1. Engineering Economics
Internal Rate of Return Analysis
and Project Balance
Lecture # 8
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

2. 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

3. Rate of Return – Definition
Definition: Rate of return (ROR) is the interest rate, i*, at which the net present worth of a project is zero.
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

4. Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

5. Calculating Rate of Return
The IRR is the interest rate at which the benefits equal the costs.
Find IRR (= i*) such that:
PW Benefit - PW Cost = 0
PW Benefit/PW Cost = 1
PW Benefit = PW Cost
NPW = 0
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

6. Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

7. Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
IRR Calculation
NPW=+10.2 +
i* = 13.5%
X=?
Y=1.6%
NPW
i*%
10%
15%
NPW=-4.02 -
X=3.5%
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

8. and the graphical method ………
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

9. Direct Solution Method
$ -2000
$1500
$1300 1 2
If MARR is 20 % is the
project economical
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

10. Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
$ -2000
$1500
$1300 1 2
Since IRR > MARR
Project is economical
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

11. Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
Trial and Error Method
Aiming for i that makes PW(i)=0
Guess a value of i*
Compute the PW of net cash flows
Observe if PW is +, -, or zero
PW(i) is negative, lower the interest rate
PW(i) is positive, raise the interest rate
Continue until PW(i) is approximately zero
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

12. Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

13. Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

14. Rate of Return Analysis
An initial investment of $500 is being considered. The revenues from this investment are $300 at the end of the first year, $300 at the end of the second, and $200 at the end of the third. If the desired return on investment is 15%, is the project acceptable?
In this example we will take benefits and costs to the present time and their present values are then equated
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

15. Rate of Return Analysis
$500 = $300(PF, i, n=1) + 300(PF, i, n=2) + $200(PF, i, n=3)
Now solve for i using trial and error method
Try 10%: $500 = ? $272 + $247 + $156 = $669 (not equal)
Try 20%: $500 = ? $250 + $208 + $116 = $574 (not equal)
Try 30%: $500 = ? $231 + $178 + $91 = $500 (equal)  i = 30%
The desired return on investment is 15%, the project returns 30%, so it should be implemented
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

16. Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
Project Balance
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

17. 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 Profit
At Risk
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

18. Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS
Project Balance
If the project is to be terminated at certain time “t”, project balance gives exact standing of the project
Project balance is related to future worth and not the present worth
Advantages of project balance
Describes exposure to loss / risk
Describes Profit potential
Describes Pay back period for a project
Identifies net future worth
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

19. Project Balance Formula
PB =  F (1+ i)N-t
PB = Project Balance
F = Future worth
i = interest rate
t = 0, 1, 2, 3…….
N = Particular year like 1, 2, 3
t=0 N
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

20. Example of Project Balance
PB =  F (1+ i)N-t
$-10000
$1000
$5000
$8000
$6000
$3000 1 2 3 4 5
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

21. Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

22. Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

23. Internal rate of return (IRR)
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 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 the project should be preferred.
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 indicates that it is more favorable.
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 rather as a tool to help decide whether any individual project has potential growth worth investing in.
Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS