engineering economics, ejaz gul, fuiems, 2009 engineering economics lecture # 8 marr, analysis of...

Engineering Economics, Ejaz Gul, FUIEMS, 2009

Engineering EconomicsEngineering Economics

Lecture # 8Lecture # 8MARR, Analysis of AlternativesMARR, Analysis of Alternatives


Methods of AnalysisMethods of Analysis• Present worthPresent worth

• Future worthFuture worth

• Annual Worth - Annual Worth - Finding the annual equivalent cost for Finding the annual equivalent cost for each each alternativealternative

• 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


Minimum Acceptable Rate of Return (MARR)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


MARRMARR• When a project has been proposed, it must first go When a project has been proposed, it must first go

through a preliminary analysis in order to determine through a preliminary analysis in order to determine

whether or not it has a positive whether or not it has a positive net present value using the

MARR as the discount rate

• The MARR is the target rate for evaluation of the project The MARR is the target rate for evaluation of the project

investmentinvestment

• The MARR generally increases with increased riskThe MARR generally increases with increased risk

http://en.wikipedia.org/wiki/Net_present_value


Present Worth AnalysisPresent Worth Analysis In present worth analysis, the P value, now called PW, is calculated In present worth analysis, the P value, now called PW, is calculated

at the MARR for each alternativeat the MARR for each alternative

This method is popular because it easy to determine the economic This method is popular because it easy to determine the economic

advantage of one alternative over anotheradvantage of one alternative over another

The PW comparison of alternatives is straightforwardThe PW comparison of alternatives is straightforward

A PW analysis requires a MARR for use as the “A PW analysis requires a MARR for use as the “ii” value in all PW ” value in all PW

relations.relations.

The alternatives must be compared over the be compared over the The alternatives must be compared over the be compared over the

same number of years!same number of years!


PW sh

ould

be e

qual

to

PW sh

ould

be e

qual

to

or g

reat

er th

an ze

ro

or g

reat

er th

an ze

ro


Present worth - InvestmentPresent worth - InvestmentThree purchase plans are available for a new car.Plan A: $5,000 cash immediatelyPlan B: $1,500 down and 36 monthly payments of $116.25Plan C: $1,000 down and 48 monthly payments of $120.50If 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 = $5,000PWCB = 1,500 + 116.25 (P/A) = $4,715,59PWCC = 1,000 + 120.50 (P/A ) = $5,102.18Therefore Plan B is best


I will always mention in the question I will always mention in the question

whether it is investment alternative or whether it is investment alternative or

revenue alternativerevenue alternative

NoteNote


Future Worth AnalysisFuture Worth Analysis The future worth analysis (FW) of an alternative may be determined directly 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 from the cash flows by determining the future worth value, or by multiplying the PW value by the F/P factor, at established MARRthe PW value by the F/P factor, at established MARR

Therefore, FWA is an extension of PW AnalysisTherefore, FWA is an extension of PW Analysis

FW values is especially applicable to large capitalFW values is especially applicable to large capital investment decisions investment decisions when a prime goal is to maximize the future wealth of a corporation’s when a prime goal is to maximize the future wealth of a corporation’s stockholdersstockholders

It is often utilized if the assets might be sold at some time after its start-up, It is often utilized if the assets might be sold at some time after its start-up, but before the expected life is reachedbut before the expected life is reached

Also FW can be used for the projects that will not come online until the end 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 of the investment period,e.g. electric generation facilities, roads, can be analyzed using the FW value of investment made during constructionanalyzed using the FW value of investment made during construction


Capitalized Cost (CC)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


Study Period ApproachStudy Period Approach A study period analysis is necessary if the the length of time, the A study period analysis is necessary if the the length of time, the

alternatives are needed, cannot be madealternatives are needed, cannot be made

A time horizon is chosen over which the economic analysis is A time horizon is chosen over which the economic analysis is

conducted, and only those cash flows, which occur during that time conducted, and only those cash flows, which occur during that time

period, are considered relevant to the analysisperiod, are considered relevant to the analysis

All cash flows occurring beyond the study period are ignoredAll cash flows occurring beyond the study period are ignored


Payback Period AnalysisPayback Period Analysis Also called the payout analysis, is another extension of the present Also called the payout analysis, is another extension of the present

worth method.worth method.

The payback period is the estimated time, usually in years, it will The payback period is the estimated time, usually in years, it will

take for the estimated revenues and other economic benefits to take for the estimated revenues and other economic benefits to

recover the initial investment and a stated rate of returnrecover the initial investment and a stated rate of return

The payback period should never be used as the primary measure The payback period should never be used as the primary measure

of worth to select an alternative. Rather, it should be determined in of worth to select an alternative. Rather, it should be determined in

order to provide initial screening or supplemental information with an order to provide initial screening or supplemental information with an

analysis performed using present worth or another methodanalysis performed using present worth or another method


Internal Rate of ReturnInternal 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.


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%


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


Assignment # 2Assignment # 2

engineering economics, ejaz gul, fuiems, 2009 engineering economics lecture # 8 marr, analysis of...

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