lecture 9 internal rate of return and project balance by ziafat ali
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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
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
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
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
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.
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
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
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
IRR Calculation
i*%10% 15%NPW
+
0
-
NPW=+10.2
NPW=-4.02
i* = 13.5%
X=? Y=1.6%
X=3.5%
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
and the graphical method ………and the graphical method ………
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
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
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
$ -2000$ -2000
$1500$1500$1300$1300
0011 22
Since IRR > MARRSince IRR > MARRProject is economicalProject is economical
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
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
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
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
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
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
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
Project Balance
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
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
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
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
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
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
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
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
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
Project Balance
-1840
3792
7550
-11000-10000
-8200
-12000
-8000
-4000
0
4000
8000
12000
Time (Years)
NFV
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
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.
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