Engineering Economics Internal Rate of Return Analysis and Project Balance Lecture # 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 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

Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

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

Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

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

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

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

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

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

Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

Engineering Economics, Lecture # 8 by Ejaz Gul, FUIEMS

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

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

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

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

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

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

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

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 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