capital budgeting actual

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CAPITAL BUDGETING

• Capital budgeting refers to the process where we make decisions concerning investments in the long-term assets of the firm.

• Capital budgeting is a decision situation where large funds are committed (invested) in the initial stages of the project and the returns are expected over a longer period of time usually more than one year and in case this decision goes wrong, it can not be changed which will affect the future growth of the firm.

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FEATURES OF CAPITAL BUDGETING

1. Capital budgeting decisions have long-term implications.

2. These decisions involve substantial commitment of funds.

3. These decisions are irreversible and require analysis of minute details.

4. These decisions determine and affect the future growth of the firm.

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Decision-making Criteria in Decision-making Criteria in Capital BudgetingCapital Budgeting

How do we decide if a capital investment

project should be accepted or

rejected?

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To make decisions, we need:

• Initial cash investment/outflows

• Future cash benefits/inflows

• Rate of return (why)

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A case study

Suppose ABC firm must decide whether to purchase a new machine for Rs. 1,00,000. This machine is expected to generate annual cash inflows of Rs. 20,000, Rs. 50,000 and Rs. 60,000 during next 3 years at 10% capitalisation rate. How do we decide?

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Problems and constraints in cabital budgeting

• Time factor

• Calculation of required rate of return

• Calculation of future benefits

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Capital budgeting process

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Evaluation consists of:

• Estimating relevant cash outflows and cash inflows

• Estimating Appropriate rate of return• Comparing relevant cash outflows and cash

inflows by any suitable technique to take the decision:

1. Payback period2. Average rate of return3. Net present value4. Profitability index5. Internal rate of return

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Estimating relevant cash outflows and cash inflows

• Estimating relevant cash outflows and cash inflows depend upon the nature of investment decisions:

1. Single/Independent decisions

2. Replacement decisions

3. Mutually Exclusive decisions

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Single/Independent decisions

• Calculation of CO• Cost of new plant

+ Installation expenses

+ Other Capital expenditure

+ Additional working capital

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Single/Independent decisions• Calculation of CI for subsequent years

Cash sales revenue- Cash operating cost= Cash inflows before tax (CFBT)- Depreciation= Profits before tax/Taxable income- Tax= Profit after tax + Depreciation= Cash inflows after tax (CFAT)

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Single/Independent decisions

• Calculation of CI for TERMINAL CASH FLOW:

Cash inflows after tax (CFAT) for last year

+ Working capital released

+ Scrap value of the plant (if any).

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Case• A cosmetic company is considering introducing a new

lotion. The manufacturing equipment will cost Rs. 5,60,000. Working capital requirement is expected to increase by Rs. 40,000. The expected life of the equipment is 8 years. The company is thinking of selling the lotion at Rs. 12 each pack. It is estimated that variable cost per pack would be Rs. 6 and annual fixed cost Rs. 3,50,000. The company expects to sell 1,00,000 packs of the lotion each year. Tax rate is 45% and straight-line depreciation is allowed for tax purpose. Calculate the cash flows assumimg:

• 1. Working capital requirement remains same each year.

• 2. Working capital requirement increases by Rs. 5,000 each year

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ANOTHER CASE• A manufacturing department of a firm estimates that

3,000 units of a product can be sold annually at a unit cash sale price of Rs. 14. The cash variable expenses will be Rs.9 per unit. It will also involve cash fixed cost of Rs. 5,000 yearly. The machine to manufacture the product is available at Rs. 50,000. It expected useful life is 10 years. The installation cost would amount to Rs. 10,000. As a result of the acquisition of the machine, the working capital requirement will increase by Rs. 40,000. The firm uses the straight line method (SLM) of depreciation and is in the 50% tax bracket. Your are required to compute the relevant cash flows associated with the acquisition of the machine, assuming

• There is no salvage value• The salvage value is Rs. 2,000 but for depreciation

purpose:a) It is ignoredb) it is considered

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Lets try…..

• A firm plans to buy an asset costing Rs. 1,00,000 and expects CFBT to be Rs. 30,000 p.a. Depreciation will be charged @20% WDV. Tax rate is 30%. Estimated life is 4 years after which it will be disposed off for Rs. 45,000. Your are required to compute the relevant cash flows

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REPLACEMENT PROJECTS

• Calculation of CO Cost of new plant + Installation expenses + Other Capital expenditure + Additional working capital

– Salvage value of old plant + Tax liability on account of capital gain on sale of old plant /– Tax

benefit on account of capital loss on sale of old plant

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REPLACEMENT PROJECTS• Calculation of CI for subsequent years

(incremental basis i.e., new – old)Cash sales revenue (N-O)

- Cash operating cost (N-O)= Cash inflows before tax (CFBT)- Depreciation (N-O)= Profits before tax/Taxable income- Tax= Profit after tax + Depreciation (N-O)= Cash inflows after tax (CFAT) (N-O)

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REPLACEMENT PROJECTS

• Calculation of CI for TERMINAL CASH FLOW:

Cash inflows after tax (CFAT) (N-O) for last year

+ Working capital released

+ Scrap value of the plant (if any).

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Case• A firm is currently using a machine which was purchased 2 years

ago for Rs. 70,OO0 and has a remaining useful life of 5 years. It is considering to replace the machine with a new one which will cost Rs. 1,40,000. The cost of installation will amount to Rs. 10,000. The increase in working capital will be Rs. 20,000. The expected cash inflows before depreciation and taxes are as follows

• Year Existing Machine New Machine • 1 30,000 50,000• 2 30,000 60,000• 3 30,000 70,000• 4 30,000 90,000• 5 30,000 1,00,000

The firm uses SLM and is in 40% tax bracket. Calculate cash flows assuming sale value of old machine is 1) 80,000

2) 60,000 3) 50,000 4) 30,000

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Lets try…..• ABC Ltd. in considering an investment proposal for which the

relevant information is as follows• Purchase price of the new asset Rs.I0,00,000• Installation costs 2,00,000• increase in working capital in year zero 2,50,000• Scrap value of the new asset after 4 years 3,50,000• Revenues from new asset (Annual) 21,50,000• Cash expenses on new asset (Annual) 9,50,000• Current Book value (old asset) 4,00,000• Present scrap value (old asset) 5,00,000• Revenue from old asset (Annual) 19,25,000• Cash expenses on old asset (Annual) 11,25,000• Planning period is 4 years.• Depreciation on new asset: 92% the cost is to be depreciated in the

ratio of 5:8:6:4 over 4 years. Existing asset is depreciated at a rate of Rs. 1,00,000 p.a. Tax rate is 40%. Your are required to compute the relevant cash flows

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Mutually Exclusive

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2. DECISION CRITERIA

TECHNIQUES OF EVALUATION

Traditional or Time-adjusted or

Non-discounting Discounted cash flows

1. Payback period 1. Net Present Value

2. Accounting Rate of 2. Profitability Index

Return 3. Internal Rate of Return

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Case • A company is considering an investment proposal to instal new

milling controls. It will cost Rs. 50,000. The facility has a life expectancy of 5 years and no salvage value. Company tax rate is 35%. The firm uses straight line depreciation. The estimated cash flows before depreciation and tax from the proposed investment proposal are as follows:

Year Cashflows1 Rs. 10,0002 Rs. 10,6923 Rs. 12,7694 Rs. 13,4625 Rs. 20,385

Compute the following:• (a) Payback period.• (b) Average Rate of Return.• (c) Net Present Value at 10% discount rate.• (d) Profitability Index at 10% discount rate.• (e) Internal Rate of Return

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TRADITIONAL OR NON-DISCOUNTING TECHNIQUES

I . PAYBACK PERIOD:

The number of years required to recover a project’s cost,

or how long does it take to get the business’s money back?

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Equal cash inflows

• PB = CO/equal CI

How long will it take for the project to generate enough cash to pay for itself?

00 11 22 33 44 55 8866 77

(500) 150 150 150 150 150 150 150 150 (500) 150 150 150 150 150 150 150 150

Payback period = 3.33 years.Payback period = 3.33 years.

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• Is a 3.33 year payback period good?

• Is it acceptable?

• Firms that use this method will compare the payback calculation to some standard set by the firm.

• If our senior management had set a cut-off of 5 years for projects like ours, what would be our decision?

• Accept

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Unequal Cash inflows

• PB ?

00 11 22 33 44 55 8866 77

(500) 100 150 200 100 150 100 50 150 (500) 100 150 200 100 150 100 50 150

Payback period = 3.5 years.Payback period = 3.5 years.

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TRY…..

• Delhi Machinery Manufacturing Company wants to replace the manual op’rations by new machine. There are two alternative models X and Y of the new machine. Using Payback period, suggest the most profitable investment. Ignore taxation.

X YInitial Investment (Rs.) 9,000 18,000Estimated life of the machine (Years) 4 5Estimated savings in cost (Rs.) 500 800Estimated savings in Wages (Rs.) 6000 8000Additional cost of maintenance (Rs.) 800 1000Additional cost of supervision (Rs.) 1200 1800

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Critical evaluation

Strengths of Payback:

1. Easy to calculate and understand.

2. It serves the purpose of FM as it is based on cash flow analysis.

3. Provides an indication of a project’s risk. Project with shorter PB will be less risky

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Critical evaluation

Drawbacks of Payback Period:Drawbacks of Payback Period:

1.The payback period does not indicate whether the project should be accepted or rejected. For example, we don’t know whether 4.56 years is a good payback period, or not.

2. Cash flows that occur after the end of the payback time are ignored in the calculation of payback period. Yet, these latter cash flows may be significant in making the decision.

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Example

(500) 150 150 150 150 150 (300) 0 0 (500) 150 150 150 150 150 (300) 0 0

00 11 22 33 44 55 8866 77

This project is clearly unprofitable, but we would accept it based on a 4-year paybackcriterion!

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Conti…

3.Calculation of payback period ignores the time value of money. (This is a critical flaw!)

Discounted PaybackDiscounted Payback

• Discounts the cash flows at the firm’s required rate of return.

• Payback period is calculated using these discounted net cash flows.Problems:


00 11 22 33 44 55

(500) 250 250 250 250 250 (500) 250 250 250 250 250

Discounted

Year Cash Flow CF (14%)

0 -500 -500.00

1 250 219.30


00 11 22 33 44 55

(500) 250 250 250 250 250 (500) 250 250 250 250 250

Discounted


0 -500 -500.00

1 250 219.30 1 year

280.70


00 11 22 33 44 55

(500) 250 250 250 250 250 (500) 250 250 250 250 250

Discounted


0 -500 -500.00

1 250 219.30 1 year

280.70

2 250 192.38


00 11 22 33 44 55

(500) 250 250 250 250 250 (500) 250 250 250 250 250

Discounted


0 -500 -500.00

1 250 219.30 1 year

280.70

2 250 192.38 2 years

88.32


00 11 22 33 44 55

(500) 250 250 250 250 250 (500) 250 250 250 250 250

Discounted


0 -500 -500.00

1 250 219.30 1 year

280.70

2 250 192.38 2 years

88.32

3 250 168.75


00 11 22 33 44 55

(500) 250 250 250 250 250 (500) 250 250 250 250 250

Discounted


0 -500 -500.00

1 250 219.30 1 year

280.70

2 250 192.38 2 years

88.32

3 250 168.75 .52 years


00 11 22 33 44 55

(500) 250 250 250 250 250 (500) 250 250 250 250 250

Discounted


0 -500 -500.00

1 250 219.30 1 year

280.70

2 250 192.38 2 years

88.32

3 250 168.75 .52 years

The Discounted The Discounted Payback Payback

is is 2.522.52 years years

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II . ACCOUNTING RATE OF RETURN (OR) AVERAGE RATE OF RETURN

(ARR)

# ARR is a measure based on accounting profits rather than the cash flows. The ARR may be defined as “the annualized net income earned on the average funds invested in a project.”

COMPUTATION OF ARR:

Average Annual profit (after tax)

ARR = x 100

Average Investment in the Project

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Critical evaluation

• Merits1). Easy to understand. Necessary information to calculate average rate of return are available easy. 2). This method takes into account all the profits during the life time of the project, whereas pay back period ignores the profits accruing after the pay back period

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Critical evaluation

• Demerits1). Ignores the time value of money. 2). Does not use cash flow so it does not serve the purpose of FM.3) ARR method does not consider the size of investment for each project. It may be time that the competing ARR of two projects may be the same but they may require different average investments.

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DISCOUNTED CASH FLOWS OR TIME ADJUSTED TECHNIQUES

These are based upon the fact that the cash flows occurring at different point of time are not having same economic worth i.e., Time Value of Money

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WHAT IS TIME VALUE OF MONEY?

• Time value of money refers to the fact that money received today is different in its worth from money receivable at some other time in future.

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EXAMPLE

• If an individual is given an option to receive Rs.1000 today or receive the same amount after one year, he will definitely choose to receive Rs.1000 today.

• The obvious reason for this is that rupee received today has a higher value than the rupee receivable in future.

• The English proverb ‘A BIRD IN HAND IS WORTH TWO IN BUSH’ is worth mentioning.

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REASONS OF PREFRENCE OF CURRENT MONEY

• FUTURE UNCERTAINITIES

There is certainty of current money whereas future money has uncertainty.

There may be apprehension that creditor may become insolvent.

• INFLATION

In inflationary situation money received today has greater purchasing power.

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• PREFERENCE OF PRESENT CONSUMPTION

Besides certainty every person has preference for present consumption.

Also present money may be required for some specific purpose.

• REINVESTMENT OPPORTUNITIES

Present money is preferred because individual has reinvestment opportunities.

If they have got money they can invest this money to get further returns on it.

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How can one compare amounts in different time periods?

• One can adjust values from different time periods using an interest rate.

• Two techniques:

1. Compounding Technique

2. Discounting Technique

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TECHNIQUES

1.COMPOUNDING TECHNIQUE

The compounding technique to find out the FV of a present money.

This can be explained with reference to:

-The FV of single present cash flow

-The FV of a series of unequal and equal cash flows

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FV OF SINGLE PRESENT CASH FLOW

• FV=PV(1+r)n

Where

FV=Future Value

PV=Present Value

r= Rate of Return

n= No. of years

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EXAMPLE

• Find out the compounded value of Rs.100 invested for 3 years at 10% rate of interest.

Amount at the end of one year will be:100*110/100=Rs.110Amount at the end of 2nd year will be:110*110/100=Rs.121Amount at the end of 3rd year will be:121*110/100=Rs.133.1

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The FV can be calculated by using compound value of Re. 1 table.

FV=100*CVF(10%,3years)FV=100(1+0.10)3

FV=100*1.331FV=Rs.133.1

This table is useful where the number of years are very long, say, 20

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FV OF SERIES OF CASH FLOWS

EXAMPLE OF UNEQUAL CASH FLOWS:

Mr. X invested Rs.500,Rs.1000,Rs.1500,Rs.2000, and Rs.2500 at the end of each year. Calculate the compound value at the end of 5 years compounded annually, when the interest charged is 5%.

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END OF YEAR

AMT. DEPOSITED

NO. OF YEARS COMPOUNDED

CVF @ 5%

FV

1 500 4 1.216 608

2 1000 3 1.158 1158

3 1500 2 1.103 1654.5

4 2000 1 1.050 2100

5 2500 0 1.000 2500

Amount at the end of 5th year=Rs.8020.50

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FV OF SERIES OF CASH FLOWS

EXAMPLE OF EQUAL CASH FLOWS:

Mr. X invested Rs.2000 paying 5% interest compounded annually. Determine the sum of money, he will have at the end of the 5th year.

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END OF YEAR

AMT. DEPOSITED

NO. OF YEARS COMPOUNDED

CVF @ 5%

FV

1 2000 4 1.216 2432

2 2000 3 1.158 2316

3 2000 2 1.103 2206

4 2000 1 1.050 2100

5 2000 0 1.000 2000

Amount at the end of 5th year=Rs.11054

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FV can also be calculated by using compound value of annuity table as:

2000*(CVAF 5%,5years)

FV=2000*5.526

FV=Rs. 11054

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2.DISCOUNTING TECHNIQUES

• The discounting technique is used to find out the present value of future money.

• This technique is reverse of compounding technique.

• The discounting technique to find out PV can be explained in terms of:

-The PV of a future sum

-The PV of a future unequal and equal series

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PV=FV/(1+r)n

where

FV=Future Value

PV=Present Value

r= Rate of Return

n= No. of years

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PV OF FUTURE SUMMr. X expects to get Rs.100 after one year at the rate of return 10%.Find out the amount he will have to invest today?

PV=FV/(1+r)n

PV=100/(1+0.10)=Rs.90.90

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Or

The FV can be calculated by using present value of Re. 1 table.

PV=100*PVF(10%,1year)

PV=100*0.909=Rs.90.90

This table is useful where the number of years are very long, say, 20

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PV OF A FUTURE SERIES

EXAMPLE OF UNEQUAL CASH FLOWS: Find out the PV of future cash inflows that will be received over the next 4 years.

YEAR CASH FLOWS

1 1000

2 2000

3 3000

4 4000

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YEAR CASH FLOWS

PVF @ 10%

PV

1 1000 0.909 909

2 2000 0.826 1652

3 3000 0.751 2253

4 4000 0.683 2732

PV OF CASH FLOWS=Rs.7546

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PV OF A FUTURE SERIESEXAMPLE OF EQUAL CASH FLOWS: Calculate PV of an annuity of Rs.500 received annually for 4 years at 10%

rate of return.

YEAR CASH FLOWS

PVF @ 10%

PV

1 500 0.909 454.50

2 500 0.826 413.50

3 500 0.751 375.50

4 500 0.683 341.50

PV OF CASH FLOWS=Rs.1585

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or

PV can also be calculated by using present value of annuity table as:

PV OF CASH FLOWS=500*PVAF(10%,4years) PV=500*3.170=Rs.1585

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. NET PRESENT VALUE (NPV) METHOD

• The NPV of an investment proposal may be defined as the sum of the present values of all the cash inflows less the sum of present values of all the cash outflows associated with the proposal.

• The decision rule is “ Accept the proposal if its NPV is positive and reject the proposal if the NPV is negative”.

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Case• XYZ Company is considering replacement of its existing

machine by a new machine, which is expected to cost Rs.1, 60,000. The new machine will have a life of 5 years and will yield annual cash revenue of Rs. 2,50,000 and incur annual cash expenses of Rs. 1,30,000. The estimated salvage value of the new machine is nil. The existing machine has a book value of Rs. 40,000 and can be sold for Rs. 20,000 today. It is good for next 5 years and is estimated to generate annual cash revenue Rs. 2,00,000 and to involve annual cash expenses of Rs. 1,40,000. Its salvage value after 5 years is zero. Corporate tax rate is 40%. Depreciation rate is 25% on WDV method. The company’s opportunity cost of capital is 20%. Ignore taxes on profit or loss on sale of machine. Advice whether the company should replace the machine or not.

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Case• A company has a machine which has been in operations for 2 years ;

its remaining estimated useful life is 10 years, with no salvage value. Its current market value is Rs. 1,oo,ooo. Tile management is considering a proposal to purchase an improved model of a machine, which gives increased output. The relevant particulars are as follows:

Existing Machine New Machine

• Purchase price Rs. 2,40,000 Rs. 4,00,000• Estimated life 12 years10 years• Salvage value __ __• Annual operating hours 2,000 2,000• Selling price per unit Rs. 10 Rs. 10• Output per hour 15 units 30 units• Material cost per unit Rs. 2 Rs. 2• Labour cost per hour 20 40• Consumable stores per year 2,000 5,000• Repairs per year 9,000 6,000• Working Capital 25,000 40,000

The company follows the straight-line method of depreciation and is subject to 50% tax. Should the existing machine be replaced ? Assume thai the company’s required rate of return is 15%

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Non conventional caseMachine A costs Rs. 1,00,000 payable immediately. Machine B costs Rs. 1,20,000 half payable immediately and half payable in one year’s time. The cash inflows expected are as follows:

• Year (at end) Machine A Machine B

• 1 Rs. 20,000• 2 60,000 Rs.

60,000• 3 40,000

60,000;• 4 30,000

80,000;• 5 20,000

At 7% opportunity cost, which machine should be selected on the basis of NPV?

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Try this….ABC Ltd. is in the business of manufacturing X product. It has a plant on a piece of landwhich was purchased 10 years ago for 10 lakhs. The firm now plans to set up another plant on the same land(50% of the existing plant). Capital Expenditure for setting up new plant (incurred in the beginning of the year):

Year 1 Cost of land Rs. 5,00,000Land Development 17,00,000Payment for purchase of Machine 20,00,000

Year 2 Final payment for Land Development 15,00,000Final payment to Machine supplier 70,00,000

The machine has an estimated useful life of 5 years and the company follows SL method of depreciation. The information regarding sales and operational expenses is as follows

Year 1 2 3 4 5Sales (Rs. lacs) 25 30 35 40 45Expenses (Rs. lacs) 5 7 10 12 15

If the company’s rate of discount is 15% and the tax rate is 50%, should the above proposal be accepted assuming no depreciation on land.

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Critical evaluation - merits1 It recognizes the time value of money. 2. The NPV technique considers the entire cash flow stream and all the cash inflows and outflows.3. It serves the purpose of FM as it is based on cash flow analysis.4. This method is particularly useful for the selection of Mutually Exclusive projects (mostly the case with the companies) .5. It represents the net contribution of a proposal towards the wealth of the firm and is therefore, in full conformity with the objective of maximization of the wealth of the shareholders.

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Critical evaluation - demerits

i) It involves difficult calculations . ii) The NPV technique requires the predetermination of the required rate of return, k, which itself is a difficult job. If the value of the ‘k’ is not correctly taken, then the whole exercise of the NPV may give wrong results.iii) The decision under the NPV technique is based on a value which is an absolute measure. It ignores the difference in initial outflows, size of different proposals etc. while evaluating mutually exclusive proposals.

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II. PROFITABILITY INDEX METHOD:

This technique is a variant of the NPV technique and is also known as BENEFIT - COST RATIO or PRESENT VALUE INDEX.

Total present value of cash inflows

PI =

Total present value of cash outflows.

Accept the project if its PI is more than 1 and reject the proposal if the PI is less than 1.

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III. INTERNAL RATE OF RETURN (IRR):

The IRR of a proposal is defined as the discount rate which produces a zero NPV, i.e., the IRR is the discount rate which will equate the present value of cash inflows with the present value of cash outflows.

The IRR is also known as Marginal Rate of Return or Time Adjusted Rate of Return.

Logically, if IRR > the cost of capital to finance the project, the project should be accepted.If IRR < cost of capital, the project should be rejected

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What is IRR?

• The discount rate which sets the NPV of all cash flows equal to 0.

• Helps to determine the YIELD on an investment.

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Calculation of IRR1) When CI are equal

2) When CI are unequal

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IRR- When CI are equal

• A firm is evaluating a proposal costing Rs. 1,00,000 and having annual inflows of Rs. 25,000 occurring at the end of each of next six years. Calculate the IRR of the proposal

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Step 1

• Calculate PB period = CO / Equal CI

• The payback period in the given case is 4 years.

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Step 2

• Now, search for a value nearest to PB for the year equal to the life of the project in the PVAF table. Out of the closest figures, one will be bigger and other smaller than PB. Corresponding to these , find two interest rates.

• In our case, search for a value nearest to 4 in the 6th year row of the PVAF table. The closest figures are given in rate 12% (4.111) and the rate 13% (3.998). This means that the IRR of the proposal is expected to lie between 12% and 13%.

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Step 3

• In order to make a precise estimate of the IRR, find out the NPV of the project for both these rates. One NPV will be positive and other will be negative.

• At 12%, NPV= 25,000X 4.111— 1,00,000= Rs. +2,775.• At 13%, NPV= 25,000X 3.998 — 1,00,000= Rs. -50.

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Step 4

• Calculate IRR by using interpolation technique

• IRR = L+ A x (H - L) A-B

where, • L= Lower discount rate, at

which NPV is positive• H= Higher discount rate, at

which NPV is negative..• A=NPV at Lower discount

rate, L.• B= NPV at Higher discount

rate, H.

IRR= 12% + 2,775 x (13—12)

2,775 —(—50)= 12.98%

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Try this….

• A project costs Rs. 36,000 and is expected to generate cash inflows of Rs. 11,200 annually for 5 years. Calculate IRR

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IRR- When CI are unequal

• A firm is evaluating a proposal costing Rs. 50,000 and having annual inflows of Rs. 10,000; 10,450; 11,800; 12,250; 16,750 occurring at the end of each of next 5 years. Calculate the IRR of the proposal

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Self-assessment 1• Following information regarding Machine A is available and

suggest that machine will be purchased or not on the basis of NPV method and IRR method:

Cash Outflow Rs. 50,000Cost of Capital 10%Year CFAT PVF@10 % Present Value1 Rs. 10,000 .909 90902 Rs. 10,692 .826 8831.593 Rs. 12,769 .751 9589.524 Rs. 13,462 .683 9194.555 Rs. 20,385 .621 12659.08

Total 49364.74NPV (-635.26) Reject the proposal IRR (approx 9%) Reject the proposal

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Self-assessment 2

Particulars Project A Project B

Cash Outlays (Rs. 5000) (Rs 7500)

Cash Inflow at the end of year

6250 9150

Cost of Capital 10%

NPV @10% 681.25 817.35

IRR 25% Approx 22%

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Self assessment 3

• A company is considering as to which of two mutually exclusive projects it should undertake. The Finance Director thinks that the project with the higher NPV should be chosen whereas the Managing Director thinks that the one with the higher IRR should be undertaken especially as both projects have the same initial outlay and length of life. The company anticipates a cost of capital of 10% and the net after-tax cash flows of the projects are as follows:(Figures in Rs. ‘000)

• Year 0 1 2 3 4 5• Project X (200) 35 80 90 75 20• Project Y (200) 218 10 10 4 3Required:a) Calculate the NPV and IRR of each project.b) State, with reasons, which project you would recommended.

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Typical case• A share of the face value of Rs. 100 has current

market price of Rs. 480. Annual expected dividend is 30%. During the fifth year, the shareholder is expecting a bonus in the ratio of 1:5. Dividend rate is expected to be maintained on the expanded capital base. The shareholder intends to retain the share till the end of the eighth year. At that time the value of share is expected to be Rs. 1,000. Additional expenses at the time of purchase and sale are estimated at 5% on the market price. There is no tax on dividend income and capital gain. The shareholder expects a minimum return of 15% per annum. Should he buy the share

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Mind Teaser• Following are the data on a capital project being

evaluated by the management of X Ltd.Particulars Project MAnnual cost saving Rs.40,000Useful life 4 yearsInternal rate of return 15%Profitability index 1.064Net present value ?Cost of capital ?Cost of project ?

Payback period ?Salvage value 0Find the missing figures

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Critical evaluation - merits

1. It recognizes the time value of money. 2. The NPV technique considers the entire cash flow stream and all the cash inflows and outflows.3. It serves the purpose of FM as it is based on cash flow analysis.4. Its in Percentage and not in figure. Therefore it helps managers in taking decisions easily by comparing with cut off rate

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Drawbacks of IRR

• Tedious calculations

• Reinvestment rate assumption

• Multiple IRR

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2. Reinvestment rate assumption

• The IRR criterion implicitly assumes that the cash flow generated by the projects will be reinvested at the internal rate of return, that is, the same rate as the proposal itself offers. With the NPV method, the assumption is that the funds released can be reinvested at a rate equal to the cost of capital, that is, the required rate of return.

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The crucial factor is which assumption is correct?

• The assumption of the NPV method is considered to be superior theoretically because it has the virtue of having a rate which can consistently be applied to all investment proposals.

• In contrast to the NPV method, the IRR method assumes a high reinvestment rate for investment proposals having a high IRR and a low investment rate for investment proposals having a low IRR

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Therefore it becomes important to incorporate

consistent reinvestment rate in IRR. But HOW ?????

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The Modified Internal Rate of Return

• Modified Internal Rate of Return or MIRR is the investor's required rate of return which equates the Initial Cost Outlay with the present value of future value of cash inflows

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Conti… • The modified IRR (MIRR)

is the average annual rate of return that will be earned on an investment if the cash flows are reinvested at the specified rate of return (usually, the WACC)

• To calculate the MIRR, first find the total future value of the cash flows at the reinvestment rate, and then apply the formula:

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The MIRR: An Example

• Assume that your company is investigating a new labor-saving machine that will cost $10,000. The machine is expected to provide cost savings each year as shown in the following timeline:

0 1 2 3 4 5

2000 2500 3000 3500 4000-10,000

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To calculate the MIRR for our example, first find the FV of the cash flows at 12% (the WACC):

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Conclusion

• This is the amount that you will have accumulated by the end of the life of the investment

• Now, find the average annual rate of return

Since the MIRR is greater than the WACC, this project is acceptable

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3. Multiple Rates of Return

• If a project has more than one rate of return, how would you make an accept/reject decision?

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Investment Classification

Simple Investment• Def: Initial cash flows

are negative, and only one sign change occurs in the net cash flows series.

• Example: -$100, $250, $300 (-, +, +)

• ROR: A unique ROR

Non simple Investment• Def: Initial cash flows

are negative, but more than one sign changes in the remaining cash flow series.

• Example: -$100, $300, -$120 (-, +, -)

• ROR: A possibility of multiple RORs

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Multiple Rates of Return Problem

• Find the rate(s) of return:

2

$2,300 $1,320( ) $1,000

1 (1 )

0

PW ii i

CO $1,000

CI $2,300

CO $1,320

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Let Then,

Solving for yields,

or

Solving for yields

or 20%

xi

PW ii i

x x

x

x x

i

i

1

1

000300

1

320

1

000 300 320

0

10 11 10 12

10%

2

2

.

( ) $1,$2,

( )

$1,

( )

$1, $2, $1,

/ /

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Plot for Investment with Multiple Rates of Return

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Why use MIRR versus IRR?

MIRR correctly assumes reinvestment at opportunity cost = WACC and also avoids the problem of multiple IRRs.

Managers like rate of return comparisons, so when there are non normal CFs and more than one IRR, MIRR is better than IRR

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To conclude

• The decision by the NPV criterion would be theoretically correct as it is consistent with the goal of maximization of shareholders’ wealth. Further, the reinvestment rate of funds released by the project is based on assumptions which can be consistently applied. The IRR can, of course, be modified by adopting the incremental approach to resolve the conflict in ranking. But it involves additional computation. Another deficiency of the IRR is that it may be indeterminate and give multiple rates in the case of a non-conventional cash flow pattern. In sum, therefore, the NPV emerges as a superior evaluation technique.

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Comparison of results given by Internal Rate of Return and

Net Present Value

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Similarities between results in NPV and IRR

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• Both NPV and IRR will gave the same results (i.e. acceptance and rejection) regarding an investment proposal in the following cases:– When project involving conventional cash flows– Independent Investment Proposals, i.e. ,

acceptance of which does not preclude the acceptance of the others (Single Machine)

• Reason for the same results is, NPV will be positive only when the actual return on investment is more than the cut-off rate (required rate of return/ cost of capital), whereas IRR support projects in whose case the IRR is more than the cut-off rate

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Consider the following case

• Following information regarding Machine A is available and suggest that machine will be purchased or not on the basis of NPV method and IRR method:

Cash Outflow Rs. 50,000Cost of Capital 10%Year CFAT PVF@10 % Present Value1 Rs. 10,000 .909 90902 Rs. 10,692 .826 8831.593 Rs. 12,769 .751 9589.524 Rs. 13,462 .683 9194.555 Rs. 20,385 .621 12659.08

Total 49364.74NPV (-635.26) Reject the proposal IRR (9.625%) Reject the proposal

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The big Q?Will the two methods always give the same answer?No, unfortunately not

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Dissimilarities between results given by NPV and IRR

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• In certain situations NPV and IRR gives contradictory results such that if NPV methods find one proposal acceptable, while IRR favors the other

• This sort of problems will be faced in mutually exclusive projects

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Conti…

• The problem of the conflicting results can be classified due to the following differences in the projects

– Size Disparity problem

– Time Disparity problem

– Unequal expected lives

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Size Disparity Problem• It arises when the initial investment in

mutually exclusive projects are different (Done Earlier)

Particulars Project A Project B

Cash Outlays (Rs. 5000) (Rs 7500)

Cash Inflow at the end of one year

6250 9150

Cost of Capital 10%

NPV @10% 681.25 817.35

IRR 25% Approx 22%

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Time Disparity Problem• This problem arises when the cash flow pattern of

mutually exclusive projects is different. i.e., most of the cash flows from one project come in the early years, while most of the cash flows from the other project come

in the later years (Done Earlier)

(Figures in Rs. ‘000)

Year 0 1 2 3 4 5

Project X (200) 35 80 90 75 20

Project Y (200) 218 10 10 4 3

Calculate NPV at 10% and IRR.

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Proposals having unequal lives

• If a firm is evaluating two mutually exclusive proposals having unequal lives, then the decision may be taken in normal course on the basis of NPV of the two proposals. The proposal with the higher NPV will be selected. The difference in economic lives may not be of much importance, unless they can be repeated indefinitely.

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Example• A firm is evaluating the following two proposals @ 15%

discount rate

Year X Y• 0 —24,000 —44,000• 1 14,000 16,000• 2 14,000 16,000• 3 14,000 16,000• 4 — 16,000• 5 — 16,000

Evaluate the proposal if:

1) They are one off investment

2) They can be repeated indefinitely.

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They can be repeated indefinitely.

• This is done by Equivalent Annuity Method (EAM).

• The equivalent annuity is defined as the amount of annuity for ‘n’ years, which has a present values discounted at ‘r’ percent per annum equivalent to the given amount.

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In our case,

• The project X has the NPV of Rs. 7,962. Considering this to be the present value of annuity of three years at discount rate of 15%, the annuity amount can be calculated as

X/1.15+ X/(1.15)(1.15)+ X/(1.15)(1.15)(1.15)=7962Annuity Amount (X) = Rs.7,962/2.283

= Rs.3,488.• Similarly, for project Y,

Annuity Amount (Y) = Rs.9,632/3.352 = Rs.2,873.

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Interpretation• Project X Project X is giving NPV of Rs. 7,962

after a period of every three years. This can also be considered as an annuity of Rs. 3,488 for three years; and with replacement every three years, this can be considered as a perpetuity of Rs.3,488 forever.

• Project Y: Project Y is giving NPV of Rs. 9,632 after a period of every five years. This can also be considered as an annuity of Rs. 2,873 for five years; and with replacement every five years, this can be considered as a perpetuity of Rs. 2,873 forever.

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Question is

• To select between the NPV of Rs. 7,962 (Project X) every three years or the NPV of’ Rs. 9,632 (Project Y) every five years. Now, in the light of the above, the same can be expressed as a choice between a perpetuity of Rs. 3,488 (Project X) and Rs. 2,873 (Project Y). The choice now, is obvious and the firm will like to select project X only.

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Conclusion • To conclude, the two methods would give similar accept-

reject decisions in the case of independent conventional investments. They would, however, rank mutually exclusive projects differently in the case of the (i) size-disparity problem, (ii) time-disparity problem, and (iii) unequal service life of projects.

• Whenever there is a conflict between NPV and another decision rule, you should always use NPV

• Why NPV? Why not IRR?• The answer should be related to the effect of the

decision on the maximization shareholders’ wealth

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CAPITAL BUDGETING PRACTICES IN INDIA

1. Capital budgeting decisions are undertaken at the top management level and are planned in advance. The Corporates follow mostly top-down approach in this regard.

2. Discounted cash flow techniques are more popular now.

3. High growth firms use IRR more frequently whereas Payback period is more widely used by small firms.

4. PI technique is used more by public sector units than by private sector units.

capital budgeting actual

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