engineering economics, lecture # 8 by ejaz gul, fuiems engineering economics internal rate of return...

Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

Engineering EconomicsEngineering Economics

Internal Rate of Return AnalysisInternal Rate of Return Analysisand Project Balanceand Project Balance

Lecture # 8Lecture # 8


Minimum Attractive Rate of Return (MARR)

• The interest rate or rate of return, RR, expected on an investment

would normally include a reasonable profit.

• MARR is the Rate of return or rate of interest for analysis of

alternative

• The expected rate of return should be equal to or greater than

MARR for a alternative to economically viable

• ROR MARR > cost


Rate of Return – Definition

• DefinitionDefinition: Rate of return (ROR) is the interest : Rate of return (ROR) is the interest

rate, rate, ii*, at which the net present worth of a project *, at which the net present worth of a project

is zero.is zero.


Calculating Rate of Return

• The IRR is the interest rate at which the The IRR is the interest rate at which the

benefits equal the costs. benefits equal the costs.

• Find IRR (= i*) such that:Find IRR (= i*) such that:

– PW Benefit - PW Cost = 0PW Benefit - PW Cost = 0

– PW Benefit/PW Cost = 1PW Benefit/PW Cost = 1

– PW Benefit = PW CostPW Benefit = PW Cost

– NPW = 0NPW = 0


IRR Calculation

i*%10% 15%NPW

+

0

-

NPW=+10.2

NPW=-4.02

i* = 13.5%

X=? Y=1.6%

X=3.5%


and the graphical method ………and the graphical method ………


Direct Solution Method

$ -2000$ -2000

$1500$1500$1300$1300

0011 22

If MARR is 20 % is the If MARR is 20 % is the project economicalproject economical


$ -2000$ -2000

$1500$1500$1300$1300

0011 22

Since IRR > MARRSince IRR > MARRProject is economicalProject is economical


Trial and Error MethodTrial and Error Method

• Aiming for i that makes PW(i)=0Aiming for i that makes PW(i)=0• Guess a value of iGuess a value of i* *

• Compute the PW of net cash flowsCompute the PW of net cash flows• Observe if PW is Observe if PW is ++, -, or zero, -, or zero• PW(i) is negative, lower the interest ratePW(i) is negative, lower the interest rate• PW(i) is positive, raise the interest ratePW(i) is positive, raise the interest rate• Continue until PW(i) is approximately zeroContinue until PW(i) is approximately zero


Rate of Return AnalysisRate of Return Analysis• An initial investment of $500 is being considered. An initial investment of $500 is being considered.

The revenues from this investment are $300 at The revenues from this investment are $300 at

the end of the first year, $300 at the end of the the end of the first year, $300 at the end of the

second, and $200 at the end of the third. If the second, and $200 at the end of the third. If the

desired return on investment is 15%, is the desired return on investment is 15%, is the

project acceptable?project acceptable?

• In this example we will take benefits and costs to In this example we will take benefits and costs to

the present time and their present values are the present time and their present values are

then equatedthen equated


Rate of Return AnalysisRate of Return Analysis

• $500 = $300(P$500 = $300(PF, i, n=1) + 300(PF, i, n=1) + 300(PF, i, n=2) + $200(PF, i, n=2) + $200(PF, i, n=3)F, i, n=3)

• Now solve for i using trial and error methodNow solve for i using trial and error method

• Try 10%: $500 = ? $272 + $247 + $156 = $669 (not equal)Try 10%: $500 = ? $272 + $247 + $156 = $669 (not equal)

• Try 20%: $500 = ? $250 + $208 + $116 = $574 (not equal) Try 20%: $500 = ? $250 + $208 + $116 = $574 (not equal)

• Try 30%: $500 = ? $231 + $178 + $91 = $500 (equal) Try 30%: $500 = ? $231 + $178 + $91 = $500 (equal) i = 30% i = 30%

• The desired return on investment is 15%, the project returns 30%, The desired return on investment is 15%, the project returns 30%,

so it should be implementedso it should be implemented


Project Balance


Project Balance

• Time profile chart of cash

flow

• Present worth at each

point of time over the life

of a project

• Represented by PB

• Represents the loss or

profit associated with the

cash flow at any moment

of the project life

At Risk

At Profit


Project BalanceProject Balance

• If the project is to be terminated at certain time “t”, project If the project is to be terminated at certain time “t”, project

balance gives exact standing of the project balance gives exact standing of the project

• Project balance is related to future worth and not the present Project balance is related to future worth and not the present

worthworth

• Advantages of project balanceAdvantages of project balance

– Describes exposure to loss / riskDescribes exposure to loss / risk

– Describes Profit potentialDescribes Profit potential

– Describes Pay back period for a projectDescribes Pay back period for a project

– Identifies net future worthIdentifies net future worth


Project Balance FormulaProject Balance Formula

PB = PB = F (1+ i) F (1+ i)N-tN-t

• PB = Project BalancePB = Project Balance

• F = Future worthF = Future worth

• i = interest ratei = interest rate

• t = 0, 1, 2, 3……. t = 0, 1, 2, 3…….

• N = Particular year like 1, 2, 3N = Particular year like 1, 2, 3

t=0

N


Example of Project BalanceExample of Project Balance

$-10000

$1000$5000

$8000

$6000$3000

1 2 3 4 5

PB = PB = F (1+ i) F (1+ i)N-tN-t

t=0

N


Project Balance

-1840

3792

7550

-11000-10000

-8200

-12000

-8000

-4000

0

4000

8000

12000

Time (Years)

NFV


Internal rate of return (IRR)• Is a discount rate frequently used in capital budgeting. Typically, the higher Is a discount rate frequently used in capital budgeting. Typically, the higher

internal rate of return of a project, the higher it would be considered, and internal rate of return of a project, the higher it would be considered, and

the more willing the company would be to undertake it. If a project's the more willing the company would be to undertake it. If a project's

internal rate of return is higher than its cost of capital, that indicates that internal rate of return is higher than its cost of capital, that indicates that

the project should be preferred.the project should be preferred.

• Internal rate of return may be simply thought of as the growth rate a project Internal rate of return may be simply thought of as the growth rate a project

is hoped to generate. A higher IRR for one project as compared to another is hoped to generate. A higher IRR for one project as compared to another

indicates that it is more favorable.indicates that it is more favorable.

• Internal rate of return is not commonly used to rate two projects which are Internal rate of return is not commonly used to rate two projects which are

mutually exclusive (for the purpose of deciding which to invest in), but mutually exclusive (for the purpose of deciding which to invest in), but

rather as a tool to help decide whether any individual project has potential rather as a tool to help decide whether any individual project has potential

growth worth investing in. growth worth investing in.

engineering economics, lecture # 8 by ejaz gul, fuiems engineering economics internal rate of return...

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