
Total contribution=5*95=475. or 4,75,000.
Depreciation / 92
Exercise 16(Activity Based costing)• A company produces four products P,Q,R and S. The data
relating to production activity are as under:
3
3
12
9
0.50
0.50
1.00
1-1/5
1/2
1/2
2
1-1/5
5
5
16
17
500
5,000
600
7000
P
Q
R
S
Direct
labour
cost/unit
Machine
hours/unit
Direct
labour/unit
Material
cost/unit
Qty.of
production
Product
Production overheads are as under:
i) Overheads applicable to machine oriented activity-37,424
ii)Overhead relating to ordering materials-Rs.1920
iii) Setup Costs-Rs.4355
iV) Administration overheads for spare parts: Rs.8600
v) Materials handling costs-7580
• The following further information have been compiled:
2
5
1
4
2
10
3
12
1
4
1
4
1
6
2
8
P
Q
R
S
No.of
spareparts
No.of times
materials
handled
No. of
materials
order
No.of setupProduct
Required:1) Select a suitable cost driver for each item of overhead expenses and
calculate the cost per unit of cost driver
2.Using the concept of activity based costing , compute the factory cost per unit
Of each product.
These overhead costs are observed by products on a machine hour rate of
Rs.4.80 per hour having an overhead cost per product of:
A=Rs.1.20, B=Rs.1.20, C=4.8 D=Rs.7.2
Answer for 16:
Depreciation / 93
Factory overhead applicable to machine oriented activity = Rs.37,424/-
Total machine Hours = Volume x Machine hour required for each period
= (500 x 1/4)+(5,000 x 1/4)+(600 x 1)+(7,000 x 1.5)
= 12,475 hrs.
Machine overhead charged =37,424/12,475 hrs = Rs.3 per hour
Set up costs = 4355/17(i.e. total number of set ups) = Rs.256.18
Material ordering cost = 1920/10 operations = Rs.192
Material handling cost = 7580/27 operations = Rs.280.74
Spare parts = 8600/12 parts = 716.67
Answer-16….
3/2*3=4.5
8*256.18/7
000=0.29
4*192/
7000=0.11
12*280.74/
7000=0.48
4*716.67/
7000=0.41
1*.3=Rs.3
2*256.18/
600=0.85
1*92/600=
0.32
3*280.74/
600=1.40
1*716.67/
600=1.19
¼*3=0.75
6*256.18/
5000=0.31
4*192/5000
=0.15
10*280.7/
5000=0.56
5*716.67/
5000=0.72
¼*Rs.3=.0.75
1*256.18/500=
0.51
1*192/500=
0.38
2*280.74/
500=1.12
2*716.67/500=
2.87
Machine overhead
Setup cost
Material
Ordering cost
Material handling cost
Spare parts cost
DCBAOverhead items
Depreciation / 94
+4.43
+1.29
+1.96
-1.41
1.20
1.20
4.80
7.20
5.63
2.49
6.76
5.79
2.87
0.72
1.19
0.41
1.12
0.56
1.40
0.48
0.38
0.15
0.32
0.11
0.75
0.75
3.00
4.50
A
B
C
D
differenceTotal
(old
system)
Total
(ABC
syste
ms)
Spare
Parts
Mater
ial
handl
ing
Materia
l
orderin
g
Machine
overheads
product
s
traditional system does not make correct
assumptions that all overheads are
Related to volume and machine time.
Under traditional system products A and C are
under costed because it misallocates costs for small volume products.
Set ups
Rs.
0.51
0.31
0.85
0.29
Answer: Activity costing
The activity based costing recognizes the amount of input to each cost unit.
Product B previously avoided its full share of overhead because of its low machine
time and may still do so if part of Rs. 37,425 of machine oriented overhead should
be apportioned on some other basis.
Product D is over costed because the additional system loaded it with other
attributable to activities concerned with products A, B and C as result of using a
volume – based and machine oriented rate which failed to Pay proper attention to
activity costing.
Exercise-2: Activity Costing
A Company manufactures several products of varying levels of designs and
models. It uses a single overhead recovery rate based on direct labour hours. The
overheads incurred by the company in the first half of the year are as under.
Machine operating expenses 10,12,500
Machine maintenance expenses 1,87,500
Salaries to technical staff 6,37,500
Wages and salaries of stores staff 2,62,500
During the period, the company introduced activity based costing system and the
following significant activities were identified:
- receiving materials and components
Depreciation / 95
- setup of machines for production runs
- Quality inspection.
It is also determined that:
The machine operation and machine maintenance expenses should be
apportioned between stores and production activity in 20:80 ratio.
The technical staff salaries should be apportioned between machine
maintenance, set up and quality inspection in 30:40:30 ratio.
The consumption of activities during the period under review are furnished below:
Direct labour hours worked = 40,000
Direct wages @ Rs.6/- per hour
2040 Material and component consignments received from suppliers
1960
Number of quality inspections carried out = 1280
The data relating to two products manufactured by the company during the period
are as below:
Product P
(Rs)
Product Q
(Rs)
Direct material costs 6000 4000
Direct labour hours 960 100
Direct material consignment received 48 52
Production runs 36 24
Number of quality inspection done 30 10
Quantity produced 15,000 5,000
A potential customer has approached the company for the supply of 24,000 units
of a component K to be delivered in lots of 3,000 units per quarter. The job will
involve an initial design cost of Rs. 60,000 and the manufacture will involve the
following per quarter.
Direct material cost - Rs.12,000; Direct labour hours - 300; Production runs- 6;
Inspections- 24; Number of consignments of direct materials to be received -20
The company desires to mark up of 20% on cost.
Required:
(i). Calculate the cost of products P and Q based on the existing system of single
overhead recovery rate.
(ii). Determine the cost of products P and Q using activity based costing system.
(iii). Compute the sales value per quarter of component K using activity based
costing system.
Depreciation / 96
Answer:
Working notes:
1. Overhead rate=21,00,000/4000 hours=Rs.52.50
2. Apportionment of technical staff salaries:
Machine maintenance,
Set up and Quality Inspection respectively
= 6,37,500 x 30:40:30/100
= 1,91,250; 255,000 and 1,91,250.
3. Rate per Cost driver:
Store receiving = 275.89
Set-up production run = 670.59
Quality Inspection = 149.41
4. Single overhead recovery rate: Cost per Unit P= 4.144: Q=1.97
5. Store receiving = 5,40,750: set-up production run =13,68,000
6. Rate per activity 5,40,750/1960=275.89;
13,68,000/2040=670.59;
1,91,250/1280=149.41
for store receiving, setup and quality inspection respectively.
P and Q as per activity based costing system
Exercise-3(Activity Costing)
Depreciation / 97
• The data relating to two products manufactured by the company during the period are as under:
• Product P Product Q
• Direct material costs Rs.6000Rs.4000
• Direct labour hours 960 100
• Direct material consignment received 48 52
• Production runs 36 24
• Number of quality inspection done 30 10
• Quantity produced 15,000 5,000
A potential customer has approached the company for the supply of 24,000 units of a component K to be delivered in lots of 3,000 units per quarter. The job will involve an initial design cost of Rs. 60,000 and the manufacture will involve the following per quarter.
Direct material cost - Rs.12,000; Direct labour hours - 300; Production runs- 6; Inspections- 24; Number of consignments of direct materials to be received -20
5000
4000
600
14346
16094
1494
36534
7.31
15000
6000
5760
13243
24141
4482
53626
3.58
Units
Direct materials cost
Direct labour cost
Receiving /sores cost(48*275.89)
(52*275.89)
Production runs/set up cost (36* 670.59)
(24*670.59)
Inspection cost (30* 149.41)
(10* 149.41)
Total cost of products
Cost per unit
QPParticulars
Depreciation / 98
Computation of sales value per quarter of component K(Activitity
based costing)
3000
7500
12000
1800
5518
4024
3586
34428
8607
43035
14.34
Units
Components of initial design(Rs.60000/8)
Direct materials cost
Direct labour cost (300 hours 8 Rs.6)
Receiving /sores cost(20*275.89))
Production runs/set up cost (6* 670.59)
Inspection cost (24* 149.41)
Total cost of products
Add: Mark up( 25% of cost)
Sales value
Selling price per unit of K(43035/3000 units)
KParticulars
Exercise-17(Optimal safety
stock option)• The consumption pattern of component used in an assembly is
as under:
• The stock out cost is 18 per unit and the two monthly holding cost is also 18 per unit.
• Determine the optimal safety stock.
0.15
0.20
0.30
0.20
0.15
500
600
700
800
900
probabilityTwo monthly consumption
units
Depreciation / 99
5000
4000
600
14346
16094
1494
36534
7.31
15000
6000
5760
13243
24141
4482
53626
3.58
Units
Direct materials cost
Direct labour cost
Receiving /sores cost(48*275.89)
(52*275.89)
Production runs/set up cost (36* 670.59)
(24*670.59)
Inspection cost (30* 149.41)
(10* 149.41)
Total cost of products
Cost per unit
QPParticulars
Exercise 18(Break even sales)
• A newspaper presently sells 1,00,000 copies of its morning daily. It wants to publish evening daily. Particulars are :
• Sale of morning daily will come down by @1 copy of every 10 copies sold of evening daily.
• Calculate :Break even sales for evening daily week.
Rs.0.50 per paper
Rs.0.22 per paper
Rs.10,000 per week
Rs.2 per paper
Rs.1.20 per paper
Rs.2.4 lakhs per week
Sales price
Variable Cost
Fixed Cost
Estimates for eveningActual for morning
Depreciation / 100
Answer-18
• morning daily Evening Daily
• Sale price per paper Rs.2.00 Rs.0.50
• Variable cost Rs.1.20 Rs. 0.22
• Contribution per paper Rs.0.80 Rs.0.28
• The sale of ten evening daily will reduce one morning daily.
• Lost in contribution in morning daily=0.8/10=Rs.0.08
• Net contribution from evening daily= 0.28-0.08=0.20
• Breakeven sales of evening daily=Fixed cost/Net contribution
per copy
• =10000/0.20=50,000 copies
Exercise-19 (EOQ):
G limited produces a product which has a monthly demand of 4000 units. The
product requires a component X which is purchased at Rs.20. For every finished
product, one unit of component is required. The ordering cost is Rs.120 per order
and the holding cost is 10%p.a.
You are required to calculate:
(i). EOQ
(ii). If minimum lot size to be supplied is 4000 units, what is extra cost the
company has to incur?
(iii). What is the minimum carrying cost the company has to incur?
Answer-19:
1) EOQ=Root of 2AB/C
=Root of (2*12*4000*120)/(20*0.10)
=2400 UNITS
2) Extra costs if 4000 units are ordered instead of EOQ i.e. 2400 units.
Carrying cost + ordering cost
= 1/2(4000*Rs.20*0.10) + (48,000/4000)Rs.120
Depreciation / 101
= 5440
Cost at EOQ =1/2(2400*20*0.10)+(48000/2400)120
= 4800
Extra cost = 5440-4800=640
3) Minimum Carrying cost= 2400
Excercise-20 (Linear application):
The company has derived the following functions:
Total cost (Rs.)=1,00,000 +20q+0.005q2
Price per unit (Rs.)=76-0.002q
Where q=quantity
Determine the production level which will maximise profit.
AAnnsswweerr--2200 MR=MC to maximise profit
Revenue = Price*Quantity
= q (76-0.002q)
=76q-0.002q2
Marginal revenue=dR/dq=76-0.004q
Marginal cost=dc/dq=differentiate total cost=20+0.01q
Maximize profit 76-0.004q=20+0.01q
Q=4000 units.
Depreciation / 102
Exercise:21(Linear equations)
• The details of production department
involving two processes are as under:
2.5
2
100
3
2
200
2
3
Rs.400
Process I hours/unit
Process II hours/unit
Contribution per unit
Maximum capacity of process I is
1920 hours and of process II is
2200 hours.Maximum sales of A
will be 200 units.
Formulate LPP.
CBAProduct
Solution-21 :linear equation with learning curve effect)
Maximize Z=400A+200B+100C
Subject to:
2A+3B+2.5C<=1920
3A+2B+2C<= 2,200
A<=200
Where A,B,C>=0
Exercise-22:
A company manufactures specialized equipment. Direct labour required to make
the first equipment is 2000 hours. Learning curve is 80%. Direct labour cost is
Rs.40/- per hour. Direct material needed for one equipment is Rs.7200/- Fixed
overheads are Rs.32, 000/-
Required:
(i). Using the Learning curve concept calculate the expected average unit cost
of making an equipments b) 8 equipments.
(ii). After manufacturing 8 equipments, if a repeat order for manufacture of 8
equipments is received, what lowest price could be quoted for the repeat
order?
Depreciation / 103
23. Investigation to be done or not
Arbitrary Criteria: Investigating if the absolute size of a variance is greater than
a certain amount or if the variance exceeds the standard cost by a predetermined
percentage say 1%
Example: If standard usage for a particular component was 10 Kg if actual output
for a period is 1000 units the variance is with in 9,900 and 10,100.
This method is simple arbitrary rules are their simplicity and easy to
implementation. There are several disadvantages. Investigating all variances that
exceed the standard cost by fixed percentage can lead to investigating many
variances of small amounts.
Exercises on investigation:
A machine produces 1,00,000 standard components per day at a cost of 1.5 per
unit. If the process is in control, on an average 3% of the output is defective. If the
process is out of control the rate of defectives will be 5%. The entire cost of
defective unit is a loss.
The cost of carrying out an investigation is 600. If the process is found to be out of
control after an investigation then it costs another Rs.400 to rectify the error. The
probability of the process being in control is 0.7.
Required:
(i). Should an investigation be made or not?
(ii). What is the probability at which investigation is desirable?
Depreciation / 104
Answer-1
.7
.3
3%(1,50,000)
Out of control
under control
600+3000
Investigate
Do not investigate
Do not rectify
Rectify
5%(1,50,000)
3%(1,50,000)
Rectify
Do not rectify
3%(1,50,000)
5%(1,50,000)
Investigate600
1. If Investigation under taken
Process under control 600*0.7=420
Process out of control 1000*0.3=300
(600+400) 720
2. Cost of not to investigate:
Extra cost =1,00,000*1.5=1,50,000
Extra loss(5%-3%)=1,50,000*2%=3000
Probability = 0.3
Expected value= 3000*.03=900
Conclusion: the cost of investigation is less than the cost of non-investigation.
Hence it should be investigated.
Depreciation / 105
• 2. Probability at which investigation is
desirable:
3000*(1-x)
600x
1000-
1000x
1000-
400x
X
1-x
600
1000
Under control
Out of control
Net cost
Cost of
investigation
Eff.costProbcostProcess
Equating both sides we get: 1000-400x=3000-3000x
X=0.77
Probability of process in control=0.77
24. Problem• The relevant data of X Ltd. For its three
products A,B and C are as under.
930
250
260
180
3
1040
300
270
230
6
860
260
300
110
12
Selling price
Direct Material
Direct Labour
Variable Overheads
Machine hours required
C
Rs. Per unit
B
Rs. Per unit
A
Rs. Per unit
Products
The estimated fixed overheads at four different levels of 3,600; 6,000; 8400;and 10,800
machine hours are Rs.1,00,000,Rs.1,50,000,2,20,000 and Rs.3,00,000 respectively.
The maximum demand of A,B and C in a cost period are 500;300 and 1,800 units
Respectively.
Required:- Find out i) the most profitable product-mix at each level and ii) the level
Of activity where the profit would be maximum.
Solution Continues
Contributions at different levels of machine hours are
2,88,000; 456,000; 5,23,000; 561,000 respectively
Depreciation / 106
Less Fixed cost:
Net Profit: 1,88,000; 3,06,000; 303,000; 261,000
At 6000 units we get maximum profit.
Exercise-25:
An agriculturist has 480 hectares of land on which he grows potatoes, peas and
carrots. Out of the total area of land 340 hectares are suitable for all four
vegetables but the remaining 140 hectares of land are suitable only for growing
peas and carrots. Labour for all kinds of form works is available in plenty.
The market requirement is that all the four types of vegetables must be produced
with the minimum of 5000 boxes of any one variety. The former has decided that
the area devoted to any one crop should be in terms of complete hectares and not
in fractions of a hectare. The only other limitations is that not more than 1,13,750
boxes of any one vegetables should be produced.
• The relevant data concerning
production, market prices and costs are
as under:
180
Rs.
624
1056
10.40
19.20
44.55
70
Rs.
384
744
8.80
8.0
36.80
100
Rs.
432
1216
6.56
10.40
31.76
350
Rs.
952
1792
7.20
10.4
30.76
Annual yield :
Boxes per hectare
Cost:
Direct Material per hectare
Direct Labour:
Growing per hectare
Harvesting and packing per box
Transport per box
Market price per box
TomatoesCarrotsPeasPotatoesParticulars
It is possible to make the land presently suitable for peas and carrots, viable for
growing potatoes and tomatoes if certain land development work is
undertaken. This work will involve a capital expenditure of Rs.6,000/- per
hectare which a bank is prepared to finance at the rate of 15% per annum. If
such improvement is undertaken, harvesting cost of the entire crop of tomatoes
will decrease on an average by Rs.2.60 per box.
Depreciation / 107
Required:
(i). Calculate the area to be cultivated in respect of each crop with in the
constraints and profits before land development work is undertaken.
(ii). After development of land find the acres of land for each product and
maximum profits.
26.Replacement Problem
• A Super market is trying to determine the optimal replacement policy for its fleet of delivery vehicles. The total price of the fleet is Rs.2,20,000.
• The running costs and scrap values of the fleet at the end of each year are:
• The super market’s cost of capitial is 12% per annum.
• Ignore tax and inflation.
• Required: When to replace fleet of delivery vehicles ?
1,76,000
25,000
1,65,000
55,000
1,54,000
66,000
1,32,000
88,000
1,10,000
1,21,000
Running cost
Scrap value
Year 5Year 4Year 3Year 2Year 1
Depreciation / 108
Answer for replacement
-110
-132
-154
-165
-151(176-
25)
503.64
220
723.64
3.605
200.73
-110
-132
-154
-110(165-
55)
383.04
220
603.04
3.037
198.56
-110
-132
-88(154-66)
266.09
220
486.09
2.402
202.37
-110
-44(132-88)
133.30
220
353.30
1.690
209.05
+11(100-121)
9.83
220
210.17
o.893
235.35
Cash out flow at the
end of year
1
2
3
4
5
Present value of
outflows
Present cost
Present value
Annuity factor
Equivalent annual
cost
When to replace?
5
(000)
4
(000)
3
(000)
2
(000)
1
(000)
The lowest equivalent annual cost is Rs.198,560/- Therefore the fleet should be
replaced at the end of 4 years.
Exercise-27:
A company purchases 6000 components per annum at Rs.60/- each. The
management desires to install a machine to manufacture the components. The cost
of the machine is Rs.3,00,000/- It has a capacity to produce 10,000 components
per annum. The life of the machine is 5 years. The variable cost to manufacture
the components is Rs.48 per unit and a sum of Rs.20,000/- has been allocated to
this machine as a fair share of general factory overheads per annum.
(i). Should the company make or buy the components?
(ii). If an offer to buy 2500 components at Rs.50 each is received from another
company, should the company accept the offer to manufacture and supply?
Evaluation of make or buy decision:
Purchase price per component 60
Less: variable cost 48
Savings if component manufactured 12
Total savings (6000 x 12) 72,000
Less: Depreciation (3,00,000/5) 60,000
Net savings 12,000
Recommended to install special machine.
Depreciation / 109
Exercise-28: Special Order with Learning Curve
An electronic firm which has developed a new type of fire alarm system has been
asked to quote for a prospective customer. The customer requires separate price
quotations for each of the possible orders.
Order First Second Third
No. of fire and alarm system 100 60 40
The firm estimates the following cost per unit for the first order:
Materials Rs.500/-
Direct labour
Department A (Highly automated) 20 hours at Rs.10/- per hour
Department B (Skilled labour) 40 hours at Rs.15/- per hour
Variable overheads Rs.8/- per direct labour hour
Fixed overhead absorbed
Department A: Rs.8/- per hour
Department B: Rs.5/- per hour
Determine a price per unit for each of the three orders assuming the firm uses a
mark up of 25% on total costs and allows for 80% learning curve. Each from 80%
learning curve table
Learning Curve Table:
X 1.0 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
Y% 100 91.7 89.5 87.6 86.1 84.4 83.0 81.5 80.0
Where X represents the cumulative total volume produced to date expressed as
a multiple of the initial order.
Y represents the learning curve factor, for a given X value, expressed as a
percentage of the cost of the initial order.
Answer:
First order:
Material = 500,
Direct Labour: A = 20 x 10 = 200, B= 40 x 15 = 600
Prime Cost = 1300,
Variable overheads = Rs.800(20/100) = 160
Fixed overheads: A = 20 x 8=160, B = 40 x 5=20
Total cost =1820, Profit=1850 x 0.25 = 455: Sales = 2275
Second order:
Cumulative out put = 100 + 60 = 160
Depreciation / 110
Total hours = 160units x 40 hrs x 0.861 = 5510.4 hrs
Hours for 60 units = 5510.4 – 4000 = 1510.4
Hours per unit = 1510.4/60 = 25.17 hrs
Sales per unit = Rs.1848.64
Third Order:
Labour hrs = 200 x 40 x 0.8 – 5510.4 = 889.6 hrs
Hours per unit = 889.6/40 units = 22.24
Sales =1764.40 per unit.
Exercise-29: Life Costing
A BPO Company has identified two places after spending Rs.20,00,000/- for
market study to set up its business operations. They request you to choose any one
of the places based on the following information.
Place I: Koramangala
80% of the employees are staying at 8 kilometers radius. 20% of the
employees are staying 12 kilometers radius.
Cabs are arranged for the employees both the ways.
10% of the total number of employees do not take the transport facilities
and are paid by Rs.3/- per k.m. for 10 kilometers basis per day trip
irrespective of the number of kilometers traveled by them.
A cab can bring 4 employees at a time.
The cabs while leaving the first shift employees in their houses pick up the
second shift employees. The cab is always full.
The cabs are taken on a daily rental of Rs.800/- irrespective of the
kilometers for 12 hours duration. For 18 hours duration Rs.1200/- is
charged per cab (both shifts and transport time) i.e. Rs.400/- is charged for
second shift employees to be dropped after second shift.
The rent of the building is Rs.25per month per square feet for the first year,
Rs.28/- p.m. for the second year and Rs.30/- p. m. for the third year.
Place II: Rajaji Nagar:
40% of the employees are staying in 10 kms radius and 60% of the
employees are staying at 14 kms radius. All employees prefer to take the
transport facilities.
A cab is taken on a daily rental of Rs.900/- per day irrespective of the kms
and Rs.400/- is charged per cab to drop the second shift employees in their
houses.
The rent of the building is Rs.15/- per month per square feet for the first
year, Rs.20/- p.m. for the second year and Rs.25/- p.m. for the third year.
Depreciation / 111
Other information:
The company has fixed order of 5,54,400 accounts per month. There are two shifts
in 24 hours a day. The working hours are 9 hours duration but effective working
hours are 8 hours per day. Each account is estimated to be processed in a five
minute duration.
On an average there are 22 working days in a month.
Irrespective of the place selected, the company makes a contract for three years
only. Each employee occupies on an average of 40 square feet including all other
facilities such as canteen, toilet etc.
Discounted rate is 12%.
Required:
(i). Choose the correct place to set up their business in Bangalore.
(ii). Having chosen the place, if the Company expects Rs.20,00,000/- p.m. as
profit and their variable and fixed over heads come to 70 per employee per
hour Calculate Break even employees per year and Margin of safety
employees to get a profit of Rs.20,00,00/- and also calculate break even
accounts per year and margin of safety accounts to be processed.
(iii). Should the company run in a single shift or double shift? Advice.
Answer:
Per day accounts processed = 5,54,400 /22=25200
Effective hours per day per employee = 8 hrs
Number of accounts processed per day per employee
= 8 x 60 mts/5 mts = 96 accounts
Number of employees = 25200 accounts/96 accounts per
employee
= 262.5=263employees.
Per shift = 263/2=132 employees per shift
The required space:
Per employee = 40 square feet
Total area in square feet = 40 x 132= 5840 square feet.
Rent in Koramangala in the first year = 5840 x 25 x 12 =
Rs.17,52,000
In the second year = 6000 x 28 x 12 = Rs.20,16,000
Third year = 6000 x 30 x 12 = Rs. 21,60,000/-
Depreciation / 112
Exercise-30:
Kings B&B IS A BED AND BREAKFAST ESTABLISHMENT
There are 10 rooms priced at £22 per night the B&B is open 7 nights per
week the following are typical costs:
Weekly costs
heat & light £42
Cleaning staff(basic) £100
admin £90
Breakfast staff £72
Other o/heads £60
Cost per guest night
Breakfast food £4
cleaning staff bonus £2
Laundry £3
The question asks to calculate the weekly Profit or loss if there were 42
guest nights in a week i.e.: an average of 6 guests on each of the 7 nights.
Answer:
If we start by saying that the
Weekly costs should be treated as not changing according to how many
people stay the night, so if there are 42 or 0 the cost is fixed
Cost per guest night is a variable cost and the total cost of breakfast food
etc will depend on how many people stay the night.
Total fixed cost is heat & light £42
Cleaning staff(basic) £100
admin £90
Breakfast staff £72
Other o/heads £60
£364
Total variable cost per guest night is:
breakfast food £4
cleaning staff bonus £2
Depreciation / 113
Laundry £3
Total variable cost £9
So the contribution per guest night is:-
Price - variable cost per night
£22 - £9 = £13
if there were 42 guest nights in a week
Then total contribution is
42 x £13 = £546
Fixed costs are £364
So the profit is £182
Exercise-31:
During ltd manufactures one product
no units manufactured 10000
number of units sold 8000
selling price £4 per unit
direct materials £8000
direct labour £16000
fixed production overheads £10000
There were no finished goods stock at start of month both direct materials and labour behave as
variable cost.
Produce a profit statement using marginal cost and absorption costing
On my profit statement for marginal costing I have:
sales @ £4 each = £32000
Variable cost
direct material @ £1 each = 8000
direct labour @ £2 each
less closing stock (marginal cost £6000)
2000 units x £3
fixed production o/heads £10000
profit £4000
Would really appreciate your help with this one. Trying to get through my
resubmits so I can concentrate on exam revision.
34. Special Sales Order:
Depreciation / 114
A. B. Fast is a manufacturer of automobile parts located in Texas.
Ordinarily A. B. Fast sells oil filters for $3.22 each.
R. Pino and Co., from Puerto Rico, has offered $35,400 for 20,000 oil filters, or
$1.77 per filter.
Special Sales Order
A. B. Fast‘s manufacturing product cost is $2 per oil filter which includes variable
manufacturing costs of $1.20 and fixed manufacturing overhead of $0.80.
Suppose that A. B. Fast made and sold 250,000 oil filters before considering the
special order.
Should A. B. Fast accept the special order?
Special Sales Order
The $1.77 offered price will not cover the $2 manufacturing cost.
However, the $1.77 price exceeds variable manufacturing costs by $.57 per unit.
Accepting the order will increase A. B. Fast‘s contribution margin.
20,000 units × $.57 contribution margin per unit = $11,400
35. Dropping Products, Departments, and Territories:
Assume that A. B. Fast already is operating at the 270,000 unit level (250,000 oil
filters and 20,000 air cleaners).
Suppose that the company is considering dropping the air cleaner product line.
Revenues for the air cleaner product line are $41,000.
Should A. B. Fast drop the air cleaner line?
Dropping Products, Departments, Territories
Variable selling and administrative expenses are $0.30 per unit.
Variable manufacturing expenses are $1.20 per unit.
Total fixed expenses are $335,000.
Total fixed expenses will continue even if the product line is dropped.
Depreciation / 115
Product Line
Oil Filters Air Cleaners Total
Units 250,000 20,000 270,000
Sales $805,000 $ 41,000 $846,000
Variable expenses 375,000 30,000 405,000
Contribution margin $430,000 $ 11,000 $441,000
Fixed expenses 310,185 24,815 335,000
Operating income/(loss) $119,815 ($13,815) $106,000
36.Dropping Products,
Departments, Territories
36. Dropping Products, Departments, Territories:
To measure product-line operating income, A. B. Fast allocates fixed expenses in
proportion to the number of units sold.
Total fixed expenses are $335,000 ÷ 270,000 units, or $1.24 fixed unit cost.
Fixed expenses allocated to the air cleaner product line are 20,000 units × $1.24
per unit, or $24,815.
Dropping Products, Departments, Territories
Oil Filters Alone
Units 250,000
Sales $805,000
Variable expenses 375,000
Contribution margin 430,000
Fixed expenses 335,000
Operating income $ 95,000
37. Dropping Products, Departments, Territories:
Suppose that the company employs a supervisor for $25,000.This cost can be
avoided if the company stops producing air cleaners. Should the company stop
producing air cleaners?
Yes!
$11,000 – $25,000 = ($14,000)
Depreciation / 116
38. Product Mix:
Companies must decide which products to emphasize if certain constraints prevent
unlimited production or sales.
Assume that A. B. Fast produces oil filters and windshield wipers.
The company has 2,000 machine hours available to produce these products.
Product Mix
A. B. Fast can produce 5 oil filters in one hour
or 8 windshield wipers.
ProductOil Windshield
Per Unit Filters Wipers
Sales price $3.22 $13.50
Variable expenses 1.50 12.00
Contribution margin $1.72 $ 1.50
Contribution margin ratio 53% 11%
Product Mix
Which product should A. B. Fast emphasize?
Oil filters:
$1.72 contribution margin per unit × 5 units per hour
= $8.60 per machine hour
Windshield wipers:
$1.50 contribution margin per unit × 8 units per hour
= $12.00 per machine hour
Depreciation / 117
39. Outsourcing (Make or Buy):
A. B. Fast is considering the production of a part it needs, or using a model
produced by C. D. Enterprise.
C. D. Enterprise offers to sell the part for $0.37.
Should A. B. Fast manufacture the part or buy it?
Outsourcing (Make or Buy)
A. B. Fast has the following costs for
250,000 units of Part no. 4:
Part no. 4 costs: Total
Direct materials $ 40,000
Direct labor 20,000
Variable overhead 15,000
Fixed overhead 50,000
Total $125,000
$125,000 ÷ 250,000 units = $0.50/unit
Outsourcing (Make or Buy)
A. B. Fast has the following costs for
250,000 units of Part no. 4:
Part no. 4 costs: Total
Direct materials $ 40,000
Direct labor 20,000
Variable overhead 15,000
Fixed overhead 50,000
Total $125,000
$125,000 ÷ 250,000 units = $0.50/unit
Depreciation / 118
Assume that by purchasing the part, A. B. Fast can avoid all variable
manufacturing costs and reduce fixed costs by $15,000 (fixed costs will decrease
to $35,000).
B. Fast should continue to manufacture the part.
Why?
Purchase cost (250,000 × $0.37) $ 92,500
Fixed costs that will continue 35,000
Total $127,500
The unit cost is then $0.51
($127,500 ÷ 250,000).
$127,500 – $125,000 = $2,500, which is the
difference in favor of manufacturing the part.
Outsourcing (Make or Buy)
Expected cost of obtaining 250,000 parts:
Make part $125,000
Buy part and leave facilities idle $127,500
Buy part and use facilities for gas filters $110,500*
*Cost of buying part: $127,500 less
$17,000 contribution from gasoline filters.
Best Use of Facilities
Depreciation / 119
41. Best Use of Facilities:
Assume that if A. B. Fast buys the part from C. D. Enterprise, it can use the
facilities previously used to manufacture Part no. 4 to produce gasoline filters.
The expected annual profit contribution of the gasoline filters is $17,000.
What should A. B. Fast do?
Expected cost of obtaining 250,000 parts:
Make part $125,000
Buy part and leave facilities idle $127,500
Buy part and use facilities for gas filters $110,500*
*Cost of buying part: $127,500 less
$17,000 contribution from gasoline filters.
42.Best Use of Facilities
42. Sell As-Is Or Process Further:
The sell as-is or process further is a decision whether to incur additional
manufacturing costs and sell the inventory at a higher price, or sell the inventory
as-is at a lower price.
Suppose that A. B. Fast spends $500,000 to produce 250,000 oil filters.
A. B. Fast can sell these filters for $3.22 per filter, for a total of $805,000.
Sell As-Is Or Process Further
Alternatively, A. B. Fast can further process these filters into super filters at an
additional cost of $25,000, which is $0.10 per unit ($25,000 ÷ 250,000 = $0.10).
Super filters will sell for $3.52 per filter for a total of $880,000.
Should A. B. Fast process the filters into super filters?
Sell As-Is Or Process Further
A. B. Fast should process further, because the $75,000 extra revenue ($880,000 –
$805,000) outweighs the $25,000 cost of extra processing.
Extra sales revenue is $0.30 per filter.
Extra cost of additional processing is $0.10 per filter.
Depreciation / 120
Sell As-Is Or Process Further
Cost to produce 250,000 parts: $500,000
Sell these parts for $3.22 each: $805,000
Cost to process original parts further: $ 25,000
Sell these parts for $3.52 each: $880,000
Sales increase ($880,000 – $805,000) $ 75,000
Less processing cost 25,000
Net gain by processing further $ 50,000
Explain the difference between correct analysis and incorrect analysis of a
particular business decision.
CCoorrrreecctt AAnnaallyyssiiss A correct analysis of a business decision focuses on differences in revenues and
expenses.
The contribution margin approach, which is based on variable costing, often is
more useful for decision analysis.
It highlights how expenses and income are affected by sales volume.
IInnccoorrrreecctt AAnnaallyyssiiss The conventional approach to decision making, which is based on absorption
costing, may mislead managers into treating a fixed cost as a variable cost.
Absorption costing treats fixed manufacturing overhead as part of the unit cost.
43. Opportunity Cost (with Average rate of return, NPV)
Is the benefit that can be obtained from the next best course of action.
Opportunity cost is not an outlay cost, so it is not recorded in the accounting
records.
Suppose that A. B. Fast is approached by a customer that needs 250,000 regular
oil filters.
Opportunity Cost is equal to the customer is willing to pay more than $3.22 per
Depreciation / 121
filter
.
A. B. Fast‘s managers can use the $855,000 ($880,000 – $25,000) opportunity
cost of not further processing the oil filters to determine the sales price that will
provide an equivalent income i.e. $855,000 ÷ 250,000 units = $3.42
Use four capital budgeting
Models to make longer-term
Investment decisions
Accounting Rate of Return Example Assume that a machine costs $200,000, has no residual value, and has a useful life
of 8 years.
How much is the straight-line depreciation per year?
$25,000
Management expects the machine to generate annual net cash inflows of $40,000.
Accounting Rate of Return Example
HHooww mmuucchh iiss tthhee aavveerraaggee ooppeerraattiinngg iinnccoommee?? $40,000 – $25,000 = $15,000
HHooww mmuucchh iiss tthhee aavveerraaggee iinnvveessttmmeenntt?? $200,000 ÷ 2 = $100,000
WWhhaatt iiss tthhee aaccccoouunnttiinngg rraattee ooff rreettuurrnn?? $15,000 ÷ $100,000 = 15%
NNeett PPrreesseenntt VVaalluuee The (NPV) method computes the expected net monetary gain or loss from a
project by discounting all expected cash flows to the present.The amount of
interest deducted is determined by the desired rate of return.This rate of return is
called the discount rate, hurdle rate, required rate of return, or cost of capital.
NNeett PPrreesseenntt VVaalluuee EExxaammppllee
A. B. Fast is considering an investment of $450,000.
This proposed investment will yield periodic net cash inflows of $225,000,
$230,000, and $210,000 over its life.
A. B. Fast expects a return of 16%.
Should the investment be made?
Depreciation / 122
Net Present Value Example
Periods Amount PV Factor Present Value
0 ($450,000) 1.000 ($450,000)
1 225,000 0.862 193,950
2 230,000 0.743 170,890
3 210,000 0.641 134,610
Total PV of net cash inflows $499,450
Net present value of project $ 49,450
Internal Rate of Return is another model using discounted cash flows.The
internal rate of return (IRR) is the rate of return that a company can expect to earn
by investing in a project.The higher the IRR, the more desirable the
investment.The IRR is the rate of return at which the net present value equals zero.
Investment = Expected annual net cash inflow × PV annuity factor
Investment ÷ Expected annual net cash inflow = PV annuity factor
Internal Rate of Return Example
Assume that A. B. Fast is considering investing $500,000 in a project that will
yield net cash inflows of $152,725 per year over its 5-year life. What is the IRR of
this project?
$500,000 ÷ $152,725 = 3.274 (PV annuity factor)
The annuity table shows that 3.274 is in the 16% column for a 5-period row in this
example.
Therefore, 16% is the internal rate of return of this project.
If the minimum desired rate of return is 16% or less, A.B. Fast should undertake
this project.
Depreciation / 123
The discounted cash-flow models, net present value, and internal rate of return are
conceptually superior to the payback and accounting rate of return models. It is
easy to calculate, highlights risks, and is based on cash flows. Its weaknesses are
that it ignores cash flows beyond the payback, the time value of money, and
profitability. The strength of the accounting rate of return is that it is based on
profitability. Its weakness is that it ignores the time value of money.
Outsourcing (Make or Buy)
B. Fast has the following costs for
250,000 units of Part no. 4:
Part no. 4 costs:
Total
Direct materials $ 40,000
Direct labor 20,000
Variable overhead 15,000
Fixed overhead 50,000
Total $125,000
$125,000 ÷ 250,000 units = $0.50/unit
176
Exercise A2
Customer per month 8000 Music & Entertainment $100
Check Average $6,5 Marketing $1.250
% of Food Sales 85,0% Utilities $1.250
Other Income $0 Repair & Maintenance $500
Food Cost 25% Administration $500
Beverage Cost 20% Rent $2.800
Employee wages 15,0% Interest $1.000
Management salaries 5,0% KDV taxes 18%
Employee Benefit 2,0% Refund $4.500
Direct Operating Expenses $2.000
1) Calculate the Cash Balance $4.690
2) Calculate the guest needed monthly (break even) 5.982
3) Calculate the guest needed daily to reach a profit of 10,0% 277
4) Calculate the guest needed daily to reach a profit of $6.500 293
Depreciation / 124
178
Exercise A2 (&
result)Total Labor Cost 22,0% $11.440
Operating Expenses
Direct Operating Expenses 3,8% $2.000
Music & Entertainment 0,2% $100
Marketing 2,4% $1.250
Utilities 2,4% $1.250
Repair & Maintenance 1,0% $500
Administration 1,0% $500
Rent 5,4% $2.800
Interest 1,9% $1.000
Total Operating expenses 18,1% $9.400
Restaurant Profit before taxes & refund $18.550
KDV taxes 18% of Total Sales $9.360
Refund $4.500
Cash Balance 9,0% $4.690
177
Exercise A2 (&
result)F&B Sales
Food 85,0% $44.200
Beverage 15,0% $7.800
Total F&B Sales 100,0% $52.000
Cost of Sales
Food: 25% of Food Sales 21,3% $11.050
Beverage: 20% of Beverage Sales 3,0% $1.560
Total Cost of Sales 24,3% $12.610
Gross Profit $39.390
Other Income $0
Total Income $39.390
Labor Cost
Employee wages 15,0% $7.800
Management salaries 5,0% $2.600
Employee Benefit 2,0% $1.040
Total Labor Cost 22,0% $11.440
Depreciation / 125
178
Exercise A2 (&
result)Total Labor Cost 22,0% $11.440
Operating Expenses
Direct Operating Expenses 3,8% $2.000
Music & Entertainment 0,2% $100
Marketing 2,4% $1.250
Utilities 2,4% $1.250
Repair & Maintenance 1,0% $500
Administration 1,0% $500
Rent 5,4% $2.800
Interest 1,9% $1.000
Total Operating expenses 18,1% $9.400
Restaurant Profit before taxes & refund $18.550
KDV taxes 18% of Total Sales $9.360
Refund $4.500
Cash Balance 9,0% $4.690
Depreciation / 126
180
Exercise A1 (&
result)
Total Operating Expenses $11.900
Principle on note (refund) $3.000
Total Fixed Cost $14.900
Other Income (without KDV) $0
Total $14.900
1-(%Total Variable Cost / 100) 0,3300
% of Total Cost of Sales0,2900
% of Total Labor Cost 0,2000
% KDV 0,1800
% of Total Variable Cost0,6700
Check Average $7
Customer needed monthly to break even: 6.450
Number of days in one month 30
Customers needed daily to break even: 215
Calculate the breakeven for the exercise A-2
Total Operating Expenses $9.400
+ Principle on note (refund) $4.500
Total Fixed Cost $13.900
- Other Income (without KDV) $0
Total $13.900
./. 1-(%Total Variable Cost / 100) 0,3575
% of Total Cost of Sales 0,2425
% of Total Labor Cost 0,2200
% KDV 0,1800
% of Total Variable Cost 0,6425
./. Check Average $7
Customer needed monthly to break even: 5.982
./. Number of days in one month 30
Customers needed daily to break even: 199
Depreciation / 127
1. I had purchased $20,000 worth of shares at Rs 125 per share in Indian market(1$
=Rs42) on 1st January 200X. I plan to sell sell 75% of such number of shares on
31st December 200X at Rs 150 per share. The expected market value 1$ = Rs45.
The cost of capital(Discounting rate) is 10% per annum.
Calculate the following:
a) What is the purchase price in Indian rupee?
b) What is the total sales in dollar?
c) What is the net profit /loss incurred in dollar?
d) If we use cost of capital 10%, what is the present value of selling price in
Indian Rupee?
e) What is the absolute profit/loss in dollars and present value of profit/loss
in dollars?
Production, purchases and sales budgets. 2. The management of AE Manufacturing Co.Ltd. produce a range of components
and products. They are considering next year‘s production, purchases and sales
budgets. Shown below are the budgeted total unit costs for two of the components
and two of the products manufactured by the company.
Particulars Component
1
Rs. Per unit
Components
2
Rs. Per unit
Product
P1
Rs.per
unit
Product
P2
Rs.per unit
Direct Material
Direct Labour
Variable overhead
Fixed overhead
18
16
8
20
62
26
4
2
5
37
12
12
6
15
45
28
24
12
30
94
Components 1 and 2 are incorporated into other products manufactured and sold by
the company, but they are not incorporated into the two products shown above.
It is possible to purchase components 1 and 2 from other companies for Rs.60nper
unit and Rs.30 per unit respectively.
The current selling prices of products P1 and P2 respectively.
Required:
a) Evaluate, clearly indicating all the assumptions you make as to whether it would
be profitable in the year ahead for the company to
i) Purchase either of the components
ii) Sell either of the above products.
b) Prepare statements for management with supporting explanations as to how the
following additional information would affect your evaluation in a) above if next
year‘s production requirements for the components are 7,000 units of component
1 and 6,000 units of component 14 and the budgeted sales for the two products
P1 and P2 are 5000 units and 4,000 units respectively when a special machine,
AMC is required.
Depreciation / 128
The AMC machine is needed exclusively for these two components and two
products because of specific customer requirements but for technical reasons the
machine can only be used for a maximum of 80,000 hours in the year.
The budgeted AMC machine usage for any one year is 80,000 hours and
requirements per unit for the various items are as follows:
Component 1 8 Machine hours
Component 2 2 machine hours
Product P1 6 machine hours
Product P2 12 machine hours
The operating costs of the AMC machine have been included in the unit costs shown
in (a) above.
Answer:a)
Particulars Component
1
Rs. Per unit
Components
2
Rs. Per unit
Product
P1
Rs.per
unit
Product
P2
Rs.per unit
Purchase /Selling price
Variable cost
Saving/contribution
60
42
(18)
30
32
2
33
30
3
85
64
21
(i) The company should continue to manufacture component 1
but should purchase component 2 from other companies, at a
saving of Rs.2 per unit.
Assumptions:-
1. No fixed over head would be saved if the production of
any component was ceased.
2. Variable costs vary in direct proportion of output.
3. The quality and reliabllity of external supplies is
acceptable
4. The moral of staff would would be adversely affected by
purchasing externally.
5. Suppliers prices and variable use for the capacity which
will be stable for the year ahead.
6. There is no more profitable use for the capacity which
will be used to manufacture component 1.
ii)The company should continue to produce and sell both products since
each of them makes a contribution towards fixed over head and profit.
Depreciation / 129
• 1. After spending Rs. 20,00,000 for market study a BPO Company has
identified two places to set up its business operations. They request you to choose
any one of the places based on the following information.
• Place I:- Koramangala:
• 80% of the employees are staying in 8 kilometres radious and 20% of the
employees are staying in 12 kilometres radius. Cabs are arranged for the
employees both the ways.10% of the total number of employees do not take the
transport facilities and are paid by Rs.3 per Kilometre for 10 kilometres basis per
day trip irrespective of the number of kilometres traveled by them. A cab can
bring 4 employees at a time. The cabs while leaving the first shift employees in
their houses pick up the second shift employees to the company.
• The cab is always full. The cabs are taken on a daily rental of Rs.800 irrespective
of the kilometres for 12 hours duration. For 18 hours duration Rs.1200 is charged
per cab(both shifts and transport time)ie.Rs. 400 charged the company for second
shift employees to be dropped after second shift.
• The rent of the building is Rs. 25per month per square feet for the first year, Rs.28
Per month for the second year and Rs.30 per month for the third year.
• Place II:- Rajaji Nagar:-
• 40% of the employees are staying 10 kilometres radius and 60% of the
employees are staying 14 Kilometres radius. All employees prefer to take the
transport facilities. A cab is taken on a daily rental of Rs.900 per day irrespective
of the kilometres and Rs. 400 is charged per cab to drop the second shift
employees in their houses.
• The rent of the building is Rs. 15 per month per square feet for the first year,
Rs.20 Per month for the second year and Rs.25 per month for the third year.
• Other informations:
• The company has a fixed order of 5,54,400 accounts per month to be processed.
There are two shifts in 24 hours a day. The working hours are 9 hours duration
but effective working hours are 8 hours per day. Each account is estimated to be
processed in a 5 minutes duration.
• On an average there are 22 working days in a month.
• Irrespective of the place selected, the company makes a contract for three years
only. Each employee occupies on an average of 40 square feet including all other
facilities such as canteen, toilet etc.
. wage per hour is Rs.60. The company charges $4,$4.5 and $5 per account for the fist
year, second year and third year respectively. The expected currency value for three
years respectively $1=Rs39 in the first year $1=Rs.38 in the second year; and
$1=Rs35.0.
• Discounted rate is 12%.
• Required:-
• A) Choose the correct place to set up their business in Bangalore.
Depreciation / 130
• B) Having chosen the place If the company expects Rs.20,00,000 per month as
profit. Calculate Break even employees per year and Margin of safety employees
to get a profit of Rs.20,00,000 and also calculate break even accounts per year and
margin of safety accounts to be processed.
• C) Should the company run in a single shift or double shift? Advice.
Rules of Merger
A LTD AMALGAMATES WITH B LTD
AS ON 2007
NO CAPITAL
GAIN TAX &
ACCUMULATED
LOSSES &
UNABSORBED
DEPERICIATION
CAN BE
CARRIED
FORWARD
DOES NOT
ATTRACT
CAPITAL GAIN
FOR A BUT NO
GAIN FOR B
NO BENEFIT
TO A & B
A MERGES WITH
B (A GOES OUT)
SATISFIES
BOTH 2(1B) & 72
A
SATISFIES 2(1B)
BUT DOES NOT
SATISFY 72 A
DOES NOT
SATISFY SEC
2(1B) & 72 A
PARTICULARS
CONDITIONS OF AMALGAMATION UNDER INCOME TAX ACT SEC 2 (1B)
1.ALL ASSETS AND LIABILITIES OF TRANSFEROR CO. TO BE THE
ASSETS OF THE TRANSFREE CO.
2.SHARE HOLDERS HOLDING NOT LESS THAN 3/4TH IN VALUE OF
SHARES OTHER THAN SHARES ALREADY HELD SHOULD BECOME
SHARE HOLDERS OF AMALGAMATED COMPANY
EX. NO. OF SHARES OF Altd CO. 1,00,000
NO. OF SHARES HELD BY Bltd IN Altd IS 20,000
NOMINAL VALUE OF SHARE IS RS.10
ASSUME Altd MERGE WITH Bltd THEN 75% OF 1,00,000- 20,000 = 60,000
TO BE THE SHARE HOLDES OF B CO.
NOTE:SHARE HOLDERS MAY BE EQUITY OR PREFERNCE SHARE
HOLDERS
Other conditions
•THE AMALGAMATED CO. IS AN INDIAN CO.
EXCEPTION
1.IF SHARES OF INDIAN CO.HELD BY FOREIGN BEFORE MERGER AND
SUCH FOREIGN CO. TAKEN OVER BY ANOTHER FOREIGN CO.
2.ATLEAST 25% OF THE FOREIGN CO. (BEFORE MERGER) TO BE SHARE
HOLDERS OF THE NEW FOREIGN CO.
Depreciation / 131
? WHAT IS THE BENEFIT TO THE AMALGAMATED CO. AMALGAMATING
CO.(OLD CO.)
•
•NO CAPITAL GAIN ON TRANSFER ON CAPITAL ASSETS BY THE
TRANSFEROR CO. UNDER SEC 47(VI) OF I.T ACT
? CAN NEW CO. CARRY FORWAD AND SET OF LOSS AND
DEPRECIATION
SEC 72 A of Income tax Act
1.ACCUMULATED LOSSES REMAIN UNABSORBED FOR 3 OR MORE
YEARS
2.75% OF BOOK VALUE TO BE HELD ATLEAST FOR 2 YEARS BEFORE
AMALGAMATION
3.THE AMALGAMATED CO. CONTINUES TO HOLD 3/4TH OF BOOK
VALUE ATLEAST FOR 5 YEARS
4.NEW CO. SHOULD CONTINUE FOR ANOTHER 5 YEARS
5.NEW CO. SHOULD ACHIEVE ATLEAST 50%OF INSTALLED CAPACITY
BEFORE END OF 5 YEARS AND SHOULD CONTINUE FOR 5 YEARS
THE NEW AMALGAMATED CO. SHOULD FURNISH TO ASSESSING
OFFICER ABOUT PARTICULARS OF PRODUCTION
BENEFIT
•THIS SCHEME IS ALSO APPLICABLE TO BANKING INSTITUTIONS
•?TATA VOLTAS & KELVINATOR HYDERABAD DIVISION vs. CBDT•
Rules of Merger
A LTD AMALGAMATES WITH B LTD
AS ON 2007
NO CAPITAL
GAIN TAX &
ACCUMULATED
LOSSES &
UNABSORBED
DEPERICIATION
CAN BE
CARRIED
FORWARD
DOES NOT
ATTRACT
CAPITAL GAIN
FOR A BUT NO
GAIN FOR B
NO BENEFIT
TO A & B
A MERGES WITH
B (A GOES OUT)
SATISFIES
BOTH 2(1B) & 72
A
SATISFIES 2(1B)
BUT DOES NOT
SATISFY 72 A
DOES NOT
SATISFY SEC
2(1B) & 72 A
PARTICULARS
Depreciation / 132
EXERCISE
4070MARKET PRICE
810P/E RATIO
57EPS
7,50020,000NO. OF SHARES
37,5001,40,000EAT
CO. BCO. APARTICULARS
•
Co. A is acquiring co. B Exchanging one share for every 1.5 shares of B ltd & p/e ratio
will continue even after merger
? Are they better or worse of than they were before in merger
? Determine the range of minimum & maximum ratio between the two firms
? A is an Indian co.
? A is a foreign co.
? A merges with T & formed a new co. AT ltd
? What are the tax planning required before & after merger
•
Depreciation / 133
EXAMPLE
7.58P/E RATIO(TIMES)
18,75,00050,00,000TOTAL MARKET
VALUE (N*MPS) OR
(EAT*P/E RATIO)
18.7525MARKET PRICE PER
SHARE(MPS)
2.53.125EPS
1,00,0002,00,000NO. OF SHARES
2,50,0006,25,000EAT
FIRM BFIRM APRE MERGER
SITUATION
•
? IF EXCHANGE RATIO IS 2.5:1 WHO GAINS WHO LOSES
? IF EXCHANGE RATIO IS 1:1 WHO GAINS WHO LOSES
? HOW TO CALCULATE TOLERABLE SHARE EXCHANGE RATIO
•
Answer:
Depreciation / 134
7.58P/E RATIO
(ASSUMED TO BE THE
SAME)
21.8253.125*8=25MPS
65,47,50070,00,000TOTAL MARKET VALUE
8,75,000/3,00,000=2.91/8.75/2.8=3.125EPS
2,00,000+1,00,000=3,00,0
00
2.8 lakhsNO. OF SHARES
8,75,0006.25+2.5=8.75EAT(COMBINED FIRM)
1 : 12.5:3.125=.8EXCHANE RATIO/ SWAP
RATIO (ASSUMING)
SITUATION 2SITUATION 1
(BASED ON CURRENT
MARKET PRICE
POST MERGER
TOTAL MV
LESS: MINIMUM TO BE GIVEN TO B
75,00,000
10,00,000
NET BENEFIT TO A
65,00,000
NO. OF SHARES OF A TO A CO. SHARE HOLDERS
1,00,000
DESIRED POST MERGER MPS
65 PER SHARE
NO. OF EQUTY SHARES TO BE ISSUED BASED ON DESIRED MARKET PRICE
10,00,000/65 = 15,385 SHARES
TOLERANCE SHARE EXCHANGE RATIO
50,000/15385 = 3.25 SHARES OF FIRM B, 1 SHARE IN FIRM A
1:3.25
CCOONNCCLLUUSSIIOONNSS--11
•• EEXXCCHHAANNGGEE AATT EEPPSS –– NNOO EEFFFFEECCTT OONN EEPPSS AAFFTTEERR
MMEERRGGEERR
•• EEXXCCHHAANNGGEE MMOORREE TTHHAANN EEPPSS RRAATTIIOO –– CCOOMMPPAANNYY
WWIITTHH LLOOWWEERR EEPPSS GGAAIINNSS
•• IIFF LLEESSSS TTHHAANN EEPPSS RRAATTIIOO –– CCOOMMPPAANNYY WWIITTHH
HHIIGGHHEERR EEPPSS BBEEFFOORREE MMEERRGGEERR GGAAIINNSS
Depreciation / 135
CCoonncclluussiioonn--22 •IF SHARES ARE EXCHANGED BASED ON CURRENT MARKET PRICE PER
SHARE , POST MARKET PRICE SHARE INCREASED AT HIGHER RATE THAN
EXCHANGED BELOW THIS RATIO
•Boot strap effect
Conclusion-3
•FIRM WITH HIGHER P/E RATIO CAN ACQUIRE FIRM WITH LOWER P/E
RATIO WHICH WILL INVARIABLY INCREASES MARKET VALUE AFTER
MERGER
Conversion of sole proprietorship into a company
ccoonnddiittiioonnss
•• AAllll aasssseettss aanndd LLiiaabbiilliittiieess ooff tthhee ssoollee pprroopprriieettaarriillyy
ccoonncceerrnn lleeaaddiinngg ttoo tthhee bbuussiinneessss iimmmmeeddiiaatteellyy
bbeeffoorree tthhee ssuucccceessssiioonn sshhaallll bbeeccoommee tthhee AA//LL ooff
tthhee ccoommppaannyy
•• SSoollee pprroopprriieettoorr sshhoouulldd hhoolldd nnoott lleessss tthhaann 5500%% ooff
tthhee ttoottaall vvoottiinngg ppoowweerr iinn tthhee ccoommppaannyy
•• TThhee ssoollee pprroopprriieettoorr sshhoouulldd ccoonnttiinnuuee ffoorr aa
mmiinniimmuumm ppeerriioodd ooff 55 yyeeaarrss..
•• TThhee ssoollee pprroopprriieettoorr sshhoouulldd rreecceeiivvee tthhee
ccoonnssiiddeerraattiioonn oonnllyy iinn tthhee ffoorrmm ooff sshhaarreess iinn tthhee
ccoommppaannyy CCoonnsseeqquueenncceess iiff nnoott ffuullffiilllleedd
•• WWiitthhddrraawwaall ooff eexxeemmppttiioonn UU//SS 4477AA((33))
•• TThhee ccaappiittaall ggaaiinn wwhhiicchh wwaadd nnoott ttaaxxeedd eeaarrlliieerr wwiillll
bbeeccoommee ttaaxxaabbllee iinn tthhee hhaannddss ooff tthhee ccoommppaannyy CCoonnvveerrssiioonn ooff FFiirrmm iinnttoo aa ccoommppaannyy
•• CCoonnddiittiioonnss::
•• 11.. AAllll aasssseettss aanndd LLiiaabbiilliittiieess ooff tthhee ffiirrmm lleeaaddiinngg ttoo
tthhee bbuussiinneessss iimmmmeeddiiaatteellyy bbeeffoorree tthhee ssuucccceessssiioonn
sshhaallll bbeeccoommee tthhee AA//LL ooff tthhee ccoommppaannyy..
•• 22.. AAllll tthhee ppaarrttnneerrss ooff tthhee ffiirrmm bbeeccoommee tthhee
sshhaarreehhoollddeerrss ooff tthhee ccoommppaannyy iinn tthhee ssaammee
Depreciation / 136
pprrooppoorrttiioonn ooff tthheeiirr ccaappiittaall aaccccoouunntt ssttoooodd bbeeffoorree
tthhee ssuucccceessssiioonn..
•• 33..EEvveerryy tthhiinngg sshhoouulldd bbee rreecceeiivveedd iinn SShhaarreess ooff
tthhee ccoommppaannyy bbyy tthhee ppaarrttnneerrss..
•• 44..NNoott lleessss tthhaann 5500%% ooff vvoottiinngg ppoowweerr iinn tthhee
ccoommppaannyy bbyy aallll tthhee ppaarrttnneerrss aanndd hhoolldd ssuucchh
sshhaarreehhoollddiinnggss ffoorr aa ppeerriioodd ooff 55 yyeeaarrss ffrroomm tthhee
ddaattee ooff ssuucccceessssiioonn.. FFaaiilleedd ttoo ffuullffiillll tthhee ccoonnddiittiioonnss
•• WWiitthhddrraawwaall ooff eexxeemmppttiioonn UU//SS 4477AA((33))
•• TThhee ccaappiittaall ggaaiinn wwhhiicchh wwaadd nnoott ttaaxxeedd eeaarrlliieerr wwiillll
bbeeccoommee ttaaxxaabbllee iinn tthhee hhaannddss ooff tthhee ccoommppaannyy
••
•• IIff SShhaarreehhoollddeerr YY ttrraannssffeerrss hhiiss sshhaarreess ttoo ZZ oonn 55tthh
MMaarrcchh 22001111 wwhhaatt iiss tthhee ccoonnsseeqquueenncceessttoo tthhee ffiirrmm
aanndd CCoommppaannyy aanndd ppaarrttnneerrss((sshhaarreehhoollddeerrss))??
•• HHooww ddoo yyoouu ccoommppuuttee ccaappiittaall ggaaiinn ttaaxx??
•• SSuuppppoossee tthhee ffiirrmm hhaass aa llaanndd wwoorrtthh RRss.. 5500 ccrroorreess
aanndd sseellllss wwhhiicchh aattttrraaccttss 88 ccrroorreess IInnccoommee ttaaxx.. IIss
tthheerree ttaaxx ppllaannnniinngg ttoo aavvooiidd ttaaxx lliiaabbiilliittyy??
Depreciation / 137
Exercise-1-Case study
Plant 80,000
House property 2,00,000
(acquired in 1982-83)
Stock in trade 40,000
Debtors 70,000
Bank 10,000
Capital
X 1,00,000
Y 2,00,000
Sundry credi 1,00,000
AssetsLiabilities
Balance Sheet as on 1st April 2008
•• AA LLttdd.. iiss iinnccoorrppoorraatteedd oonn AApprriill 11sstt
22000088 wwhhiicchh
ttaakkeess oovveerr tthhee aasssseettss aanndd lliiaabbiilliittiieess aatt tthhee aaggrreeeedd
vvaalluuaattiioonn ooff XX CCoo.. aass ffoolllloowwss::
•• PPllaanntt--22,,8800,,000000,, HHoouussee pprrooppeerrttyy--1100,,0000,,000000,,
ssttoocckk--6600,,000000,, ddeebbttoorrss--7700,,000000,,BBaannkk ––1100,,000000..
??????
•• HHooww iiss iitt ttrreeaatteedd aass ppeerr IITT??
•• IIff ffiirrmm sseellllss tthhee wwhhoollee bbuussiinneessss aatt tthhee aaggrreeeedd
vvaalluuee wwhhaatt iiss tthhee ttaaxx iimmpplliiccaattiioonn??
•• CCaallccuullaattee tthhee ttoottaall ccoonnssiiddeerraattiioonn tthhee ccoommppaannyy iiss
wwiilllliinngg ttoo ggiivvee tthhee ppaarrttnneerrss aanndd aallssoo ffiinndd oouutt tthhee
nnuummbbeerr ooff sshhaarreess aallllootteedd ttoo eeaacchh ppaarrttnneerr??
•• IIff SShhaarreehhoollddeerr YY ttrraannssffeerrss hhiiss sshhaarreess ttoo ZZ oonn 55tthh
MMaarrcchh 22001111 wwhhaatt iiss tthhee ccoonnsseeqquueenncceessttoo tthhee ffiirrmm
aanndd CCoommppaannyy aanndd ppaarrttnneerrss((sshhaarreehhoollddeerrss))??
•• HHooww ddoo yyoouu ccoommppuuttee ccaappiittaall ggaaiinn ttaaxx??
•• SSuuppppoossee tthhee ffiirrmm hhaass aa llaanndd wwoorrtthh RRss.. 5500 ccrroorreess
aanndd sseellllss wwhhiicchh aattttrraaccttss 88 ccrroorreess IInnccoommee ttaaxx.. IIss
Depreciation / 138
tthheerree ttaaxx ppllaannnniinngg ttoo aavvooiidd ttaaxx lliiaabbiilliittyy??
AAnnsswweerr
11..SShhoorrtt tteerrmm ccaappiittaall ggaaiinn oonn ppllaanntt aanndd MMaacchhiinneerryy aass aa
ddeepprreecciiaatteedd aasssseett==22,,0000,,000000
HHoouussee pprrooppeerrttyy –– LLoonngg tteerrmm aass nnoo ddeepprreecciiaattiioonn
pprroovviiddeedd uussee iinnddeexx ccoossttooff aaccqquuiissiioonn
SSttoocckk iinn ttrraaddee 6600,,000000--4400,,000000==2200,,000000 iiss bbuussiinneessss
iinnccoommee..
•• IIff aallll tthhee ccoonnddiittiioonnss ffuullffiilllleedd aass ppeerr 4477((xxiiiiii))
•• NNoo ccaappiittaall ggaaiinn ttaaxx..HHoowweevveerr bbuussiinneessss iinnccoommee
aarriisseess oonn ssttoocckk wwhhiicchh aattttrraaccttss ttaaxx aass bbuussiinneessss
iinnccoommee aanndd ttoo bbee ppaaiidd bbyy tthhee ffiirrmm..
•• SSttoocckk iiss aa ccuurrrreenntt aasssseett wwhhiicchh iiss uusseedd aass aa ssttoocckk
iinn ttrraaddee ddooeess nnoott aammoouunntt ttoo ccaappiittaall aasssseett..
•• IIff YY ttrraannssffeerrss hhiiss sshhaarreess ttoo ZZ tthhee ccaappiittaall ggaaiinn
eeaarrlliieerr eexxeemmpptteedd wwiillll bbee ttaaxxeedd aass iitt wwaass
oorriiggiinnaallllyy ccaallccuullaatteedd..LLoonngg tteerrmm ccaappiittaall ggaaiinn oonn
hhoouussee pprrooppeerrttyy aanndd sshhoorrtt tteerrmm ccaappiittaall ggaaiinn oonn
ppllaanntt aanndd mmaacchhiinneerryy..
Bond valuation
C M
Bond valuation ———— + ——————
t =1 (1+i)t (1+i) n
Where:
C1.. Cn = period coupon payment from year 1 to n
Depreciation / 139
i = market interest rates, prevailing
n = period to maturity
MM == PPrriinncciippaall wwiitthh // wwiitthhoouutt rreeddeemmppttiioonn
pprreemmiiuumm
Yield to maturity
This term popularly known as YTM connotes redemption yield and is very useful for
Treasury Managers whose investment horizon is long term. YTM can be interpreted as
the bond‘s average compounded rate of return if the bond is bought at the current asked
price and held until it matures and the face value is repaid. That is, YTM can be defined
as the discount rate that equates present value of all cash flows to the present market price
of the Bond. Future cash flows includes interest and capital gain/loss. This can be
algebraically expressed as follows: Let the Bond with a face value of ‗A‘ of coupon ‗C‘
with a term to maturity of ‗n‘ years is quoted/traded at a market price of P, then
C C C (C + A)
P = ———— + ———— + ————+ ———— + ————
(1+y)1 (1+y)2 (1+y)3 (1+y)n
Where ‗y‘ is the discount rate (to be found by trial & error method ) at which the cash
flows are discounted so that the right hand side of the above equation tallies/equates with
the Price P (left hand side) of the Bond.
The 'y' so derived would be the Yield to maturity (YTM) of the bond. It implies that, if
the Bond is held till maturity and the Coupons/Cash flows received are reinvested at the
'y' rate itself, the overall yield on the Bond will be 'y', which is its YTM.
Depreciation / 140
An example would further help to understand the mechanics of the YTM. Suppose the
market value of Rs 100 (face value) bond carrying coupon of 13 per cent p.a. maturing
after 7 years is quoted Rs 109.45 in the market. The YTM of the bond is found by
discounting the yearly coupon flows of Rs 13 in the next 6 years and Rs 113 (Principal of
Rs 100 + coupon of Rs 13) at the end of 7 year at a rate (to be found by trial & error
method), say ‗r‘ so that the Present value of such cash flows sums to Rs 109.45 Rs 13
(PVIFA) + Rs 100 (PVIF) = Rs 109.45 PVIFA being the Price Value Interest Factor for
the 7 year Annuity and PVIF the Price Value Interest Factor for 7 years to be taken from
the PVIFA table and PVIF table (available in all standard Finance Text Books) for a 7
year term, by trial and error method.
Accordingly for 7 years (PVIFA) at 11% = 4.712
and for 7 years (PVIF) at 11% = 0.482
Then LHS of the equation becomes 13 x (4.712) + 100 x (0.482) = Rs 109.45
Then 11 per cent is said to be the YTM of the bond, also described as the Internal Rate of
Return, (IRR). In other words, in the above example, if the above bond is held by the
buyer till maturity the overall return from the Bond will be 11 per cent. However as the
above process will be time consuming, YTM can be found by approximation as follows.
C + (A – P)/n
YTM = ————————— X 100
(A + P) /2
Where C = coupon
A = Face Value/maturity Value
P = Price paid for the Bond
n = term to maturity
Applying this in the above example,
13 + (100 –109.45)/ 7 13 + (– 9.45/7)
YTM = ————————————— = —————————
Depreciation / 141
(100 + 109.45)/ 2 104.725
13 – 1.35
= —————— X 100 = 11.12%
104.725
However underlying assumption in the YTM concept is that the coupons/cash flows
received during the tenure of the bond is reinvested at YTM rate, which may not be true
since the market interest rates will always be changing from time to time.
Yield on Discounted instruments:
The issue price of a discounted instrument is calculated as follows:
F
D = ———————————————
1 + {( r x n)/36500}
where,
D = Discounted value of the instrument
F = Maturity Value
r = Effective rate of interest per annum
n = Tenure of the instrument ( in days)
Conversely to find out the yield from a discounted instrument, the following formula can
be derived from the above one,
(F –D) 365
r = —————— X ——————— X 100
D n
where,
D = Discounted value of the instrument
F = Maturity Value
r = Effective rate of interest per annum
n = Tenure of the instrument ( in days)
Depreciation / 142
REPO Transactions—calculations:
Assume Bank ‗A‘ borrows from Bank ‗B‘ an amount of Rs 10 crores for a period of 14
days from 10.10.2005 to 24.10.2005, at an interest rate of 8 per cent against its holding of
11.50 per cent GOI 2007 (Interest Payment dates of this stock are 5th April and 5th
October of the year). As already stated earlier, the transaction involves 2 legs—First
leg/Ready leg and Second leg/Forward leg. The calculation for both legs are explained
below:
Working
(Note: While calculating interest accrued on Government securities, 360 days are
considered for an year.)
FIRST LEG/READY LEG on 10.10.2005: (Bank A sold 11.50 per cent GOI 2007 to
Bank B)
Calculation for first leg is as if Bank A is selling the security (11.5 per cent GOI 2007)
outright to Bank B at the market price of Rs 100. This is as follows:
Principal (Rs 10 crs. @ 100.00) = Rs 10,00,00,000.00
Accrued int.on the stock
= (10 crs x 11.5% x 5/360) = Rs 1,59,722.22
First/Ready leg settlement amount...(1) = Rs 10,01,59,722.22
(It may be understood from the above transaction, that Bank A borrowed Rs
10,01,59,722.22 from Bank B)
FORWARD/SECOND LEG on 24.10.2005: (Bank A bought back the stock from Bank
B)
Though the second leg transaction is to be calculated as if Bank A is buying outright the
security from Bank B, to arrive at the buying rate/price, the calculation has to be done on
the reverse way, as follows:
Depreciation / 143
1. Calculate the settlement amount Bank A has to pay Bank B which is = Amount
borrowed + interest @ 8% for 14 days (Repo rate)
= Rs 10,01,59,722.22 + Rs 3,07,339.42
Settlement amount = Rs 10,04,67,061.64
2. From this subtract accrued interest on the stock till date.
Accrued interest on the stock
= 10,00,00,000 x 11.5% x 19
---------
360
= Rs 6,06,944.44
Settlement amt. – Accrued interest = 10,04,67,061.64
6,06,944.44
Rs 9,98,60,117.20
3. Resulting amount of Rs 9,98,60,117.20 is the principal amount for the Rs 10 crore
value stock. Hence to get rate of repurchase, divide this value by nominal value
i.e. 9,98,60,117.20
------------------ = 99.860117
10,00,00,000
Now based on this rate, the accounting is done as follows:
Principal (Rs 10 crs. @99.860117) = Rs 9,98,60,117.20
Accrued int. on the stock
= (10 crs x 11.5% x19/360) = Rs 6,06,944.44
Forward/second leg settlement amt
= (1) + int @ 8% for 14 days = (2) = Rs 10,04,67,061.64
Depreciation / 144
3.Dilip Company currently produces two products. The cost per unit of Product are as
follows:
Product Y Product Z
Selling price 110
Less : Variable Cost
Material ( 8 units at Rs.4) 32
Labour ( 6 hrs at Rs.10) 60
Variable Overheads ( 4 Machine hrs at Rs.1) 4
96
Contribution 14
Selling price 118
Less : Variable Cost
Material ( 4 units at Rs.4) 16
Labour ( 8 hrs at Rs.10) 80
Variable Overheads ( 6 Machine hrs at
Rs.1) 6
102
Contribution 16
During the 4th
coming accounting period the availability of labour hrs will be restricted to
2880 hrs.Material availability is limited to 3440 units . the machine has the capacity to
produce 2760 units . The marketing manager expects the maximum sales potential for y
is 420 units with respect to Product z there is no sales Limitations
Required
Formulate Linear Programing Model and solve by simplex and interpret the final /matrix
and also from the final /matrix find shadow price or opportunity cost
Solution
Maximise C = 14y+16z subject to
8y + 4Z < 3440 ( Material Constraint)
6Y + 8Z < 2880 ( Labour Constraint)
Depreciation / 145
4Y + 6Z < 420 ( maximum and minimum sales limitation)
Z > 0
First Matrix
QQuuaannttiittyy YY ZZ
S1 = 3440 -8 -4 (1) Material Constraint
S2 = 2880 -6 -8 (2) Labour constraint
S3 = 2760 -4 -6 (3) Machine hours constraint
S4 = 420 -1 0 (4) Sales Constraint
C = 0 +14 +16 (5) Contribution
Note that the quantity column in the matrix indicates the resources available or the slack
that is not taken up when production is zero. For example, the S1 row of the matrix
indicates that 3440 units of materials are available when production is zero. Column Y
indicates that 8 units of materials, 6 labour hours and 4 machine hours are required to
produce 1 unit of product Y, and this will reduce the potential sales of y by 1. You will
also see from column Y that the production of 1 unit of Y will yield Rs.14 contribution.
Similar reasoning applies to column Z. Note that the entry in the contribution row (i.e.
The C row) for the quantity column is zero because this first matrix is based on nil
production, which gives a contribution of zero.
Second Matrix
Quantity Y S2
S1 = 2000 -5 +1/2 (1) Material Constraint
Z = 360 -3/4 -1/8 (2)
S3 = 600 +1/2 +3/4 (3) Machine hours Constraint
S4 = 420 -1 0 (4) Sales Constraint
C = 5760 +2 -2 (5)
Depreciation / 146
The substitution process obtained for the second matrix has become more complex, but
the logical basis still remains. For example, the quantity column of the second matrix
indicates that 2000 units of materials are unused,360 units of Z are to be made, 600
machine hours are still unused and sales of product Y can still be increased by another
420 units before the sales limitation is reached. The contribution row indicates that a
contribution of Rs. 5760 will be obtained from the production and sale of 360 units of
product Z. Column Y indicates that production of 1unit of product Y uses up 5 units of
the stock of materials,but, because no labour hours are available , ¾ units of product Z
must be released. This will release 3 units of materials (3/4 x 4), 6 labour hours ( ¾ x 8)
And 4 ½ machine hours ( ¾ x 6). From this substitution process we now have 8 units of
materials ( 5 units + 3 units ), 6 labour hours and 4 ½ machine hours.
From the standard cost details one unit of Y requires 8 units of materials, 6 labour hours
and 4 machine hours. This substitution process thus provides necessary resources for
producing 1 unit of product Y, as well as providing an additional half an hour of machine
capacity. This is because production of 1 unit of product Y requires that production of
item Z be reduced by ¾ units, which releases 4 ½ machine hours. However product Y
requires only 4 machine hours, so production of 1unit of Y will increase the available
machine capacity by half an hour. This agrees with the entry in column Y of the second
matrix for machine capacity . Column Y also indicates that production of 1 unit of Y
reduces the potential sales of product Y (S4) by 1 unit.
The optimum solution is achieved when the contribution row contains only negative or
zero values. Because row C contains a positive item, our current solution can be
improved by choosing the product with the highest positive contribution. Thus we should
choose to manufacture product Y, since this is the only positive item in the contribution
row. The second matrix indicates that the contribution can be increased by Rs. 2 by
substituting 1 unit of Y for ¾ units of Z. We therefore obtain an additional contribution
of Rs.14 from Y but lose at Rs.12 from Z ( ¾ x 16) by this substitution process. The
overall result is an increased contribution of Rs.2 by adopting this substitution process.
The procedure is then repeated to formulate the third matrix. Column Y of
The second matrix indicates that we should use 5 units of materials and release ¾ units of
Z to obtain an additional unit of Y, but there are limitations in adopting this plan. The
unused materials are 2000 units, and each unit of y will require 5 units, giving a
maximum production of 400 units of Y. We have 360 units of Z allocated to production,
and each unit of Y requires us to release ¾ units of Z. A maximum production of 480
units of Y (360/ ¾ ) can therefore be obtained from this substitution process. There is no
limitaion on machine hours, since the second matrix indicates that the substitution
process increases machine hours by half an hour for each unit of Y produced. The sales
limitaion of Y indicates that a maximum of 420 units of Y can be produced. The
following is the summary of the limitations in producing product Y:
S1 (materials) = 400 units (2000 / 5)
Z ( substitution of product Z ) = 480 units ( 360/ ¾ )
S4 ( maximum sales of Y) = 420 units ( 420/1)
Depreciation / 147
In other words, we merely divide the negative items in column Y into the quantity
column. The first limitation we reach is 400 units, and this indicates the maximum
production of Y because of the impact of the material constraint.
Third Matrix
Quantity S1 S2
Y = 400 -1/5 +1/10 (1)
Z = 60 +3/20 -1/5 (2)
S3 = 800 -1/10 +4/5 (3)
S4 = 20 +1/5 -1/10 (4)
C = 6560 -2/5 -1 4/5 (5)
The contribution row (equation 5) contains only negative items, which signifies that the
optimal solution has been reached. The quantity column for any products listed on the left
hand side of the matrix indicates the number of units of the product that should be
manufactured when the optimum solution is reached. 400 units of Y and 60 units of Z
Should therefore be produced, giving a total contribution of Rs.6560. This aggress with
the results we obtained using the graphical method. When an equation appears for slack
variable, this indicates that unused resources exist. The third matrix therefore indicates
that the optimal plan will result in 800 unused machine hours ( S3) and an unused sales
potential of 20 units for product Y (S4). The fact that there is no equation for S1 and S2
means that these are the inputs that are fully utilized and that limit further increases in
output and profit.
IInntteerrpprreettiinngg tthhee FFiinnaall MMaattrriixx
The S1 column (materials) of the third matrix indicates that the materials are fully
utilized. (Whenever resources appear as column headings in the final matrix, this
indicates that they are fully utilized.) So, to obtain a unit of materials, the column for S1
Indicates that we must alter the optimum production programme by increasing production
of product Z by 3/20 of a unit and decreasing production of product Y by 1/5 of a unit.
If we increase production of product Z by 3/20 of a unit the more machine hours will be
required, leading to the available capacity being reduced by 9/10 of an hour. Each unit of
Depreciation / 148
Product Z requires 6 machine hours, so 3/20 of a unit will require 9/10 of an hour (3/20 x
6). Deceasing production of product Y by 1/5 unit will release 4/5 of a machine hour,
given that 1 unit of product Y requires 4 machine hours. The overall effect of this process
is to reduce the available machine capacity by 1/10 of a machine hour.
The S1 column indicates that to release 1 unit of materials from the optimum production
programme we should increase the output of product Z by 3/20, and decrease product Y
by 1/5 of a unit. This substitution process will lead to the unused machine capacity being
reduced by 1/10of a machine hour, an increase in the unfulfilled sales demand of product
Y (S4) by 1/5 of a unit and a reduction in contribution of rs.2/5. All this information is
obtained from column S1 of the third matrix.
Opportunity Cost:
The contribution row of the final matrix contains some vital information for the
accountant. The figures in this row represent opportunity costs (also known as shadow
prices) for the scarce factors of materials and labour. For example the reduction in
contribution from the loss of 1 unit of materials is Rs.2/5 (Rs.0.40) and from the loss of
one labour hour is rs.1 4/5 (Rs.1.80). Our earlier studies have indicated that this
information is vital for decision-making, and we shall use this information again shortly
to establish the relevant costs of the resources.
S3 S4 S1 S2
Machine Sales of Materials Labour Contribution (Rs.)
Capacity Y
Increase
Product Z
By 3/20 of
A unit -9/10(3/20x6) ------ -3/5(3/20x4) -1 1/5(3/20x8)
+2 2/5(3/20x6)
Decrease
Product Y
By 1/5 of
A unit +4/5(1/5x4) +1/5 +1 3/5(1/5x8) +1 1/5(1/5x6) -
2 4/5(1/5x14)
Net Effect -1/10 +1/5 +1 Nil -2/5
Depreciation / 149
OOppppoorrttuunniittyy ccoosstt--aann aapppplliiccaattiioonn ooff mmaatthheemmaattiiccaall pprrooggrraammmmiinngg
•• IItt iiss aallssoo kknnoowwnn aass sshhaaddooww pprriicceess.. SShhaaddooww pprriiccee oorr ssccaarrccee rreessoouurrccee
iiss tthhee iinnccrreeaassee iinn tthhee vvaalluuee ooff oobbjjeeccttiivvee ffuunnccttiioonn wwhhiicchh wwoouulldd bbee
aacchhiieevveedd iiff oonnee oorr mmoorree uunniitt ooff tthhee rreessoouurrccee wwaass aavvaaiillaabbllee..
•• SShhaaddooww pprriicceess ccaann pprroovviiddee gguuiiddaannccee ttoo ddeecciissiioonn mmaakkeerrss..
•• IIff ssoommee oonnee ooffffeerrss tthhee ddeecciissiioonn mmaakkeerr tthhee aaddddiittiioonnaall rreessoouurrcceess aatt aa
pprriiccee lleessss tthhaann tthhee sshhaaddooww pprriiccee iitt iiss aallwwaayyss bbeenneeffiicciiaall..
LLEEAARRNNIINNGG OOBBJJEECCTTIIVVEESS
•• DDiissccoovveerr hhooww ttoo iiddeennttiiffyy tthhee sshhaaddooww pprriicceess aanndd ppeennaallttyy ccoossttss ffrroomm
tthhee ssoolluuttiioonn ooff aa lliinneeaarr pprrooggrraammmmiinngg pprroobblleemm..
•• UUnnddeerrssttaanndd tthhee rroollee tthheessee pprriicceess aanndd ccoossttss ppllaayy iinn ppoosstt--ooppttiimmaalliittyy
aannaallyyssiiss..
•• AAsssseessss tthhee eeffffeeccttiivveenneessss ooff yyoouurr tteeaamm iinn mmaaxxiimmiizziinngg lleeaarrnniinngg..
SShhaaddooww PPrriicceess
•• TThhee sshhaaddooww pprriicceess ffoorr aa LLiinneeaarr PPrrooggrraammmmiinngg pprroobblleemm aarree tthhee
ssoolluuttiioonnss ttoo iittss dduuaall.. TThhee iitthh sshhaaddooww pprriiccee iiss tthhee cchhaannggee iinn tthhee
oobbjjeeccttiivvee ffuunnccttiioonn rreessuullttiinngg ffrroomm aa oonnee uunniitt iinnccrreeaassee iinn tthhee iitthh
ccoooorrddiinnaattee ooff bb.. AA sshhaaddooww pprriiccee iiss aallssoo tthhee aammoouunntt tthhaatt aann iinnvveessttoorr
wwoouulldd hhaavvee ttoo ppaayy ffoorr oonnee uunniitt ooff aa rreessoouurrccee iinn oorrddeerr ttoo bbuuyy oouutt tthhee
mmaannuuffaaccttuurreerr
FFoorr eexxaammppllee
•• wwhhaatt iiss tthhee pprriiccee ooff kkeeeeppiinngg aa pprroodduuccttiioonn lliinnee ooppeerraattiioonnaall ffoorr aann
aaddddiittiioonnaall hhoouurr iiff tthhee pprroodduuccttiioonn lliinnee iiss aallrreeaaddyy ooppeerraatteedd aatt iittss
mmaaxxiimmuumm 4400 hhoouurrss lliimmiitt?? TThhaatt pprriiccee iiss tthhee sshhaaddooww pprriiccee
•• FFoorr iinnssttaannccee iiff yyoouu hhaavvee aa ccoonnssttrraaiinntt tthhaatt lliimmiittss tthhee aammoouunntt ooff llaabboorr
aavvaaiillaabbllee ttoo 4400 hhoouurrss ppeerr wweeeekk,, tthhee sshhaaddooww pprriiccee wwiillll tteellll yyoouu hhooww
mmuucchh yyoouu wwoouulldd bbee wwiilllliinngg ttoo ppaayy ffoorr aann aaddddiittiioonnaall hhoouurr ooff llaabboorr.. IIff
yyoouurr sshhaaddooww pprriiccee iiss RRss..5500 ffoorr tthhee llaabboorr ccoonnssttrraaiinntt,, ffoorr iinnssttaannccee,, yyoouu
sshhoouulldd ppaayy nnoo mmoorree tthhaann RRss5500 aann hhoouurr ffoorr aaddddiittiioonnaall llaabboorr.. LLaabboorr
ccoossttss ooff lleessss tthhaann RRss..5500//hhoouurr wwiillll iinnccrreeaassee tthhee oobbjjeeccttiivvee vvaalluuee;; llaabboorr
ccoossttss ooff mmoorree tthhaann RRss..5500//hhoouurr wwiillll ddeeccrreeaassee tthhee oobbjjeeccttiivvee vvaalluuee..
LLaabboorr ccoossttss ooff eexxaaccttllyy RRss..5500//--wwiillll ccaauussee tthhee oobbjjeeccttiivvee ffuunnccttiioonn vvaalluuee
ttoo rreemmaaiinn tthhee ssaammee..
OOppppoorrttuunniittyy ccoosstt--ssiinnggllee ssoouurrccee ccoonnssttrraaiinnttss
Depreciation / 150
•• AAssssuummee pprroodduucctt XX ccoonnttrriibbuutteess RRss1144((66 llaabboouurr hhoouurrss)) aanndd pprroodduucctt YY
ccoonnttrriibbuutteess 1166((88 llaabboouurr hhoouurrss))
•• WWhhiicchh pprroodduucctt ddoo yyoouu ccoonncceennttrraattee iiff llaabboouurr iiss aa ccoonnssttrraaiinntt??
•• IIff llaabboouurr hhoouurr iiss ccoonnssttrraaiinntt,, tthheenn ccoonnttrriibbuuttiioonn ppeerr lliimmiittiinngg ffaaccttoorr ttoo
bbee ccaallccuullaatteedd..
•• IIff 22552200 llaabboouurr hhoouurrss aarree aavvaaiillaabbllee aanndd XX ccaann nnoott bbee ssoolldd mmoorree tthhaann
332200 uunniittss WWhhaatt iiss tthhee ttoottaall ccoonnttrriibbuuttiioonn??
•• DDoo wwee aappppllyy OORR tteecchhnniiqquuee??
TTwwoo rreessoouurrccee ccoonnssttrraaiinnttss
••CCoonnssiiddeerr ttwwoo rreessoouurrccee ccoonnssttrraaiinnttss::
••11..LLaabboouurr ccoonnssttrraaiinnttss ttoo 22888800 hhoouurrss
••22..MMaatteerriiaall ccoonnssttrraaiinnttss ttoo 33444400 uunniittss
••XX ccoonnssuummeess 88 uunniittss ooff mmaatteerriiaall aanndd YY ccoonnssuummeess 44 uunniittss ooff mmaatteerriiaall
••XX ccoonnssuummeess 66 hhoouurrss ooff llaabboouurr aanndd YY ccoonnssuummeess 88 hhoouurrss ooff llaabboouurr
••XX’’ss ccoonnttrriibbuuttiioonn RRss..1144 aanndd YY’’ss ccoonnttrriibbuuttiioonn RRss..1166
••CCoonnttrriibbuuttiioonn ppeerr ssccaarrccee rreessoouurrcceess??
•• PPrroodduucctt XX PPrroodduucctt YY
•• LLaabboouurr 22..3333{{1144//66}} 22..0000{{1166//88}}
•• MMaatteerriiaall 11..7755{{1144//88}} 44..0000{{1166//44}}
••HHooww ddoo yyoouu aannaallyyssee aanndd iinntteerrpprreett??
AAnnaallyyssiiss ••PPrroodduucctt XX yyiieellddss tthhee llaarrggeerr ccoonnttrriibbuuttiioonn ppeerr llaabboouurr hhoouurr aanndd PPrroodduucctt
YY yyiieellddss llaarrggeerr ccoonnttrriibbuuttiioonn ppeerr uunniitt ooff ssccaarrccee rreessoouurrcceess..
••HHooww ddoo wwee kknnooww tthhee qquuaannttiittyy ooff ssccaarrccee rreessoouurrcceess sshhoouulldd bbee
aallllooccaatteedd ttoo eeaacchh pprroodduucctt..
•• SSoolluuttiioonn??
••
••HHiigghheerr ppoowweerreedd mmaatthheemmaattiiccaall tteecchhnniiqquueess ttoo ggeett ooppttiimmaall oouuttppuutt
pprrooggrraammmmee..
••LLiinneeaarr pprrooggrraammmmiinngg iiss aa ppoowweerrffuull mmaatthheemmaattiiccaall tteecchhnniiqquuee..
••TTaakkee aann eexxaammppllee::
••MMaaxxiimmiissee:: ZZ==1144 XX++1166YY
••SSuubbjjeecctt ttoo::88XX++44YY<<==33444400((MMAATTEERRIIAALL CCOONNSSTTRRAAIINNTT))
Depreciation / 151
•• 66XX ++88YY<<==22888800((LLAABBOOUURR CCOONNSSTTRRAAIINNTT))
•• 44XX++66YY<<==22776600((MMAACCHHIINNEE CCAAPPAACCIITTYY CCOONNSSTTRRAAIINNTT))
•• XX<<==442200 BBUUTT TTHHEERR IISS NNOO LLIIMMIITTAATTIIOONNSS OONN YY
BBYY UUSSIINNGG GGRRAAPPHHIICCAALL SSOOLLUUTTIIOONN WWEE GGEETT XX==440000 AANNDD YY==6600
TTOO MMAAXXIIMMIISSEE PPRROOFFIITT..
TTHHEERREE AARREE EEFFFFEECCTTIIVVEE CCOONNSSTTRRAAIINNTTSS.. WWhhaatt aarree tthheeyy??
EEffffeeccttiivvee ccoonnssttrraaiinnttss
•• MMaatteerriiaall aanndd llaabboouurr aarree ttwwoo eeffffeeccttiivvee ccoonnssttrraaiinnttss oouutt ooff ffoouurr
ccoonnssttrraaiinnttss..
•• IIss iitt ppoossssiibbllee ttoo rreemmoovvee tthheessee ccoonnssttrraaiinnttss?? AAnndd aaccqquuiirree aaddddiittiioonnaall
llaabboouurr aanndd mmaatteerriiaall bbyy ppaayyiinngg pprreemmiiuumm oovveerr aanndd aabboovvee tthhee
aaccqquuiissiittiioonn ccoosstt..??
•• HHooww mmuucchh sshhoouulldd tthhee ccoommppaannyy bbee pprreeppaarreedd ttoo ppaayy ??
IIff OOnnee mmoorree uunniitt ooff mmaatteerriiaall iiss aavvaaiillaabbllee
••88XX++44YY==33444411{{IINNSSTTEEAADD OOFF 33444400}}
••66XX++88YY==22888800{{UUNNCCHHAANNGGEEDD }}
••TTHHEE RREEVVIISSEEDD OOPPTTIIMMAALL SSOOLLUUTTIIOONN::
••XX==440000..22;; YY==5599..8855UUNNIITTSS
••EEXXPPLLAANNAATTIIOONN!!
••XX SSHHOOUULLDD BBEE IINNCCRREEAASSEEDD BBYY 00..22 AANNDD YY SSHHOOUULLDD BBEE DDEECCRREEAASSEEDD BBYY
00..1155UUNNIITTSS..TThhee ooppttiimmaall rreessppoonnssee ffrroomm aann iinnddeeppeennddeenntt mmaarrggiinnaall
iinnccrreeaassee iinn aa rreessppoonnssee iiss ccaalllleedd tthhee ““mmaarrggiinnaall rraattee ooff ssuubbssttiittuuttiioonn””
••TThhee nneeww ccoonnttrriibbuuttiioonn ::
••XX==..0022**1144==22..88
••YY==..1155**1166==((22..44))
••IInnccrreeaassee iinn ccoonnttrriibbuuttiioonn==00..4400
••WWhhaatt ddoo yyoouu ssaayy aabboouutt 00..4400??
MMaarrggiinnaall rraattee ooff ssuubbssttiittuuttiioonn
••TThhee ccoommppaannyy ccaann ppaayy RRss.. 00..4400 ttoo bbuuyy oonnee mmoorree uunniitt ooff mmaatteerriiaall..
••TThhee vvaalluuee ooff iinnddeeppeennddeenntt mmaarrggiinnaall iinnccrreeaassee ooff ssccaarrccee rreessoouurrccee iiss
ccaalllleedd tthhee ooppppoorrttuunniittyy ccoosstt oorr
•• sshhaaddooww pprriiccee..
•• HHooww mmuucchh ooppppoorrttuunniittyy ccoosstt ooff llaabboouurr??
OOppppoorrttuunniittyy ccoosstt ooff llaabboouurr
••88xx++44yy==33444400
••66xx++88yy==22888811
••SSoollvvee
••XX==339999..99 aanndd yy==6600..22
Depreciation / 152
••EExxppllaaiinn!!
EExxppllaannaattiioonnss
•• DDeeccrreeaassee iinn ccoonnttrriibbuuttiioonn ooff XX==00..11**1144==((11..44)) » Y = .2*16= 3.2
•• OOppppoorrttuunniittyy ccoosstt==11..88 The company should be willing to forgo 1.80 additionally to acquire new labour per hour.
Now see simplex method .
SSiimmpplleexx mmeetthhoodd aanndd iinntteerrpprreettaattiioonn
••MMaaxxiimmiissee:: ZZ==1144 XX++1166YY
••SSuubbjjeecctt ttoo::88XX++44YY<<==33444400((MMAATTEERRIIAALL CCOONNSSTTRRAAIINNTT))
•• 66XX ++88YY<<==22888800((LLAABBOOUURR CCOONNSSTTRRAAIINNTT))
•• 44XX++66YY<<==22776600((MMAACCHHIINNEE CCAAPPAACCIITTYY CCOONNSSTTRRAAIINNTT))
•• XX<<==442200 ((ssaalleess ccoonnssttrraaiinntt))
••IInnttrroodduuccee SS11,,SS22,,SS33 AANNDD SS44 SSLLAACCKK VVAARRIIAABBLLEESS
••SS11-- IINNDDIICCAATTEESS UUNNUUSSEEDD MMAATTEERRIIAALL RREESSOOUURRCCEESS
••SS22--IINNDDIICCAATTEESS UUNNUUSSEEDD LLAABBOOUURR RREESSOOUURRCCEESS
••SS33--IINNDDIICCAATTEESS UUNNUUSSEEDD MMAACCHHIINNEE CCAAPPAACCIITTYY
••SS44--IINNDDIICCAATTEESS UUNNUUSSEEDD PPOOTTEENNTTIIAALL SSAALLEESS OOUUTTPPUUTT
EEXXPPLLAANNAATTIIOONNSS
••FFOORR LLAABBOOUURR((66 HHOOUURRSS**XX))++88 HHOOUURRSS **YY)) PPLLUUSS AANNYY UUNNUUSSEEDD
LLAABBOOUURR HHOOUURRSS SS22 WWIILLLL EEQQUUAALL 22888800 HHOOUURRSS WWHHEENN OOPPTTIIMMUUMM
SSOOLLUUTTIIOONN IISS RREEAACCHHEEDD..
••SSIIMMIILLAARR RREEAASSOONNIINNGG AAPPPPLLIIEESS TTOO TTHHEE OOTTHHEERR PPRROODDUUCCTTIIOONN
CCOONNSSTTRRAAIINNTTSS..
••TTHHEE SSAALLEESS LLIIMMIITTAATTIIOONN IINNDDIICCAATTEESS TTHHAATT TTHHEE NNUUMMBBEERR OOFF UUNNIITTSS
OOFF XX SSOOLLDD PPLLUUSS AANNYY SSHHOORRTTFFAALLLL OONN MMAAXXIIMMUUMM DDEEMMAANNDD WWIILLLL
EEQQUUAALL 442200 UUNNIITTSS..
•• FFiinnaall mmaattrriixx--??
Depreciation / 153
16
Final matrix
• Quantity S1 S2
• X=400 -1/5 +1/10 1
• Y=60 +3/20 -1/5 2
• S3=300 -1/10 +4/5 3
• S4=20 +1/5 -1/10 4
• C=6560 -2/5 -1 4/5 5
IIMMPPOORRTTAANNTT EEXXPPLLAANNAATTIIOONNSS
•• TThhee ccoonnttrriibbuuttiioonn rrooww ((55)) ccoonnttaaiinnss oonnllyy nneeggaattiivvee iitteemmss,, wwhhiicchh
ssiiggnniiffiieess tthhaatt ooppttiimmaall ssoolluuttiioonn hhaass bbeeeenn rreeaacchheedd..
•• TThhee qquuaannttiittyy ccoolluummnn iinnddiiccaatteess tthhaatt xx==440000 aanndd yy==6600 hhaavvee ttoo bbee
pprroodduucceedd ggiivviinngg aa ttoottaall ccoonnttrriibbuuttiioonn ooff RRss..66556600
•• SSllaacckk vvaarriiaabblleess iinnddiiccaattee uunnuusseedd ccaappaacciittyy
•• iiee..,, 330000 mmaacchhiinnee hhoouurrss((SS33)),, UUNNUUSSEEDD SSAALLEESS PPOOTTEENNCCIIAALLOOFF 2200 UUNNIITTSS
FFOORR PPRROODDUUCCTT XX((SS44))
•• SS11 AANNDD SS22 AARREE FFUULLLLYY UUTTIILLIISSEEDD
•• OOPPPPOORRTTUUNNIITTYY CCOOSSTTSS CCAANN BBEE CCAALLCCUULLAATTEEDD OONNLLYY FFOORR SS11 AANNDD SS22..
IInntteerrpprreettiinngg ffiinnaall mmaattrriixx
•• SS11 CCoolluummnn((mmaatteerriiaallss)) –– MMaatteerriiaallss aarree ffuullllyy uuttiilliizzeedd..
•• IInnccrreeaassee pprroodduuccttiioonn ooff YY bbyy 33//2200 ooff aa uunniitt aanndd ddeeccrreeaassiinngg pprroodduuccttiioonn
ooff pprroodduucctt XX bbyy 11//55 ooff aa uunniitt..
•• IIff wwee iinnccrreeaassee pprroodduuccttiioonn ooff YY BBYY 33//2200 ooff aa uunniitt tthheenn mmoorree mmaacchhiinnee
hhoouurrss wwiillll bbee rreeqquuiirreedd,, lleeaaddiinngg ttoo tthhee aavvaaiillaabbllee ccaappaacciittyy rreedduucceedd bbyy
99//1100 ooff aann hhoouurr tthhaatt iiss,, pprroodduucctt YY rreeqquuiirreess 66 mmaacchhiinnee hhoouurrss ssoo 33//2200
ooff aa uunniitt wwiillll rreeqquuiirree 99//1100 ooff aann hhoouurr..((33//2200**66..))
•• DDeeccrreeaassee iinn pprroodduucctt XX bbyy 11//55 uunniitt wwiillll rreelleeaassee 44//55 ooff aa mmaacchhiinnee hhoouurr
ggiivveenn tthhaatt pprroodduucctt XX rreeqquuiirreess 44 mmaacchhiinnee hhoouurrss..
•• TThhee oovveerraallll eeffffeecctt ooff tthhiiss pprroocceessss iiss ttoo rreedduuccee tthhee aavvaaiillaabbllee mmaacchhiinnee
ccaappaacciittyy bbyy 11//1100 ooff tthhee mmaacchhiinnee hhoouurrss..
Depreciation / 154
19
The effect Of removing One Unit of material
from the optimum production Program
• Particulars S3 S4 S1 S2 Contributionmachine Sales Materials Labour
Capacity Of X
Increase product Y by
3/20 of a unit -9/10(3/20*6) -- -3/5(3/20*4) -11/5 (3/20*8) -22/5 (3/20*16)
Decrease product X by +4/5(1/5* 4) +1/5 +!3/5(1/5*8) +11/5(1/5+*6) -24/5(1/5*14)
1/5 of a unit
Net effect -1/10 +1/5 +1 Nil -2/5
CCoonncclluussiioonnss
•• TThhee rreedduuccttiioonn ffrroomm tthhee lloossss ooff 11 uunniitt ooff mmaatteerriiaallss iiss 22//55((RRss..00..4400)) aanndd
ffrroomm tthhee lloossss ooff oonnee llaabboouurr hhoouurr iiss RRss..11 44//55((RRss..11..8800))
•• TThhiiss iinnffoorrmmaattiioonn iiss vviittaall ffoorr ddeecciissiioonn mmaakkiinngg..
•• PPrroodduucctt XX sshhoouulldd bbee iinnccrreeaasseedd bbyy 11//55 ooff aa uunniitt aanndd pprroodduucctt YY
rreedduucceedd bbyy 33//2200
•• .. TThhiiss iinnccrreeaasseess mmaacchhiinnee hhoouurr ooff 11//1100 hhoouurr((SS33)) aanndd ddeeccrreeaassee iinn
ppootteennttiiaall ssaalleess ooff pprroodduucctt XX bbyy 11//55((SS44))
•• IIff wwee oobbttaaiinn aaddddiittiioonnaall llaabboouurr hhoouurr wwee sshhoouulldd iinnccrreeaassee pprroodduuccttiioonn ooff
YY bbyy11//55 ooff aa uunniitt aanndd ddeeccrreeaassee tthhee pprroodduuccttiioonn bbyy XX bbyy 11//1100 ooff aa uunniitt
wwhhiicchh wwiillll iinnccrreeaassee ccoonnttrriibbuuttiioonn bbyy RRss..11..8800..
•• SSuuppppoossee tthhee ccoommppaannyy ggeettss aaddddiittiioonnaall llaabboouurr hhoouurrss hhooww ddooeess iitt aaffffeecctt
tthhee ssaalleess aanndd ccoonnttrriibbuuttiioonn??
OOppttiimmaall pprroodduuccttiioonn ppllaann wwhheenn 220000 aaddddiittiioonnaall hhoouurrss
•• YY iinnccrreeaasseess bbyy4400 uunniittss((220000**11//55 ooff aa uunniitt))
•• XX ddeeccrreeaasseess bbyy 2200 uunniittss
•• MMaacchhiinnee ccaappaacciittyy bbeeiinngg rreedduucceedd bbyy 116600 hhoouurrss
•• PPootteennttiiaall ssaalleess ooff pprroodduucctt XX bbeeiinngg iinnccrreeaasseedd bbyy 2200 uunniittss..
RReelleevvaanntt ccoossttss
•• RRuullee::
•• AACCQQUUIISSIITTIIOONN CCOOSSTT OOFF RREESSOOUURRCCEE
Depreciation / 155
•• ++
•• OOPPPPOORRTTUUNNIITTYY CCOOSSTT
RREELLEEVVAANNTT CCOOSSTTSS
•• MMAATTEERRIIAALL ==RRSS..44..44
•• LLAABBOOUURR ==RRSS..1111..8800
•• VVAARRIIAABBLLEE OOVVEERRHHEEAADDSS ==RRSS.. 11..0000
•• FFIIXXEEDD OOVVEERRHHEEAADDSS == NNIILL
•• SSUUPPPPOOSSEE NNEEWW PPRROODDUUCCTT(( LL)) TTOO BBEE MMAANNUUFFAACCTTUURREEDD WWHHIICCHH
RREEQQUUIIRREESS 1100 UUNNIITTSS OOFF MMAATTEERRIIAALL AANNDD 1100 HHOOUURRSS OOFF LLAABBOOUURR
WWHHAATT PPRRIICCEE TTHHEE NNEEWW PPRROODDUUCCTT TTOO BBEE SSOOLLDD??
PPRROODDUUCCTT LL TTOO BBEE SSOOLLDD
•• RReelleevvaanntt ccoosstt::
•• MMaatteerriiaall ((1100**RRss..44..4400)) RRss.. 4444
•• LLaabboouurr((1100**1111..8800)) RRss..111188
•• VVaarriiaabbllee oovveerrhheeaadd((1100**11..0000)) 1100
••TToottaall RRss.. 117722
••IIff oovveerrttiimmee iiss tthhee oonnllyy ooppttiioonn tthheenn hhooww mmuucchhwwiillll tthhee ccoommppaannyy
bbee aabbllee ttoo ppaayy oovveerrttiimmee ppeerr hhoouurr?? AAddddiittiioonnaall llaabboouurr hhoouurr
•• RRss.. 1111..88 ffoorr ppeerr llaabboouurr hhoouurr
•• RRss.. 44..4400 ppeerr uunniittss ooff mmaatteerriiaall
PPeennaallttyy CCoossttss
•• PPeennaallttyy CCoossttss aarree tthhee aammoouunnttss tthhee ooppttiimmaall vvaalluuee ooff tthhee oobbjjeeccttiivvee
ffuunnccttiioonn wwoouulldd cchhaannggee ffoorr eeaacchh uunniitt iinnccrreeaassee iinn tthhee nnoonn--bbaassiicc
vvaarriiaabblleess.. TThheeyy aarree tthhee nneeggaattiivveess ooff tthhee nnoonn--bbaassiicc bboottttoomm rrooww
eennttrriieess iinn tthhee ffiinnaall ttaabblleeaauu..
MMOODDEELL:: MMiinniimmiizzee
•• MMiinniimmiizzee ..0055xx11 ++ ..0077xx22
•• SSuubbjjeecctt ttoo:: ..22xx11 ++ 11..55xx22 >>== 1100 30x1 + 35x2 >= 300
•• aallll xxii >>== 00
•• mmaaxxiimmiissee 1100yy11 ++ 330000yy22
•• SSuubbjj ttoo:: 00..22yy11 ++ 3300yy22 <<==00 ..0055
11..55yy11 ++ 3355yy22 <<== ..0077
aallll yyii >>== 00
EExxaammppllee
•• MMaaxxiimmiizzee 2200xx ++ 3300yy++5500zz
•• SSuubbjjeecctt ttoo::
Depreciation / 156
•• 22xx++33yy++zz<<== 440000 ((mmaacchhiinnee hhoouurrss ccoonnssttrraaiinnttss))
xx++ zz<<== 115500((ccoommppoonneenntt ccoonnssttrraaiinntt))
22xx++zz<<==220000((aallllooyy ccoonnssttrraaiinntt))
yy<<==5500 (( ssaalleess ccoonnssttrraaiinnttss))
WWhheerree xx,,yy aanndd zz aarree tthhee nnuummbbeerr ooff uunniittss ooff pprroodduucctt AA,,BB aanndd CC
rreessppeeccttiivveellyy..
29
Solution variable profit products slack solution qty Ratio
X y z̀ S1 S2 S3 S4 LEAST
8 5 10 0 0 0 0 positive
S1 0 2 3 1 1 0 0 0 400 400/2 S2 0 1 0 1 0 1 0 0 150 150/1
S3 0 2 0 4 0 0 1 0 200 200/2
S4 0 0 1 0 0 0 0 1 50 50/0
Z 8 5 10 0 0 0 zero
30
Solution variable profit products slack solution qty Ratio
X y z̀ S1 S2 S3 S4 LEAST
8 5 10 0 0 0 0 positive S1 0 0 3 -3 1 0 -1 0 200 200/3
S2 0 0 0 -1 0 1 -1/2 0 50 &
x 8 1 0 2 0 0 1/2 0 100 -&
S4 0 0 1 0 0 0 0 1 50 50/1
Z 0 5 -6 0 0 -4 0 800
Depreciation / 157
31
Solution variable profit products slack solution qty Ratio
X y z` S1 S2 S3 S4 LEAST
8 5 10 0 0 0 0 positive S1 0 0 0 -3 1 0 -1 -3 50
S2 0 0 0 -1 0 1 -1/2 0 50
x 8 1 0 2 0 0 ½ 0 100
y 5 0 1 0 0 0 0 1 50
Z 0 0 - 6 0 0 -4 -5
HHooww ddoo yyoouu ffiinndd tthhee ooppttiimmaall ssoolluuttiioonn??
•• IInn tthhee ZZ rrooww aallll tthhee vvaalluueess eeiitthheerr zzeerroo oorr nneeggaattiivvee..
•• TThhee ffoolllloowwiinngg tthhiinnggss aarree oobbsseerrvveedd ffrroomm tthhee ooppttiimmaall ssoolluuttiioonn..
•• 11..TThheerree aarree nnoo ppoossiittiivvee vvaalluueess iinn tthhee bboottttoomm rrooww iiee nnoo ffuurrtthheerr ggaaiinnss
iinn ccoonnttrriibbuuttiioonn ccaann bbee mmaaddee bbyy aalltteerriinngg pprroodduuccttiioonn lleevveell..
•• 22.. TThhee ssoolluuttiioonn SS11==5500;; SS22==5500;;XX==110000;;YY==5500
•• 33.. OOPPTTIIMMUUMM PPRROODDUUCCTTIIOONN PPLLAANN 110000 UUNNIITTSS OOFF PPRROODDUUCCTT XX AANNDD 5500
UUNNIITTSS OOFF YY..
•• TTOOTTAALL CCOONNTTRRIIBBUUTTIIOONN::
XX :: 110000**88==880000
YY :: 5500**55 ==225500
TTOOTTAALL 11005500
TTHHEERREE AARREE UUNNUUSSEEDD CCAAPPAACCIITTYY ::
SS11--5500 MMEEAANNSS TTHHAATT TTHHEERREE AARREE 5500 HHOOUURRSS OOFF UUNNUUSSEEDD MMAACCHHIINNEE
CCAAPPAACCIITTYY
SS22--5500 MMEEAANNSS UUNNUUSSEEDD CCOOMMPPOONNEENNTTSS
NNOO PPRROODDUUCCTTIIOONN OOFF ZZ
220000 KKGGSS OOFF SSPPEECCIIAALL AALLLLOOYY AARREE FFUULLLLYY UUTTIILLIISSEEDD..
TTHHEE SSAALLEESS CCOONNSSTTRRAAIINNTT BBIINNDDIINNGG..
WWHHAATT EEXXPPLLAANNAATTIIOONNSS CCAANN YYOOUU GGIIVVEE FFOORR TTHHEE BBOOTTTTOOMM LLIINNEE??
EEXXPPLLAANNAATTIIOONN
•• 11.. zz CCOOLLUUMMNN==--66
Depreciation / 158
– S3 COLUMN=-4
– S4 COLUMN=-5
– THESE ARE CALLED SHADOW PRICES.
– THESE ARE ALSO KNOWN AS SCARECE RESOURCES.
– What explanations can you give for S3=-4?
SS33--eexxppllaannaattiioonn
•• IIff oonnee mmoorree kkiillooggrraamm ooff tthhee ssppeecciiaall aallllooyy wwaass mmaaddee aavvaaiillaabbllee
ccoonnttrriibbuuttiioonn wwoouulldd iinnccrreeaassee bbyy RRss..44..
•• WWhhaatt ddoo yyoouu mmeeaann bbyy zz==--66??
ZZ==--66
•• IIff zz iiss pprroodduucceedd oonnee uunniitt ooff zz wwiillll ddeeccrreeaassee tthhee ccoonnttrriibbuuttiioonn bbyy RRss..66..
•• WWhhaatt ccaann yyoouu ssaayy aabboouutt SS44==--55??
SS44==--55
•• IIff ssaalleess ccoonnssttrraaiinntt ccoouulldd bbee lliifftteedd eevveerryy eexxttrraa uunniitt ooff pprroodduucctt yy tthhaatt
ccoouulldd bbee ssoolldd wwoouulldd iinnccrreeaassee ccoonnttrriibbuuttiioonn bbyy RRss..55..
•• IIff rreessoouurrcceess aarree nnoott ffuullyy uuttiilliisseedd hhooww ddoo yyoouu ggeett tthhee ooppppoorrttuunniittyy
ccoosstt??
RReessoouurrcceess ffuullllyy uuttiilliisseedd??
•• TThhee sshhaaddooww pprriiccee iiss zzeerroo.. TThheerree aarree nnoo ooppppoorrttuunniittiieess lloosstt..
•• IIff tthhaatt iiss tthhee ccaassee,, wwhhaatt eexxppllaannaattiioonnss ccaann yyoouu ggiivvee ffoorr SS11 aanndd SS22??
SS11 aanndd SS22
•• MMaacchhiinnee hhoouurrss aanndd ccoommppoonneennttss iieeSS11 aanndd SS22 hhaavvee nnoo sshhaaddooww pprriicceess..
TThhiiss iiss eexxppeecctteedd aass tthheerree aarree ssuurrpplluuss mmaacchhiinnee hhoouurrss aanndd ccoommppoonneennttss
aavvaaiillaabbllee..
•• IIss tthheerree aannyy ootthheerr mmeetthhoodd ttoo ccaallccuullaattee tthhee ttoottaall ccoonnttrriibbuuttiioonn?? HHooww
mmuucchh iiss tthhee ttoottaall ccoonnttrriibbuuttiioonn??
TToottaall ccoonnttrriibbuuttiioonn
•• AAllllooyy ccoonnssttrraaiinntt 220000**44==880000
•• SSaalleess ccoonnssttrraaiinntt 5500**55==225500
•• TToottaall ccoonnttrriibbuuttiioonn== 11005500??
•• TThhee ooppppoorrttuunniittyy iiss lloosstt wwhheenn nnoott uuttiilliisseedd tthhee eeffffeeccttiivvee ccoonnssttrraaiinnttss;;
wwee lloooossee ccoonnttrriibbuuttiioonn..
AAlltteerrnnaattiivvee mmeetthhoodd ttoo ffiinndd sshhaaddooww pprriicceess
•• PPrriimmaall//dduuaall pprroobblleemmss
•• FFoorr eevveerryy mmiinniimmiissaattiioonn pprroobblleemm tthheerree iiss aann eeqquuaall bbuutt ooppppoossiittee
mmaaxxiimmiissaattiioonn pprroobblleemm aanndd vviiccee vveerrssaa..
•• TThhee oorriiggiinnaall pprroobblleemm iiss kknnoowwnn aass pprriimmaall pprroobblleemm aanndd tthhee eeqquuaall bbuutt
ooppppoossiittee ffoorrmmuullaattiioonn aass tthhee dduuaall oorr iinnvveerrssee
MMaaxxiimmiissaattiioonn ccoonnvveerrtteedd iinnttoo mmiinniimmiissaattiioonn
•• MMaaxxiimmiissee 33XX++44YY
Depreciation / 159
SSuubbjjeecctt ttoo 44XX++ 22YY<<==110000((MMAATTEERRIIAALLSS))
44XX++66YY<<==118800((LLAABBOOUURR))
TTHHEE OOPPTTIIMMAALL SSOOLLUUTTIIOONN WWAASS XX==1155,,YY==2200 UUNNIITTSS GGIIVVIINNGG
CCOONNTTRRIIBBUUTTIIOONN==RRss..112255
HHOOWW DDOO WWEE CCOONNVVEERRTT TTHHEEMM IINNTTOO DDUUAALL PPRROOBBLLEEMM?? HHOOWW DDOO YYOOUU
CCAALLCCUULLAATTEE SSHHAADDOOWW PPRRIICCEESS??
CCOONNVVEERRTTIIOONN
•• AASSSSUUMMEE AA ==SSHHAADDOOWW PPRRIICCEE PPEERR
MMAACCHHIINNEE HHOOUURR AND B = SHADOW PRICE PER LABOUR
HOUR
THE DUAL MINIMISATION FORMULATION WILL BE:
4A+4B=3…….EQUATION
2A+6B=4…….EQUATION
SOLVING THE EQUATION?
SSOOLLVVIINNGG
•• AA==00..112255;; BB==00 ..662255
•• TTHHUUSS TTHHEE SSHHAADDOOWW PPRRIICCEESS AARREE
•• RRss..00..112255 PPEERR MMAACCHHIINNEE HHOOUURR RRAATTEE
•• RRss..00..662255 PPEERR LLAABBOOUURR HHOOUURR
HHOOWW DDOO YYOOUU VVEERRIIFFYY??
CCOONNTTRRIIBBUUTTIIOONN== 110000**..112255++118800**..662255==RRss112255
MMiinniimmiissaattiioonn eexxaammppllee
•• PPllaassttiicc mmaannuuffaaccttuurreerr ccaann uuttiilliissee tthhrreeee rraaww mmaatteerriiaallss,, ppoollyy,, ggiimmss aanndd
MMooxx iinn vvaarryyiinngg pprrooppoorrttiioonnss ttoo pprroodduuccee tthhrreeee pprroodduuccttss XX,, YY aanndd zz.. TThhee
ffiirrmm wwiisshheess ttoo pprroodduuccee aatt lleeaasstt 220000 uunniittss ooff XX,, 330000 uunniittss ooff YY aanndd 8800
uunniittss ooff ZZ..
•• EEaacchh kkiilloo ooff PPoollyy yyiieellddss 44 ooff XX,, 33 ooff YY aanndd 22 ooff ZZ
•• EEaacchh kkiilloo ooff GGiimmpp yyiieellddss 55 ooff XX,, 66 ooff YY aanndd 11 ooff ZZ
•• EEaacchh kkiilloo ooff MMooxx yyeeiillddss 11 ooff XX 33 ooff YY aanndd 11 ooff CC
•• IIff PPoollyy ccoossttss 2200 pp aa kkiilloo,, GGiimmpp ccoossttss 3300 pp ppeerr kkiilloo aanndd MMooxx ccoossttss 5500 pp
wwhhaatt iiss tthhee mmiinniimmuumm ppuurrcchhaassee ppllaann ttoo pprroodduuccee tthhee rreeqquuiirreedd oouuttppuutt??
EEXXCCEERRCCIISSEE
•• MMIINNIIMMIISSEE 2200AA++3300BB++5500CC
•• SSUUBBJJEECCTT TTOO:: 44AA++55BB++CC>>==220000 3A+6B+3C>=300
2A+B+C>=80
WHERE A,B AND C>=0
HOW DO YOU CONVERT THEM INTO DUAL PROBLEM?AND SOLVE BY
SIMPLEX METHOD.
DDUUAALL PPRROOBBLLEEMM
•• MMAAXXIIMMIISSEE::
Depreciation / 160
•• 220000XX++330000YY++8800ZZ
•• SSUUBBJJEECCTT TTOO:: 44XX++33YY++22ZZ<<==2200 5X+6Y+1Z<=30
1X+3Y+1Z<=50
HERE OBJECTIVE FUNCTION BECOMES CONSTRAINTS AND VICE VERSA.
48
Initial simplex solution
Solution variable X Y Z S1 S2 S3 COST
S1 4 3 2 1 0 0 20
S2 5 6 1 0 1 0 30
S3 1 3 1 0 0 1 50
QTY 200 300 80 0 0 0 0
49
FINAL SIMLEX TABLEAU
Solution variable X Y Z S1 S2 S3 COST
C 1 0 1 2/3 -1/3 0 3 1/3
B 2/3 1 0 -1/9 1/9 0 4 4/9
S3 -2 0 0 -1/3 -2/3 1 33 1/6
QTY -80 0 0 -20 -40 0 -1600
THESE ARE THE FIGURES UNDER THE SLACK VARIABLE COLUMN ie
S1=-20 PURCHASE 20 KGS OF POLY
S2=-40 PURCHASE 40 KGS OF GIMS
S3= 0 NIL PURCHASE OF MOX
TTOOTTAALL CCOOSSTT
•• 2200**2200++3300**4400== RRss 11660000
Depreciation / 161
•• SShhaaddooww pprriicceess:: Z=3 1/3; y=4 4/9; S3=33 1/6
Explanations: If either of the two quantity constrains z and y is changed by one unit then
the total cost will change by 3 1/3 or 4 4/9 respectively.
The S2 valuation means that if any of the material mox, is purchased, total cost will
increase by 33 1/3 per kilogram purchased.
Production: -80 under X column indicates an overproduction of product X by 80 units.
How do you prove?
PPrrooooff
•• PPrroodduucctt XX 8800 uunniittss ++220000 uunniittss==228800uunniittss 8800 ssuurrpplluuss
•• PPrroodduucctt YY6600 uunniittss ++224400 uunniittss==330000 uunniittss mmiinniimmuumm rreeqquuiirreedd
•• PPrroodduucctt ZZ 4400 uunniittss ++4400 uunniittss ==8800 uunniittss iiee mmiinniimmuumm rreeqquuiirreedd..
Course Integration
4. Statistical, mathematical and Economic Applications
After studying this chapter you will understand how statistics, mathematics, Operation
research are used in business decisions.
Statistical tools for decision-making:
Various techniques we have in statistics up to 2nd
year degree. We see now how they are
applied in business decisions.
The most powerful techniques are mean and standard. Mean explains the average values
of the variable whereas standard deviation explains how far the variable values are
deviating from the mean. The coefficient of variation links standard deviation with mean.
i.e. S.D x 100/Mean. We know that the lesser the C.V the greater the consistency and
vice-versa. Co-efficient of variation measures the spread of a set of data as a proportion
of mean. It is used in problems situations where we want to compare the variability,
homogeneity, stability and consistency.
For example: An investor, Mr. Miky in many portfolios studied 100 companies and
obtained the following results for the year 2008
Returns 10-20 20-30 30-40 40-50
Number of
companies
19 32 41 8
The average = 18.8%; S.D=8.81; C.V=46.86%
Suppose the entire investors C.V. is 30% Mr.Miky‘s portfolio is much riskier comparing
to market risk.
The next question asked by Mr. Miky is that what the probability that will he get assured
return of atleast 15%?
Depreciation / 162
In such situation we use normal curve or we use Z distribution to determine the
probability of getting at least 15% assured return on his portfolio.
Z=(X- )/
where - Average
- Standard deviation
15%
Z= (15-18.8)/ 8.81
= 0.43
The value for 0.43 in normal distribution table gives probability i.e. 0.6664. This
probability explains that 67% chance of assured return of 15%.
Suppose he wants to know the probability of return beyond 20%.
Z=(X- )/ = (20-18.8)/8.81=0.136
The Z table gives the probability i.e. 0.5-0.0557=0.444
44% chance to earn beyond 20%
This helps a person or organization to understand what extent they are taking risk before
going for the project.
There are standard probabilities
1 =0.68
2 =0.95
3 =0.99
Next question that comes to my mind is that interval estimates and confidence intervals.
What do you mean by confidence interval and interval estimates?
In statistics the probability that we associate with an interval estimate is called the
confidence level. This probability indicates how confident we are that interval estimate
will include the population parameter. A higher probability means more confidence. In
estimation, the most commonly used confidence levels are 90%, 95%, and 99%, but we
are free to apply any confidence level.
Confidence interval is the range of estimate we are making. If we report that we are 90%
confident that the mean of the population of returns of portfolio will lie between 17% to
19% and then the range 17%-19% is our confidence interval. Often we express the
confidence interval in standard errors rather than in numerical values. The confidence
intervals like 1.64 where
+ 1.64 = Upper limit of the confidence interval
- 1.64 + lower limit of the confidence interval.
High confidence levels will produce large confidence intervals and such large intervals
are not precise.
For example: the return ranges bet ween 17% -19% is more precise than 15%-22%.
Exercise:1
Students can try out with their average and standard deviation marks in five semesters to
find probability of scoring beyond 70% or 80% in the last semester.
Exampe-2
Depreciation / 163
Return on market index and a security are given below .
Period Return on Market Index(A) Return on Security(B)
1
2
3
4
5
6
7
8
9
10
10
24
-16
36
32
20
14
30
60
50
12
20
-8
26
28
26
8
36
48
44
1. Calculate regression equation B on A
2. Explain the correlation between return on Market Index and Return on Security
The regression equation B = 4.24 + 0.76A, here b = +0.76 which indicates 1 rupee
change in return of market index. 76 paise change in return on security. b also indicates
there is a positive correlation between these two variables because b is positive.
We can use regression equation to answer certain vital questions under cost volume
analysis. Some of the questions are as follows
1. The firms break-even sales volume
2. How sensitive is the profit in variations in the output.
3. How sensitivity is the profit in variations in selling prices.
4. What should be the sales level in quantitative terms for the firm to earn target
level of earnings.
The regression equation
Y= a + bX, where a = fixed cost
b = variable cost
y = total cost
Example: 3
The following table gives the repairs and maintenance cost incurred in a cost center for
various levels of annual production. If the budgeted production of the cost center in the
forthcoming year is 8500 units, what would be the estimated repairs and maintenance
cost ignoring possible increase in price levels?
Output (in thousands of
units)
Repairs and Maintenance
Cost Rs.(in thousands
Depreciation / 164
1 15
2 21
2.5 24
3 26
3.5 29
4 32
5 36
6 40
7 44
8 49
Students are expected to calculate by using the formula
Interpretation: b = 4.71 and a = 11.818
Therefore y = 11.818 + 4.71X
The fixed cost is rs.11818 and the variable return and maintenance cost is rs.4.71 per unit
produced.
The total cost when 8500 units are produced (budgeted ) = Fixed component + variable
component = 11818 + (8500 x 4.71) = 51, 853
4.The Board of directors of Shanthi Ltd. would like to merge with one of the less risky
firms so as to reduce risk in future. The two company‘s returns on capital employed for
the last five years given to you.
Company A
Company B
Average return 28%
Standard deviation 5.1%
37%
4.7%
If we take relative dispersion is the criteria which of these two companies has been
considered risky?
Answer:
CV for Company A= X 100/ =5.1 X 100/28 =18.21%
CV for Company B = 4.7 X 100/37= 12.7%
Based on the relative dispersion company B is less riskier as co-efficient of variation is
lesser than Company A.
Depreciation / 165
SSttaannddaarrdd EErrrroorr ooff tthhee EEssttiimmaattee ((11 ooff 33))
Regression line is the line that minimizes the sum of squared deviations of prediction
(also called the sum of squares error).
The standard error of the estimate is a measure of the accuracy of predictions made with a
Regression line Consider the following data.
Depreciation / 166
The second column (Y) is predicted by the first column (X). The slope and Y- Intercept
of the regression line are 3.2716 and 7.1526 respectively. The third column, (Y'),
contains the predictions and is computed according to the formula:
Y' = 3.2716X + 7.1526.
The fourth column (Y-Y') is the error of prediction. It is simply the difference between
what a subject's actual score was (Y) and what the predicted score is (Y').
The sum of the errors of prediction is zero. The last column, (Y-Y')², contains the squared
errors of prediction.
SSttaattss:: CCooeeffffiicciieenntt ooff DDeetteerrmmiinnaattiioonn
CCooeeffffiicciieenntt ooff DDeetteerrmmiinnaattiioonn
The coefficient of determination is ...
the percent of the variation that can be explained by the regression equation.
the explained variation divided by the total variation
the square of r
What's all this variation stuff?
Every sample has some variation in it (unless all the values are identical, and that's
unlikely to happen). The total variation is made up of two parts, the part that can be
explained by the regression equation and the part that can't be explained by the regression
equation.
Depreciation / 167
Well, the ratio of the explained variation to the total variation is a measure of how good
the regression line is. If the regression line passed through every point on the scatter plot
exactly, it would be able to explain all of the variation. The further the line is from the
points, the less it is able to explain.
CCooeeffffiicciieenntt ooff NNoonn--DDeetteerrmmiinnaattiioonn
The coefficient of non-determination is ...
The percent of variation which is unexplained by the regression equation
The unexplained variation divided by the total variation
1 - r^2
--------------------------------------------
Decision under uncertainty
Origin of probabilities
Probability is derived from the verb to ―probe‖ meaning to "find out" what is not too
easily accessible or understandable. The word "proof" has the same origin that provides
necessary details to understand what is claimed to be true.
Probabilistic models are viewed as similar to that of a game; actions are based on
expected outcomes.
Probabilistic models
The center of interest moves from the deterministic to probabilistic models using
subjective statistical techniques for estimation, testing, and predictions
In probabilistic modeling, risk means uncertainty for which the probability distribution is
known. Therefore risk assessment means a study to determine the outcomes of decisions
along with their probabilities.
Problem of decision maker?
Problem of decision maker
Decision-makers often face a severe lack of information.
Probability assessment quantifies the information gap between what is known, and what
needs to be known for an optimal decision. The probabilistic models are used for
protection against adverse uncertainty, and exploitation of propitious uncertainty.
Difficulty in probability assessment
arises from information that is scarce, vague, inconsistent, or incomplete
A statement such as "the probability of a power outage is between 0.3 and 0.4" is more
natural and realistic than their "exact" counterpart such as "the probability of a power
outage is 0.36342.―
Depreciation / 168
What are the challenging tasks?
challenging task
compare several courses of action and then select one action to be implemented
The limited information-processing capacity of a decision-maker can be strained when
considering the consequences of only one course of action. Yet, choice requires that the
implications of various courses of action be visualized and compared. In addition,
unknown factors always intrude upon the problem
challenging task
seldom are outcomes known with certainty. Almost always, an outcome depends upon
the reactions of other people who may be undecided themselves
It is no wonder that decision-makers sometimes postpone choices for as long as possible.
Then, when they finally decide, they neglect to consider all the implications of their
decision.
What are the other factors play in decision making?
Emotions and Risky Decision
Most decision makers rely on emotions in making judgments concerning risky decisions.
Many people are afraid of the possible unwanted consequences.
Even though emotions are subjective and irrational (or a-rational), they should be a part
of the decision making process since they show us our preferences. Since emotions and
rationality are not mutually exclusive, because in order to be practically rational, we need
to have emotions. This can lead to an alternative view about the role of emotions in risk
assessment
Fundamental concerns of decision making
The fundamental concerns of decision making are combining information about
probability with information about desires and interests.
For example: how much do you want to meet her, how important is the picnic, how much
is the prize worth?
Does business decision away from all?
Business decision
Always accompanied by conditions of uncertainty
Treating decisions as if they were gambles is the basis of decision theory.
we have to trade off the value of a certain outcome against its probability.
Canons of decision theory
we must compute the value of a certain outcome and its probabilities; hence, determining
the consequences of our choices.
The origin of decision theory is derived from economics by using the utility function of
payoffs. It suggests that decisions be made by computing the utility and probability, the
ranges of options, and also lays down strategies for good decisions.
What are the process of decision making?
Depreciation / 169
Drawback in the Decision Analysis Approach
Criteria always result in selection of only one course of action.
Many decision problems, the decision-maker might wish to consider a combination of
some actions.
For example, in the Investment problem, the investor might wish to distribute the assets
among a mixture of the choices in such a way to optimize the portfolio's return.
Depreciation / 170
Consider the following Investment Decision-Making Example
States of Nature(%)
Actions Growth Medium G No Change Low
G MG NC L
Bonds 12% 8 7 3
Stocks 15% 9 5 -2
Deposit 7 % 7 7 7
States of Nature
Depreciation / 171
The States of Nature are the states of economy during one year. The problem is to decide
what action to take among three possible courses of action with the given rates of return
as shown in the body of the table.
Uncertainties
Make serious business decisions one is to face a future in which ignorance and
uncertainty increasingly overpower knowledge, as ones planning horizon recedes into the
distance.
The deficiencies about our knowledge of the future may be divided into three domains,
each with rather murky boundaries
Risk, uncertainty and black swans
Risk: One might be able to enumerate the outcomes and figure the probabilities.
Uncertainty: One might be able to enumerate the outcomes but the probabilities are
murky. Most of the time, the best one can do is to give a rank order to possible outcomes
and then be careful that one has not omitted one of significance.
Black Swans: The name comes from an Australian genetic anomaly. This is the domain
of events which are either ―extremely unlikely‖ or ―inconceivable‖ but when they
happen, and they do happen, they have serious consequences, usually bad.
Black swan
In fact, all highly man-made systems, such as, large communications networks, nuclear-
powered electric-generating stations and spacecraft are full of hidden ―paths to failure‖,
so numerous that we cannot think of all of them, or not able to afford the time and money
required to test for and eliminate them. Individually each of these paths is a black swan,
but there are so many of them that the probability of one of them being activated is quite
significant.
Probability is an instrument
Continuum of pure uncertainty and certainty: The domain of decision analysis models
falls between two extreme cases. This depends upon the degree of knowledge we have
about the outcome of our actions, as shown below:
Continuum of pure uncertainty and certainty: The domain of decision analysis models
falls between two extreme cases. This depends upon the degree of knowledge we have
about the outcome of our actions, as shown below:
Ignorance Risky Situation Complete Knowledge
Pure Uncertainty Probabilistic Deterministic
Model Model Model
Probability is an instrument
Probability is an instrument used to measure the likelihood of occurrence for an event.
When you use probability to express your uncertainty, the deterministic side has a
probability of 1 (or zero),
while the other end has a flat (all equally probable) probability. For example, if you are
certain of the occurrence (or non-occurrence) of an event, you use the probability of one
(or zero).
If you are uncertain, and would use the expression "I really don't know," the event may
or may not occur with a probability of 50%.
Depreciation / 172
This is the Bayesian notion that probability assessment is always subjective. That is, the
probability always depends upon how much the decision maker knows.
If someone knows all there is to know, then the probability will diverge either to 1 or 0.
Quantification
The decision situations with flat uncertainty have the largest risk
Probability assessment is nothing more than the quantification of uncertainty.
Different types of decision models
Three most widely used types are:
Decision-making under pure uncertainty
Decision-making under risk
Decision-making by buying information (pushing the problem towards the deterministic
"pole")
Decision-making under pure uncertainty
the decision maker has absolutely no knowledge
not even about the likelihood of occurrence for any state of nature.
In such situations, the decision-maker's behavior is purely based on his/her attitude
toward the unknown.
Some of these behaviors are optimistic, pessimistic, and least regret, among others.
The most optimistic person I ever met was undoubtedly a young artist in Chennai who,
without a franc in his pocket, went into a swanky restaurant and ate dozens of oysters in
hopes of finding a pearl to pay the bill.
Optimist and pessimist
Optimist: The glass is half-full.
Pessimist: The glass is half-empty.
Manager: The glass is twice as large as it needs to be.
Or, as in the following metaphor of a captain in a rough sea:
The pessimist complains about the wind;
the optimist expects it to change;
the realist adjusts the sails.
Optimists are right; so are the pessimists. It is up to you to choose which you will be.
The optimist sees opportunity in every problem; the pessimist sees problem in every
opportunity.
Both optimists and pessimists contribute to our society.
The optimist invents the airplane and the pessimist the parachute.
investment decision-making situation
What will the state of the economy be next year?
Suppose we limit the possibilities to Growth (G), Same (S), or Decline (D). Then, a
typical representation of our uncertainty could be depicted as follows:
Decision Making Under Pure Uncertainty
Depreciation / 173
In decision making under pure uncertainty, the decision-maker has no knowledge
regarding any of the states of nature outcomes, and/or it is costly to obtain the needed
information. In such cases, the decision making depends merely on the decision-maker's
personality type.
Personality Types and Decision Making
1.Pessimism, or Conservative (MaxMin). Worse case scenario. Bad things always happen
to me.
B 3
a) Write min # in each action row S -2) b)Choose max # and do that action. D 7*
Optimism, or Aggressive (MaxMax)
Good things always happen to me.
B 12
a) Write max # in each action row, S 15
b) Choose max # and do that action. D 7
Coefficient of Optimism (Hurwicz's Index)
Middle of the road: I am neither too optimistic nor too pessimistic.
a) Choose an a between 0 & 1, 1 means optimistic and 0 means pessimistic,
b) Choose largest and smallest # for each action,
c) Multiply largest payoff (row-wise) by a and the smallest by (1- a ),
d) Pick action with largest sum.
Example, for a = 0.7,
B(0.7*12)+(0.3*3)=9.3
S(0.7*15)+0.3*(-2)=9.9
*D(0.7*7)+(0.3*7)=7
Minimize Regret: (Savag's Opportunity Loss)
I hate regrets and therefore I have to minimize my regrets. My decision should be made
so that it is worth repeating. I should only do those things that I feel I could happily
repeat. This reduces the chance that the outcome will make me feel regretful, or
disappointed, or that it will be an unpleasant surprise
Regret payoff
Regret is the payoff on what would have been the best decision in the circumstances
minus the payoff for the actual decision in the circumstances. Therefore, the first step is
to setup the regret table:
Regret table
) Take the largest number in each states of nature column (say, L).
b) Subtract all the numbers in that state of nature column from it (i.e. L - Xi,j).
c) Choose maximum number of each action.
d) Choose minimum number from step (d) and take that action.
Depreciation / 174
8(7-7)(7-7)(9-7)(15-7)Deposit
9(7+2)(7-5)(9-9)(15-15)Stocks
4 *(7-3)(7-7)(9-8)(15-12)Bonds
LNCMGG
The Regret Matrix
Limitations of Decision Making under Pure Uncertainty
1.Decision analysis in general assumes that the decision-maker faces a decision problem
where he or she must choose at least and at most one option from a set of options. In
some cases this limitation can be overcome by formulating the decision making under
uncertainty as a zero sum two person game.
2.In decision making under pure uncertainty, the decision-maker has no knowledge
regarding which state of nature is "most likely" to happen. He or she is probabilistically
ignorant concerning the state of nature therefore he or she cannot be optimistic or
pessimistic. In such a case, the decision-maker invokes consideration of security.
Limitations
3.Notice that any technique used in decision making under pure uncertainties, is
appropriate only for the private life decisions. Moreover, the public person (i.e., you, the
manager) has to have some knowledge of the state of nature in order to predict the
probabilities of the various states of nature. Otherwise, the decision-maker is not capable
of making a reasonable and defensible decision.
Decision Making Under Risk
Risk implies a degree of uncertainty and an inability to fully control the outcomes or
consequences of such an action.
Risk or the elimination of risk is an effort that managers employ. However, in some
instances the elimination of one risk may increase some other risks.
Effective handling of a risk requires its assessment and its subsequent impact on the
decision process. The decision process allows the decision-maker to evaluate alternative
strategies prior to making any decision.
process
Depreciation / 175
The problem is defined and all feasible alternatives are considered. The possible
outcomes for each alternative are evaluated.
Outcomes are discussed based on their monetary payoffs or net gain in reference to assets
or time.
Various uncertainties are quantified in terms of probabilities.
The quality of the optimal strategy depends upon the quality of the judgments. The
decision-maker should identify and examine the sensitivity of the optimal strategy with
respect to the crucial factors.
Assign subjective probability
Whenever the decision maker has some knowledge regarding the states of nature, he/she
may be able to assign subjective probability estimates for the occurrence of each state. In
such cases, the problem is classified as decision making under risk. The decision-maker
is able to assign probabilities based on the occurrence of the states of nature
Risk process
a) Use the information you have to assign your beliefs (called subjective probabilities)
regarding each state of the nature, p(s),
b) Each action has a payoff associated with each of the states of nature X(a,s),
c) We compute the expected payoff, also called the return (R), for each action R(a) =
Sums of [X(a,s) p(s)],
d) We accept the principle that we should minimize (or maximize) the expected payoff,
e) Execute the action which minimizes (or maximize) R(a).
Expected Payoff
The actual outcome will not equal the expected value. What you get is not what you
expect, i.e. the "Great Expectations!"
a) For each action, multiply the probability and payoff and then,
b) Add up the results by row,
c) Choose largest number and take that action.
The Most Probable States of Nature
good for non-repetitive decisions
a) Take the state of nature with the highest probability (subjectively break any ties),
b) In that column, choose action with greatest payoff.
In our numerical example, there is a 40% chance of growth so we must buy stocks.
Expected Opportunity Loss (EOL):
a) Setup a loss payoff matrix by taking largest number in each state of nature column(say
L), and subtract all numbers in that column from it, L - Xij,
b) For each action, multiply the probability and loss then add up for each action,
c) Choose the action with smallest EOL.
Expected Value of Perfect Information (EVPI )
EVPI helps to determine the worth of an insider who possesses perfect information.
Recall that EVPI = EOL.
Depreciation / 176
a) Take the maximum payoff for each state of nature,
b) Multiply each case by the probability for that state of nature and then add them up,
c) Subtract the expected payoff from the number obtained in step (b)
I Know Nothing
The Laplace equal likelihood principle
Every state of nature has an equal likelihood. Since I don't know anything about the
nature, every state of nature is equally likely to occur:
a) For each state of nature, use an equal probability (i.e., a Flat Probability),
b) Multiply each number by the probability,
c) Add action rows and put the sum in the Expected Payoff column,
d) Choose largest number in step (c) and perform that action.
I Know Nothing
The Laplace equal likelihood principle
Every state of nature has an equal likelihood. Since I don't know anything about the
nature, every state of nature is equally likely to occur:
a) For each state of nature, use an equal probability (i.e., a Flat Probability),
b) Multiply each number by the probability,
c) Add action rows and put the sum in the Expected Payoff column,
d) Choose largest number in step (c) and perform that action.
Expected Opportunity Loss (Expected Regret)
Comparing a decision outcome to its alternatives appears to be an important component
of decision-making.
One important factor is the emotion of regret. This occurs when a decision outcome is
compared to the outcome that would have taken place had a different decision been
made.
This is in contrast to disappointment, which results from comparing one outcome to
another as a result of the same decision. Accordingly, large contrasts with counterfactual
results have a disproportionate influence on decision making.
regret
regret may be related to the distinction between acts and omissions
Some studies have found that regret is more intense following an action, than an
omission. For example, in one study, participants concluded that a decision maker who
switched stock funds from one company to another and lost money, would feel more
regret than another decision maker who decided against switching the stock funds but
also lost money. People usually assigned a higher value to an inferior outcome when it
resulted from an act rather than from an omission. Presumably, this is as a way of
counteracting the regret that could have resulted from the act.
Bayesian Approach
Making a Better Decision by Buying Reliable Information
In many cases, the decision-maker may need an expert's judgment to sharpen his/her
uncertainties with respect to the probable likelihood of each state of nature. For example,
Depreciation / 177
consider the following decision problem a company is facing concerning the
development of a new product:
expected payoff
The expected payoff for each action is:
A1= 0.2(3000) + 0.5(2000) + 0.3(-6000)= $ -200 and A2= 0;
so the company chooses A2 because of the expected loss associated with A1, and decides
not to develop.
However, the manager is hesitant about this decision. Based on "nothing ventured,
nothing gained" the company is thinking about seeking help from a marketing research
firm. The marketing research firm will assess the size of the product's market by means
of a survey.
reliability matrix
Now the manager is faced with a new decision to make; which marketing research
company should he/she consult? The manager has to make a decision as to how 'reliable'
the consulting firm is. By sampling and then reviewing the past performance of the
consultant, we can develop the following
1. Given What Actually Happened in the Past
2. What the Ap 0.8 0.1 0.1
Consultant Bp 0.1 0.9 0.2
Predicted Cp 0.1 0.0 0.7
A B C
Construction of a reliability matrix
All marketing research firms keep records (i.e., historical data) of the performance of
their past predictions. These records are available to their clients free of charge. To
construct a reliability matrix, you must consider the marketing research firm's
performance records for similar products with high sales. Then, find the percentage of
which products the marketing research firm correctly predicted would have high sales
(A), medium sales (B), and little (C) or almost no sales. Their percentages are presented
by
P(Ap|A) = 0.8, P(Bp|A) = 0.1, P(Cp|A) = 0.1,
Depreciation / 178
in the first column of the above table, respectively. Similar analysis should be conducted
to construct the remaining columns of the reliability matrix.
Applying the Bayes Law
a) Take probabilities and multiply them "down" in the above matrix,
b) Add the rows across to get the sum,
c) Normalize the values (i.e. making probabilities adding up to 1) by dividing each
column number by the sum of the row found in Step b,
0.230.3(0.7) = 0.210.5(0) = 00.2(0.1) = 0.02
0.530.3(0.2) = 0.060.5(0.9) = 0.450.2(0.1) = 0.02
0.240.3(0.1) = 0.030.5(0.1) = 0.0502(0.8) = 0.16
SUMCBA
0.30.50.2
(0.21/.23)=.913(0/.23)=0(.02/.23)=.087
(.06/.53)=.113(0.45/.53)=.849(.02/.53)=.038
(.03/.24)=.125(.05/.24)=.208(.16/.24)=.667
CBA
The decision tree
Many managerial problems, such as this example, involve a sequence of decisions. When
a decision situation requires a series of decisions, the payoff table cannot accommodate
the multiple layers of decision-making. Thus, a decision tree is needed.
Do not gather useless information that cannot change a decision
When the words are clear, then the thought will be also".
Decision Tree Approach
A decision tree is a chronological representation of the decision process. It utilizes a
network of two types of nodes: decision (choice) nodes (represented by square shapes),
and states of nature (chance) nodes (represented by circles).
Construct a decision tree utilizing the logic of the problem. For the chance nodes, ensure
that the probabilities along any outgoing branch sum to one.
Calculate the expected payoffs by rolling the tree backward (i.e., starting at the right and
working toward the left). You may imagine driving your car; starting at the foot of the
decision tree and moving to the right along the branches.
Depreciation / 179
At each square you have control, to make a decision and then turn the wheel of your car.
At each circle, Lady Fortuna takes over the wheel and you are powerless
DECISION TREE MODEL-1
MODEL-2
Step-by-step description
Draw the decision tree using squares to represent decisions and circles to represent
uncertainty,
Evaluate the decision tree to make sure all possible outcomes are included,
Depreciation / 180
Calculate the tree values working from the right side back to the left,
Calculate the values of uncertain outcome nodes by multiplying the value of the
outcomes by their probability (i.e., expected values
Measuring Risk.
The following table shows the risk measurements computed for the Investment Decision
Example:
0%077777D
57%5.49.5 *-25915S
32% **
2.98.937812B
C. V.St. Dev.
Exp. Value
L(0.1)
NC(0.2)
MG(0.3)
G(0. 4)
Risk assesment
0%077777D
92%6.186.75-25915S
43% **
3.20*7.537812B
C. V.St. Dev.
Exp. Value
L(0.25)
NC(0.25)
MG(0.25)
G(0.25)
AssessmetRisk
Risk measurements under pure uncertainty
Stability Analysis
Depreciation / 181
Sensitivity analysis is a technique for determining how much an expected payoff will
change in response to a given change in an input variable (all other things remaining
unchanged).
Steps in Sensitivity Analysis
Begin with consideration of a nominal base-case situation, using the expected values for
each input.
Calculate the base-case output.
Consider a series of "what-if" questions, to determine by how much the output would
deviate from this nominal level if input values deviated from their expected values.
Each input is changed by several percentage points above and below its expected value,
and the expected payoff is recalculated.
The set of expected payoff is plotted against the variable that was changed.
The steeper the slope (i.e., derivative) of the resulting line, the more sensitive the
expected payoff is to a change in the variable.
Scenario Analysis
Scenario analysis is a risk analysis technique that considers both the sensitivity of
expected payoff to changes in key variables and the likely range of variable values. The
worst and best "reasonable" sets of circumstances are considered and the expected payoff
for each is calculated, and compared to the expected, or base-case output.
Scenario analysis also includes the chance events, which could be rare or novel events
with potentially significant consequences for decision-making in some domain.
Integer Linear optimization Application:
Suppose you invest in project (i) by buying an integral number of shares in that project,
with each share costing Ci and returning Ri. If we let Xi denotes the number of shares of
project (i) that are purchased, then the decision problem is to find nonnegative integer
decision variables X1, X2,…, Xn --- when one can invest at most M in the n project --- is
to:
Integer Linear optimization Application
Maximize S Ri Xi
Subject to:
SXi Ci £ M
Application: Suppose you have 25 to invest among three projects whose estimated cost
per share and estimated return per share values are as follows:
Project Cost Return
1 5 7
2 9 12
3 15 22
Maximize 7X1 + 12X2 + 22X3
Subject to:
5X1 + 9X2 + 15X3 £ 25
Using any linear integer programming software package, the optimal strategy is X1 = 2,
X2 = 0, and X3 = 1 with $36 as its optimal return.
Depreciation / 182
Exercise-2
New Horizons Ltd wants to go in for the public share issue of Rs. 10 lakhs(1 lakhs
shares of Rs. 10 each) as a part of its effort to raise capital needed for its expansion
programme. The company is optimistic that if the issue were made now, it would be fully
taken up at a price or Rs. 30 per share.
However the company is facing situations both of which may influence the share prices
in the near future namely
a) An impending wage dispute with assembly workers which assembly workers which
could lead to strike in the whole factory could have an adverse effect on the share.
b) The possibility of a substantial business in the export market, which would increase
the share price.
The four possible events and their expected effect on the Company‘s share prices are
envisaged as:
E1: No strike and export business obtained-share price rises to Rs. 34
E2:strike and export business obtained-share price rises to Rs. 30
E3:No strike and export business lost-share price rises to Rs. 32
E4: strike and export business lost-share price drops to Rs. 16
And the management has identified three possible strategies that the company could
adopt:
S1-Issue 1,00,000 shares now.
S2- issue 1,00,000 shares only after the outcome of (a) & (b) are known.
S3- Issue 50,000 shares now and 50,000 shares after the outcome (a) & (b) are known.
Calculate 1. MINIMAX Regret 2. Maxmax 3. Expected value if probability of strike is
55% and chance of getting export business is 65% 4. Expected value of perfect
information.
Answer
Depreciation / 183
Pay off table (Rs. in lakhs)
30
16
23
30
32
31
30
32
30
30
34
32
S1
S2
S3
E4E3E2E1Event strategies
Calculations: see next page
Calculations
E1- 50,000*30+50,000*34 =32,00,000
E2- 1,00,000*30 = 30,00,000
E3- 50,000*30+ 50,000*32=31,00,000
E4- 50,000*30+ 50,000*16= 23,00,000
Depreciation / 184
Regret table
0 4
14 14
7 7
2
0
1
0
0
0
4
0
2
S1
S2
S3
E4 Max.reg
E3 E2E1Event strategies
Minimax regret solution is S1 ie 4. alternatively include Maxmin ie. Strategy
With highest minimum pay off to which is S1 i.e. 34
Joint probability
Probability of outcome are not given directly but can be easily calculated:
E1 0.45*0.65=0.2925
E2 0.55*0.65=0.3575
E3 0.45*0.35=0.1575
E4 0.55*0.35=0.1925
Depreciation / 185
Maximising expected pay off
30
28.79
29.40
30*.1975
16*.1975
23*.1975
30*.1575
32*.1575
31*.1575
30*.3575
30*.3575
30*.3575
30*.2925
34*.2925
32*.2925
S1
S2
S3
EXP.PAY OFF
E4E3E2E1Event strategies
S1 HAS THE HIGHEST EXPECTED PAYOFF I.E. 30(Rs. 30 lakhs)
Expected value of perfect information
9.94
10.72
5.04
5.78
31.48
0.2925
0.3575
0.1575
0.1925
34
30
32
30
E1
E2
E3
E4
TOTAL
EVPIJoint probability
Max.payoff
EXPECTED VALUE OF PERFECT
INFORMATION=31.48-30=1.48 OR RS.1,48,000
Example Engineering Ltd. Manufacture engines.They have been asked to bid on prospective contract for 90 engines for cars. They have completed an initial run of 30 of these mounting at the following costs:
Direct material Rs. 20,000; Direct labour(6000 hours at Rs.4 per hour)-24000; tooling cost (re-usable)- Rs.3000; variable overhead(Rs.0.50 per labour hour)-Rs.3000;Fixed overhead(Rs.0.50 per labour hour)-Rs.6000.
Depreciation / 186
If 80% learning curve is thought to be pertinent in this case. The Marketing Director believes that the quotation is unlikely to be accepted if it exceeds Rs. 1,10,000 and as the Company are short of work, he believes the contract to be vital.
You are required to comment whether it is worth accepting at Rs. 1,10,000.
No cumulative cumulative cumulative average
Qty.manufa. Hours hours per unit
1. 30 3000 200 ie 6000/30
2. 60 9600(160*60) 160 ie 80% of 200
3. 120 15,369(120*128) 128 ie.80%of 160
Additional hours for 90 additional engines= 15369-6000=9360 hours
Incremental costs for 90 engines:
direct material Rs.60,000
direct labour(9360*4) 37,440
Tooling cost nil
variable overheads(9360*0.5) 4,680
fixed overhead nil
total 1,02,120
Net saving=1,10,000-1,02,120=Rs.7880
3. Indian would like to have travelers cheques: GBP-
STERLING 72.70-73.25
A) explain the quote
B) compute the spread
C) How much would you pay for purchasing 250 pounds in
TCS?
D) If you have a balance of pounds 23 in travellers cheques ,
how many rupees would you receive if the bank in india
quotes 73.65-73.92?
4.Explain the sections 2(1B) and 72A of Income tax Act with
respect to amalgamation/absorption
1. Distinguish between Forwards and Futures
2. Distinguish between spread and swap points.
. Explain the following terms: a) Strike price b) forward price c)in
the money d)Bid and Ask e)holder and writer
4. The current market price is Rs. 50 has the following exercise
price and cal option premium. Compute intrinsic value and time
value
Exercise
price
premium
Depreciation / 187
45
48
50
52
55
5
6
4
5
7
1. consider the following Euro/USD direct quote 0.9345-0.9375
a) What is the cost of buying EURO 1,25,000?
b) How much would you receive by selling 49,300
EURO?
c) What is the cost of buying USD 78,500?
d) What is your receipt if you sell USD 63,400?