engineering decision 3

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Engineering Economics

Engr.Wajahat Maqbool



• Engineering projects – Use resources: raw materials, labor, money, time

– Can be undertaken in a variety of ways

• Choose one alternative to a problem – Determine the economically best alternative

• Need to understand the relationship betweentime and money

• In many decisions costs and benefits are themost important factors

What is Engineering Economy?




• Define problem

• Choose objectives

• Identify alternatives

• Evaluate consequences

• Select the best

• Implement

• Audit results

The Decision Making Process




• Whenever people predict the future, errorsoccur.

• Engineers estimate

– To control uncertainty, make sure the informationused is accurate

• Sensitivity analysis is to find how sensitivethe results are to the parameters defined in

the problem. – It is an integral part of EE decisions since dataregarding future activities are always uncertain.

Uncertainty and sensitivityanalysis




Principles of EngineeringEconomics (EE)

• Develop the alternative

• Focus on the differences

• Use a consistent viewpoint• Use a common unit of measure

• Consider all relevant criteria

• Make uncertainty explicit• Revisit your decision




Engineering Economics Procedure

• Problem definition

• Development of alternatives

• Development of outcomes

• Selection of a decision criterion

• Analysis and comparison of alternatives

• Selection of the preferred alternative

• Performance monitoring and evaluation of results




• The management of a small furniture manufacturingcompany is under pressure to increase profitabilityin order to get a much needed loan from the bank topurchase a more modern pattern-cutting machine.

One proposed solution is to sell waste wood chipsto a local manufacturer instead of using them to fuelspace heaters for the company’s office and factoryareas – Define the company’s problem, next reformulate the

problem in a variety of creative ways – Develop at least one potential alternative for your

reformulated problem

Example: EE procedure




• Cost accounting is a subset of accountingconcerned with decision making andcontrol in a firm.

• Determines the cost of products or services

– It is the source of some of the cost data that

are needed in EE studies

Accounting and EE




• Engineering Economy is defined as considering the timevalue of money in the decision making process of selecting alternative solutions for real projects

• If correctly done, it:

– states the consequences in a common measure – only consider differences between alternatives

– makes separable decisions separately

– adopt a systems view

– use common planning horizon• EE uses the proper steps in decision making

Summary




A Few Questions First• Do you know what anything about the following?

• 1. The GNP (Gross National Product)

• 2. Investments

• 3. Macro and micro Economics

• 4. Accounting

• 5. Finance

• 6. Statistics

• 7. What salary you would like to make upon

• graduation

• 8. Why making a profit is important for all of us

• 9. Why is a company in business




The Economic Consequences

• Capital Investments have lives of 3-50 years or more

• Often the choice between alternatives is:

Which one is cheaper?

• Don’t mix technical with economic efficiency

• The concept of time value of money is fundamental

to Engineering Economy

• The main issue usually is the decision between

current value and expected future revenue streams

• Need to balance expenses now with revenues later




Engineering Economy isImportant

• The importance of money to engineering (or more

generally) any business undertaking) has been known

for a long time:

“engineering ... is the art of doing well with one dollar which any bungler can do with two after a fashion”

- A. M. Wellington (1887)

• They say “cash is king”, so our approach is to deal withthe cash flows of a business as engineering requires it in

the firm.




What is Engineering Economy?

• Engineering projects

– Use resources: raw materials, labor, money, time

– Can be undertaken in a variety of ways

• Choose one alternative to a problem

– Determine the economically best alternative• Need to understand the relationship between time and money

• In many decisions costs and benefits are the most importantfactors

• Cost accounting is a subset of accounting concerned withdecision making and control in a firm.

– Determines the cost of products or services, it is the sourceof some of the cost data that are needed in EE studies




Engineering Economy andDecision Making

• All engineering projects use resources, such as rawmaterials, money, labour, and time

• Engineering economy draws upon knowledge of engineering and economics to address problems of

allocating scarce resources, selecting the preferredcourse of action from several technically viable ones

• Quantitative methods to present and evaluateeconomics of alternatives

• Primary purpose is to make informed decisions

• But remember that decision making is a multi leveleffort with others being part of it - so selling your ideasis a must in most instances.



http://slidepdf.com/reader/full/engineering-decision-3 15/10615Course:Centre for Management of Technology and Engr.Wajahat Maqbool



Making Decisions - the DecisionPyramid

Preferences

Politics People

Facts

Costs

Mark

et

research

Expert

opini o

n

…

Statis

tics

History




Principles for Decision Making

• The following principles will be applied to economic

evaluation of alternatives throughout this course:

1. State consequences in a common measure2. Only differences between alternatives need be

considered

3. Separable decisions should be made separately

4. Adopt a systems viewpoint

5. Use a common planning horizon




The Environment for DecisionMaking

1. The process involves parallel activities, feedback

loops and repeated steps

2. It is an iterative process and repeats as results arerefined

3. Communications skills are extremely important!

4. Each decision is one of many to be made

5. The organisation emphasises action rather than

analysis

6. Politics are very important!




To Deal with Abstraction: Model

RealWorld

The ModelAnalysis Informationfor decisionmaking




The Decision Making Process

• Real world is a “mess” of conflicting data, objectives,timing, methods etc.

• A well structured decision making process is:

1. Define/formulate problem (opportunity), boundary

2. Choose objective(s)/set goals

3. Identify alternatives

4. Evaluate consequences

5. Apply criteria for selection

6. Select preferred course of action

7. Specify and implement solution, adjust as required

8. Audit/monitor results, revise as necessary



Decision Making• Why is it difficult to make decisions?

– Complexity

– Uncertainty

– Risk

– Conflicting objectives

– Multiple decision makers

– Conflicting data, undefined constraints, incomplete data

• Can decision making be impr oved??


Th P bl S l i



The Problem SolvingProcess

• Economic analyses are typically part of the overallproblem solving process.

• The "problem solver" is involved in performing five

steps, these are:

• 1. Formulation of the problem,• 2. Analysis of the problem.

• 3. Search for alternative solutions to the problem.

• 4. Selection of the preferred solution.

• 5. Specification of the preferred solution.

• Step 4 is usually based on economic analyses




Engineering Economics &

ManagementLecturer # 2

BUITEMS




Basic Accounting Concepts

• Generally Accepted Accounting Principles(GAAP)

>guidelines that set out the manner & form

for presenting accounting information• Accrual Accounting

>the practice of recording economic

activity when recognized rather thanwaiting until realized




Basic Accounting Concepts(continued)

• Depreciation>reduction in value of a fixed asset over its expected life intended to reflect the

usage of wearing out of the asset -doesn’t affect cash

• Accumulated Depreciation

>sum of all previous depreciationamounts charged to fixed assets




Basic Balance Sheet Terms &Concepts

• Balance Sheet>financial statement that provides a

snapshot of a venture’s financialposition as of a specific date

• Balance Sheet Equation:Total Assets = Total Liabilities +

Owners’ Equity

• Assets>financial & physical items controlled

or owned by the business Engr.Wajahat Maqbool



Basic Balance Sheet Terms &Concepts (continued)

• Listing Order of Assets>assets are listed in declining order of liquidity,or how quickly the asset can be converted into

cash• Liabilities >short-

term liabilities are listed first followed by long-term debts owed by the venture

• Owners’ Equity >equitycapital contributed by the owners of the ventureis shown after listing all liabilities




Types of Balance Sheet Assets

• Current Assets>cash & other assets that are expected to

be converted into cash in less than oneyear

• Fixed Assets

>assets with expected lives of greater than one year




Types of Current Assets

• Cash>amount of coin, currency, & checkingaccount balances

• Receivables>credit sales made to customers

• Inventories

>raw materials, work-in-process, &finished products which the venturehopes to sell




Types of Current Liabilities

• Payables>short-term liabilities owed to suppliers

for purchases made on credit• Accrued Wages

>liabilities owned to employees for

previously completed work• Bank Loan

>interest-bearing loan of one year or

less from a commercial bankEngr.Wajahat Maqbool



Types of Long-Term Liabilities

• Long-Term Debts>loans that have maturities of longer thanone year

• Capital Leases >long-term, noncancelable leases whereby theowner receives payments that cover the

cost of the equipment plus a return oninvestment in the equipment




Off-Balance-Sheet Financing:Operating Leases

• Operating Leases>provide maintenance in addition tofinancing & are also usually cancelable

• Examples>Computers, copiers, & automobiles areoften financed through operating leases

• Balance Sheet Impact>for operating leases, no assets or leaseliabilities are recorded on the balance sheet




Basic Income Statement Terms& Concepts

• Income Statement>financial statement that reports the

revenues generated & expenses incurredover an accounting period

• Sales or Revenues>funds earned from selling a product or

providing a service• Gross Earnings

>net sales (after deducting returns &allowances) minus the cost of production




Basic Income Statement Terms& Concepts (continued)

• Operating Income or Earnings Before Interest &Taxes (EBIT) >indicates afirm’s profit after operating expenses, excluding

financing costs, have been deducted from netsales

• Net Income (or Profit)>bottom line measure after all operating

expenses, financing costs, & taxes have beendeducted from net sales




Internal Operating Schedules

• Cost of Production Schedule>important for preparing the incomestatement

• Cost of Goods Sold Schedule>important for preparing the incomestatement

• Inventories Schedule>important for preparing the balancesheet




Statement of Cash Flows:Definition and Use

• Statement of Cash Flows>shows how cash, reflected in accrual

accounting, flowed into & out of a firmduring a specific period of operation

• Can be Used to Determine if a Venture

has been Building or Burning Cash>”Net Cash Burn” occurs when the sumof cash flows from “operations” and“investing” is negative




Operating Breakeven Analysis:Basic Terms

• Variable Expenses>costs or expenses that vary directlywith revenues

• Fixed Expenses>costs that are expected to remainconstant over a range of revenues for a

specific time period




Engineering Economics &Management

Basics of AccountingLecturer # 3



Account Types

• Measures Performance- over a period – Revenue Accounts - records funds earned

– Expense Accounts – records expenditures

• Measures Accumulation at a point in time – Asset Accounts – Wealth

– Liability Accounts – Obligations

– Fund Balance – Net Asset



Accounting Equation

Assets – Liability = Net Asset

Assets = Liabilities + Net Asset

OR



Account Types and FinancialStatements

Operating Statement – Measures period performance

Revenue – Expenses = Surplus or Loss

Balance Sheet (Statement of Net Assets) Measure a point in time

Assets = Liabilities + Net Assets

or

Assets – Liabilities = Net Assets



Financial Statement Flow

Operating Statement

Revenue $10

Expenses 8

Surplus 2

Balance Sheet

Assets $20

=Liabilities 10+Net Assets 8

Balance Sheet

Assets $20

=Liabilities 10

+Net Assets 8

+surplus 2



Revised Accounting Equation

Asset –Liabilities = Net Asset + (Revenue – Expenses)

A ti E ti d D bit



Accounting Equation and Debitand Credits


Dr Cr Dr Increase Cr Cr

A ti E ti d D bit



Accounting Equation and Debitand Credits


Dr Cr Dr

Increase Cr Cr

General Journal

Dr Cr

Rent Expense $10

Cash $10

Pay rent from cash

T- AccountCash

Dr Cr

$100

$10

$90



The Accounting Cycle

General JournalEnter Transactions

General Ledger Post transaction to accounts

Trial BalanceVerify Debts = Credits

AdjustmentsPost Year End Adjustments

Adjusted Trial

BalanceVerify Debts = Credits

Operating Statement

Balance Sheet

Close Books-Zero out revenue and

expense accounts

E l Cit f D G l h



Example: City of Dry Gulch-Water Department

The City of Dry Gulch has no water. To ensure that they

are able to continue to growth the council has decided to

purchase the facilities of a private water company and setup a Water Department. The Council appropriates $10

million dollars to accomplish this goal and has hired a

Water Department staff. Following are the accounting

entries for the new water department of the City of Dry

Gulch.

E l Cit f D G l h




1. City gives the water department a startup fund of $10

million.

Cash ( A ) $10,000,000

Fund Balance (NA ) $10,000,000

Contribution for City

Dr Cr

E l Cit f D G l h



Example: City of Dry Gulch-Water Department Ledger

Water Revenue Rent Expense Cash

A/R Fixed Asset A/P

Salaries Expense

Fund Balance

$10,000,000

$10,000,000

E l Cit f D G l h




2. Water Department makes first of two annual payments

of $5 million for purchase of water company.

Fixed Assets (A) $10,000,000

Cash (A) $5,000,000

N/P (L)

Purchase water lines and pumping station

Dr Cr

E l Cit f D G l h





A/R Fixed Asset N/P

Salaries Expense

Fund Balance

$10,000,000

$10,000,000

$5,000,000

$5,000,000

$10,000,000

E l Cit f D G l h




3. Water Department pays for office rent in the amount of

$500,000 .

Rent Expense (E) $500,000

Cash (A) $500,000

Pay Office Rent for 2 years

Dr Cr

E l Cit f D G l h





A/R Fixed Asset N/P

Salaries Expense

Fund Balance

$10,000,000

$10,000,000

$5,000,000

$5,000,000

$10,000,000

$500,000

$500,000

E ample Cit of Dr G lch




4. Water Department pays employees salaries from cash

in the amount of $500,000 .

Salaries Expense (E) $500,000

Cash (A) $500,000

Pay Salaries

Dr Cr

Example: City of Dry Gulch





A/R Fixed Asset N/P

Salaries Expense

Fund Balance

$10,000,000

$10,000,000

$5,000,000

$5,000,000

$10,000,000

$500,000

$500,000

$500,000

$500,000





5. Water Department sends out bills to customers in the

amount of $3,000,000.

A/R (A) $3,000,000

Water Sales ( R ) $3,000,000

Customer billing

Dr Cr






A/R Fixed Asset N/P

Salaries Expense

Fund Balance

$10,000,000

$10,000,000

$5,000,000

$5,000,000

$10,000,000

$500,000

$500,000

$500,000

$500,000$3,000,000

$3,000,000





6. Water Department receives cash in partial payment of

bills mailed out. Total receipts are $2,000,000.

Cash (A) $2,000,000

A/R ( R ) $2,000,000

Customer billing receipts

Dr Cr






A/R Fixed Asset N/P

Salaries Expense

Fund Balance

$10,000,000

$10,000,000

$5,000,000

$5,000,000

$10,000,000

$500,000

$500,000

$500,000

$500,000$3,000,000

$3,000,000

$2,000,000

$2,000,000

$3,000,000 $500,000

$1,000,000 $10,000,000

$500,000 $6,000,000

$10,000,000$5,000,000




Example: City of Dry Gulch-Closing Worksheet

Accou nt D r C r D r C r D r C r D r C r D r C r

W ater Revenue 3 ,000 ,000

Rent Expense 500 ,000

Salary E xpense 500 ,000

Cash 6 ,000 ,000

A/R 1 ,000 ,000

Fixed Assets 10,000,000

N/ P 5 ,000 ,000

Fund Balance 10 ,000 ,000

Prepaid E xpense

Tota l 18,000,000 18 ,000 ,000

N et

Ba la n ce Sh e e t

F inancia l Sta tement Workshee t

T rial B alan ce Adjustme nts Adj. T rial B al O p e rating S tate me






W ater Revenue 3 ,000 ,000

Rent Expense 500 ,000 250 ,000

Salary E xpense 500 ,000

Cash 6 ,000 ,000

A/R 1 ,000 ,000

Fixed Assets 10,000,000

N/ P 5 ,000 ,000

Fund Balance 10 ,000 ,000

Prepaid E xpense 250 ,000

Tota l 18,000,000 18 ,000 ,000 250 ,000 250 ,000

N et

Ba la n ce Sh e e t



7. Adjustment Entry:

Prepaid Rent 250,000

Rent Expense 250,000

Adjust rent for a single years expense






A/R Fixed Asset N/P

Salaries Expense

Fund Balance

$10,000,000

$10,000,000

$5,000,000

$5,000,000

$10,000,000

$500,000

$500,000

$500,000

$500,000$3,000,000

$3,000,000

$2,000,000

$2,000,000

$3,000,000 $500,000

$1,000,000 $10,000,000

$6,000,000

$10,000,000$5,000,000

Prepaid Rent

$250,000

$250,000

$250,000

$250,000






W ater Revenue 3 ,000 ,000 3 ,000 ,000

Rent Expense 500 ,000 250 ,000 250 ,000

Salary E xpense 500 ,000 500 ,000

Cash 6 ,000 ,000 6 ,000 ,000

A/R 1 ,000 ,000 1 ,000 ,000

Fixed Assets 10,000,000 10 ,000 ,000

N/ P 5 ,000 ,000 5 ,000 ,000

Fund Balance 10 ,000 ,000 10,000,000

Prepaid E xpense 250 ,000 250 ,000

Tota l 18,000,000 18 ,000 ,000 250 ,000 250 ,000 18 ,000 ,000 18,000,000

N et

Ba la n ce Sh e e t








W ater Revenue 3 ,000 ,000 3 ,000 ,000 3,000,000

Rent Expense 500 ,000 250 ,000 250 ,000 250 ,000

Salary E xpense 500 ,000 500 ,000 500 ,000

Cash 6 ,000 ,000 6 ,000 ,000

A/R 1 ,000 ,000 1 ,000 ,000

Fixed Assets 10,000,000 10 ,000 ,000

N/ P 5 ,000 ,000 5 ,000 ,000

Fund Balance 10 ,000 ,000 10,000,000

Prepaid E xpense 250 ,000 250 ,000

Tota l 18,000,000 18 ,000 ,000 250 ,000 250 ,000 18 ,000 ,000 18,000,000 750 ,000 3,000,000

N et 2,250,000

Ba la n ce Sh e e t






Example: City of Dry Gulch-Operating Statement

Revenues:

Water Sales $3,000,000

Total Revenues $3,000,000

Expenses

Rent Expense (250,000)

Salary Expense (500,000)

Total Expense (750,000)

Surplus/Loss $2,250,000






W ater Revenue 3 ,000 ,000 3,000,000 3 ,000 ,000

Rent Expense 500 ,000 250 ,000 250,000 250 ,000

Salary E xpense 500 ,000 500,000 500 ,000

Cash 6,000,000 6 ,000 ,000 6,000,000

A /R 1,000,000 1 ,000 ,000 1,000,000

Fixed Assets 10 ,000 ,000 10,000,000 10 ,000 ,000

N/P 5 ,000 ,000 5,000,000 5,000,00

Fund Balance 10 ,000 ,000 10,000,000 10,000,00

Prepaid Expense 250 ,000 250,000 250 ,000

Tota l 18 ,000 ,000 18 ,000 ,000 250 ,000 250 ,000 18,000,000 18,000,000 750 ,000 3 ,000 ,000 17 ,250 ,00015,000,00

N et 2 ,250 ,000 2,250,00

17 ,250 ,00017,250,00

Ba lan c e Sh e e t


T rial B a lance Adjustme nts Ad j. T ria l B al O p e ratin g S tate me




Example: City of Dry Gulch-Balance Sheet

Assets:

Cash $6,000,000

A/R 1,000,000

Fixed Asset 10,000,000Total Assets 17,000,000

Liabilities:

N/P 5,000,000

Total 5,000,000

Net Assets 12,00





8. Close Revenue and Expense Accounts to Income

Summary.

Water Revenue $3,000,000

Income Summary $3,000,000Income Summary 750,000

Rent Expense 250,000

Salary Expense 500,000

Close Revenue & Expense Accounts

Dr Cr

Example: City of Dry Gulch-





A/R Fixed Asset N/P

Salaries Expense

Fund Balance

$10,000,000

$10,000,000

$5,000,000

$5,000,000

$10,000,000

$500,000

$500,000

$500,000

$500,000$3,000,000

$3,000,000

$2,000,000

$2,000,000

$0 $0

$1,000,000 $10,000,000

$6,000,000

$10,000,000$5,000,000

Prepaid Rent

$250,000

$250,000

$250,000

$0

$3,000,000

Income Summary

$3,000,000

$500,000

$500,000

$250,000

$250,000

$2,250,000





9. Close Income Summary Account

Fund Balance $2,500,000

Income Summary $2,500,000

Close Income Summary to Fund Balance

Dr Cr






A/R Fixed Asset N/P

Salaries Expense

Fund Balance

$10,000,000

$10,000,000

$5,000,000

$5,000,000

$10,000,000

500,000

500,000

$3,000,000

2,000,000

$2,000,000

$1,000,000 $10,000,000

$6,000,000

$12,250,000$5,000,000

Prepaid Rent

$250,000

$250,000

Income Summary

$3,000,000

$500,000

250,000

$0

2,250,000

2,250,000



Engineering Economics

Cost Concepts




Cost Estimating

• The most difficult, time-consuming part of an EEstudy is the estimation of costs and other data.

• Cost estimating is to forecast the present andfuture cost consequences of engineering design – Most projects are unique

– It requires active participation of not only engineeringdesigners but also personnel from marketing, finance,manufacturing and top management.




Cost Estimating – Cont.

• The results are used for a variety of purposes – Providing information in setting a selling price

– Determining whether a proposed product can bemade at a profit

• There are two approaches to cost estimating – Top-down: uses historical data for similar projects

– Bottom-up: a more detailed method which breaksdown the project into manageable units


Example: Estimating the cost of



Example: Estimating the cost of getting a Bachelor of Science

Year Tuition, Fees,Room

Other expenses

Totalestimated

cost

1 $15,750*1.06=$16,695

$5,000 $21,000

2 $16,695*1.06=$17,697

$5,000 $22,697

3 $17,697*1.06=$18,759

$5,000 $23,759

4 $18,759*1.06=$19,885

$5,000 $24,885

Total = $93,036

Top-down approach


Example: Estimating the cost of



Example: Estimating the cost of getting a Bachelor of Science

Bottom-up approach

Sum over 4 years toobtain Total Cost

Tuition

and Fees

Books and

Supplies

Living

Expenses

Transportation

2003, 2004, 2005, 2006

fuel

insurance

maintenance

food

rent

clothing

books

supplies

software

tuition

Activity fees

Medicalinsurance




Fixed and Variable Costs

• Fixed costs – Remain constant over a specific range of

operating conditions

– Example: general management andadministrative salaries

• Variable costs

– Vary in total with the quantity of output – Example: material and labor costs




Direct and Indirect Costs

• Direct costs• Related to a particular output

• Example: the cost of piece of wood used to make a

baseball bat• Indirect costs

• Difficult to relate to a specific output

• Example: the cost of lighting in the factory where

the bat was made




Sunk Cost

• Has occurred in the past

• Has no relevance to the future costs andbenefits

• Example: A firm is considering the replacement of a piece of equipment. It originally cost $50,000, ispresently shown on the company records with avalue of $20,000 and can be sold for an estimated

$5,000. For purpose of replacement, $50,000 is asunk cost.


P i d D d



Price and Demand

• As the selling price ( p) increases, therewill be less demand (D)

D

p

p = a - bD

a: the intersection of price axis

-b: slope

General price-demand relationship


B k E P i t



Break-Even Point

• Break-even point: Total Revenue = Total Cost

v

f

v f

v f

C p

C D

DcC pDC C pD

TC TR

−

=

+=

+=

=

Profit

Loss

D

Costand

Reven

Fixed Cost

Total Cost

Total Revenue

Break-even point


E l 1



Example 1

• The variable cost of producing a wooden diningtable is $62. The selling price is $85,56 per unit.The maximum output of the firm is 1600 per year and its fixed cost is $20,240 per year.

• For this firm, what is the break-even point in units and inpercentage of total capacity?

• Sensitivity analysis: What is the percentage reduction in thebreak-even point if fixed cost is reduced 10%, if variable costis reduced 10%, if both costs are reduced 10%, and if theselling price per unit is increased by 10%?

• To which of these changes is the break-even point more

sensitive?


P t E St di



Present Economy Studies

• When alternatives are being compared over oneyear or less and the influence of time on moneycan be ignored, engineering economic analysisis referred to as present economy studies.

– Rule 1: when revenue and other benefits are presentand vary among alternatives, choose the one thatmaximizes overall profitability.

– Rule 2: when revenues and other benefits are not

present or are constant among alternatives, select thealternative that minimizes the total cost.


E l 2



Example 2

• The production of a part canbe done with Machine A or Machine B. The importantdifferences between themachines are their production

capacity (productionrate*available productionhours) and their reject rates (%of parts produced that cannotbe sold).

Machine A Machine B

Productionrate

100 parts/hr 130 parts/hr

Hoursavailable for production

7 hr/day 6 hr/day

Percentparts

rejected

3% 10%

Material cost $6 /part $6 /part

Selling price $12 /part $12 /part

Operator cost

$15 /hr $15 /hr

Variable cost $5 /hr $5 /hr


E l 2 C t



Example 2 – Cont.

• Assume that the daily demand for this partis large enough that all defect-free partscan be sold. Which machine should be

selected?• What would the percentage of parts

rejected have to be for Machine B to be as

profitable as Machine A?




Engineering EconomicsTime Value of Money


I t t d i t t t



Interest and interest rate

• Engineering decisions involve comparing thecosts and benefits that occur in different timeperiods – Invest in a project today and get the benefits in the

future

• Interest – The cost of using capital – Having money today is preferable than having the

same amount one year later

• Interest rate – Is the percentage that borrowed money will cost




P t d F t W th



Present and Future Worth

P= amount of money todayF= future amount

i= interest rate

F=P+IF=P+PiF=P(1+i)

P P

I

F1 Period

Interest rate i


E l



Example

• You buy a one-year GIC for a $5,000 froma bank. The bank is paying 8% interest onone-year GICs. How much do you get

after one year?


I t t P i d



Interest Periods

• Semi-annual

• Quarterly

• Monthly

• Weekly

• Daily

• Continuous


Compo nd Vs Simple Interest



Compound Vs. Simple Interest

• Loans are often for several periods

• To calculate the future amount of theamount P after N periods

F=P(1+i)N

• Simple interest is not usually used inpractice

F=P(1+Ni)


Compo nd Interest Comp tation



Compound Interest Computation

Beginning of Period

Amount Lent InterestAmount

Amount Owedat Period End

1 P Pi P(1+i)

2 P(1+i) P(1+i)i P(1+i)2

3 P(1+i)2 [P(1+i)2]i P(1+i)3

… … … …

N P(1+i)N-1 [P(1+i)N-1 ]i P(1+i)N


Example



Example

• If you borrow $100 for 3 years at 10% per year compound interest, how muchinterest would you pay at the end of the

three years?I = 100(1+0.1)3-100

I = $33.10

How much would you pay if it were simpleinterest?

I =PiN = 100*0.1*3 = $30


Graphically



Graphically

0

100

200

300

400

500

600

700

800

5 10 15 20

Years

Total$

at

Year

end

Simple interest

Compound interest

Interest is 10% per annum


Nominal and Effective Interest



Rates• The difference between these two terms is the

frequency of compounding in a time period

• Given a 10% per year interest, compounded monthly,but paid yearly. What is the effective interest rate?

In effect, we have 10/12% per month compounded• The formula is: i=(1+r/m)m- 1 Where: i = effective

interest rate, r = nominal, m = number of compound-dingperiod in a year and I = number of years

• Simple interest = 10%, Effective interest for our example= 10.47% or [(1+0.1/12)12-1=0.1047]


Example



Example

• What is the effective interest year of 5%interest per month, compounded monthly?

is=0.05

m=12

ie=(1+0.05)12

-1=0.7959≈79.6%


Cash Flow Diagram



Cash Flow Diagram

• A graphical representation of cash flows – Magnitude and time

Time Period

CashFlow

0 1 2 3 4

Negative cash flow

Positive cash flow


Beginning and ending of periods



Beginning and ending of periods

1 2

Time 0

-1

Period 1 Period 2

Time period


Perspectives for cash flow



pdiagrams

+

-

Time

Loan, $

Payments, $

(expenditures)

Borrower’sviewpoint

+

-

Time

Payments, $

(receipts)

Lender’sviewpoint

0

1 2 3

Loan, $ Engr.Wajahat Maqbool

Example



Example

• Monthly income: $2200 (received at the end of eachmonth)

• Rent include utility: $700 (at the end of each month)

• Weekly food and entertainment: $120

• Telephone bill: $40 (at the end of the first week of eachmonth)

• Credit card purchases: $300 (at the end of the secondweek of each month)

• Show the cash flow diagram.


Example Cont



Example – Cont.

$2200

0 1 2 3 4

$120

$40

$300

$700


Example Cont



Example – Cont.

$1380

0 1 2 3 4

$160

$420

$120


Time Value Equivalence



Time-Value Equivalence

• Two things are equivalent when theyproduce the same effect

• A value of a cost in a time is equivalent to

the value of the related benefit received ata different time.

F=P(1+i)N

Mathematical Equivalence


Example



Example

• $1000 deposited at 10% interestcompounded annually,

$1000(1+0.10)2

=$1210

has the value of $1210 after 2 years.

Therefore, $1000 today is equivalent to$1210 in 2 years.


Summary



Summary

• Interest is an amount charged for the use of money by those who have saved.

• The relationship between interest and time leadsto the concept of the time value of money.

• Investment of money into producer goods which

increase productivity leads to the concept of theearning power of money.

engineering decision 3

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