1. Engineering Economics, Ejaz Gul, FUIEMS, 2009 Engineering Economics Lecture # 8 MARR, Analysis of Alternatives

2. Engineering Economics, Ejaz Gul, FUIEMS, 2009 Methods of Analysis Present worthPresent worth Future worthFuture worth Annual Worth - Finding the annual equivalent cost for each alternativeAnnual Worth - Finding the annual equivalent cost for each alternative Capitalized costCapitalized cost Study periodStudy period Pay back PeriodPay back Period Internal rate of return (IRR)Internal rate of return (IRR) Project balance (PB)Project balance (PB) Cost – benefit analysisCost – benefit analysis

3. Engineering Economics, Ejaz Gul, FUIEMS, 2009 Minimum Acceptable 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 The MARR (Minimum Acceptable or Attractive Rate of Return) is the minimum limit of rate of return that an investor having in mind while investing funds in a project

4. Engineering Economics, Ejaz Gul, FUIEMS, 2009 MARR When a project has been proposed, it must first go through a preliminary analysis in order to determine whether or not it has a positive net present value using the MARR as the discount rate When a project has been proposed, it must first go through a preliminary analysis in order to determine whether or not it has a positive net present value using the MARR as the discount ratenet present valuenet present value The MARR is the target rate for evaluation of the project investment The MARR is the target rate for evaluation of the project investment The MARR generally increases with increased risk The MARR generally increases with increased risk

5. Engineering Economics, Ejaz Gul, FUIEMS, 2009 Present Worth Analysis  In present worth analysis, the P value, now called PW, is calculated at the MARR for each alternative  This method is popular because it easy to determine the economic advantage of one alternative over another  The PW comparison of alternatives is straightforward  A PW analysis requires a MARR for use as the “i” value in all PW relations.  The alternatives must be compared over the be compared over the same number of years!

6. Engineering Economics, Ejaz Gul, FUIEMS, 2009 PW should be equal to or greater than zero

7. Engineering Economics, Ejaz Gul, FUIEMS, 2009 Present worth - Investment Three purchase plans are available for a new car. Plan A: $5,000 cash immediately Plan B: $1,500 down and 36 monthly payments of $116.25 Plan C: $1,000 down and 48 monthly payments of $120.50 If a customer expects to keep the car five years and her minimum attractive rate of return (MARR) is 18% yearly, which payment plan should she choose? i = 18%/12 = 1½% PWCA = $5,000 PWCB = 1,500 + 116.25 (P/A) = $4,715,59 PWCC = 1,000 + 120.50 (P/A ) = $5,102.18 Therefore Plan B is best

8. Engineering Economics, Ejaz Gul, FUIEMS, 2009 I will always mention in the question whether it is investment alternative or revenue alternative Note

9. Engineering Economics, Ejaz Gul, FUIEMS, 2009 Future Worth Analysis  The future worth analysis (FW) of an alternative may be determined directly from the cash flows by determining the future worth value, or by multiplying the PW value by the F/P factor, at established MARR  Therefore, FWA is an extension of PW Analysis  FW values is especially applicable to large capital investment decisions when a prime goal is to maximize the future wealth of a corporation’s stockholders  It is often utilized if the assets might be sold at some time after its start-up, but before the expected life is reached  Also FW can be used for the projects that will not come online until the end of the investment period,e.g. electric generation facilities, roads, can be analyzed using the FW value of investment made during construction

10. Engineering Economics, Ejaz Gul, FUIEMS, 2009 Capitalized Cost (CC)   Capitalized cost (CC) is the present worth of an alternative that will last “for ever”   Public sector projects such as bridges, dams, irrigation systems, and rail roads fall into this category   The alternative with the smaller capitalized cost will represent the more economical one   PW (CC) = A / i

11. Engineering Economics, Ejaz Gul, FUIEMS, 2009 Study Period Approach  A study period analysis is necessary if the the length of time, the alternatives are needed, cannot be made  A time horizon is chosen over which the economic analysis is conducted, and only those cash flows, which occur during that time period, are considered relevant to the analysis  All cash flows occurring beyond the study period are ignored

12. Engineering Economics, Ejaz Gul, FUIEMS, 2009 Payback Period Analysis  Also called the payout analysis, is another extension of the present worth method.  The payback period is the estimated time, usually in years, it will take for the estimated revenues and other economic benefits to recover the initial investment and a stated rate of return  The payback period should never be used as the primary measure of worth to select an alternative. Rather, it should be determined in order to provide initial screening or supplemental information with an analysis performed using present worth or another method

13. Engineering Economics, Ejaz Gul, FUIEMS, 2009 Internal Rate of Return Definition: Rate of return (ROR) is the interest rate, i*, at which the net present worth of a project is zero. The internal rate of return is the rate of return promised by an investment over its useful life. It is some time referred to simply as yield on project. The internal rate of return is computed by finding the discount rate that equates the present value of a project's cash out flow with the present value of its cash inflow. In other words, the internal rate of return is that discount rate that will cause the net present value of a project to be equal to zero.

14. Engineering Economics, Ejaz Gul, FUIEMS, 2009 Calculating Rate of Return The IRR is the interest rate at which the benefits equal the costs.The IRR is the interest rate at which the benefits equal the costs. Find IRR (= i*) such that:Find IRR (= i*) such that: –PW Benefit - PW Cost = 0 –PW Benefit/PW Cost = 1 –PW Benefit = PW Cost –NPW = 0

15. Engineering Economics, Ejaz Gul, FUIEMS, 2009 IRR Calculation i*% 10%15% NPW + 0 - NPW=+10.2 NPW=-4.02 i* = 13.5% X=? Y=1.6% X=3.5%

16. Engineering Economics, Ejaz Gul, FUIEMS, 2009 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

17. Engineering Economics, Ejaz Gul, FUIEMS, 2009 Assignment # 2