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Engineering EconomyLecture 8

Evaluating a Single ProjectIRR continued

Payback Period

NE 364 Engineering Economy

Internal Rate of Return (IRR)

The internal rate of return (IRR) method is the most

widely used rate of return method for performing

engineering economic analysis.

It is also called the investor’s method, the discounted

cash flow method, the profitability index, and also the

breakeven interest.

If the IRR for a project is greater than the MARR, then

the project is acceptable.

IRR > MARR ✔


How the IRR works The IRR is the interest rate that equates the equivalent

worth of an alternative’s cash inflows (revenue, R) to

the equivalent worth of cash outflows (expenses, E).

That’s why the IRR is sometimes referred to as the

breakeven interest rate.


The IRR is the interest i'% at which

Solving for the IRR

The method of solving for the i'% that equates

revenues and expenses normally involves trial-and-

error calculations, or solving numerically using

mathematical software.

The use of spreadsheet software can greatly assist in

solving for the IRR. Excel uses the

IRR(range, guess) or

RATE(nper, pmt, pv) functions.


Example 1AMT is considering the purchase of a digital camera for themaintenance of design specifications by feeding digital picturesdirectly into an engineering workstation where computer-aideddesign files can be superimposed over the digital pictures.Difference between the two images can be noted, andcorrections, as appropriate, can then be made by designengineers.

The capital investment requirement is $345,000 and theestimated market value of the system after a six-year studyperiod is $115,000. Annual revenues attributable to the newcamera system will be $120,000, whereas additional annualexpenses will be $22,000. You have been asked bymanagement to determine the IRR of this project and to makea recommendation. The corporation's MARR is 20% per year.

Solve first using linear interpolation and then by using aspreadsheet.


Spreadsheet Solution


Example 2 A piece of new equipment has been proposed by

engineers to increase the productivity of a certainmanual welding operation. The investment cost is$25,000 and the equipment will have a market(salvage) value of $5,000 at the end of its expected lifeof five years. Increased productivity attributable to theequipment will amount to $8,000 per year after extraoperating costs have been subtracted from the value ofthe additional production.

Is the purchase of this new equipment economicallyjustifiable if the MARR is 20%?


Spreadsheet Solution


Payback Period Method Payback period method is a simple but not accurate

method for investment evaluation.

The simple payback period is the number of years

required for cash inflows to just equal cash outflows.

It is a measure of liquidity rather than a measure of

profitability.


Payback Period

Methods

SIMPLEPayback Period

DISCOUNTEDPayback Period


Payback is simple to

calculate.The simple payback period is the smallest value of θ (θ ≤

N) for which the relationship below is satisfied.

For discounted payback future cash flows are

discounted back to the present, so the relationship to

satisfy becomes


Problems with the payback period

method.

It doesn’t reflect any cash flows occurring after θ, or θ'.

It doesn’t indicate anything about project desirability

except the speed with which the initial investment is

recovered.

Recommendation: use the payback period only as

supplemental information in conjunction with one or

more of the other methods in this chapter.



End of

YearNet Cash Flow

Cumulative PW at

0%Cumulative PW at 6%

0 -$42,000 -$42,000 -$42,000

1 $12,000-$42,000+$12,000=

-$30,000

-$42,000+$12,000*(P/F,6%,1)=

-$30,679

2 $11,000-$30,000+$11,000=

-$19,000

-$30,679+$11,000*(P/F,6%,2)=

-$20,889

3 $10,000-$19,000+$10,000=

-$9,000

-$20,889+$10,000*(P/F,6%,3)=

-$12,493

4 $10,000-$9,000+$10,000=

+$1,000

-$12,493+$10,000*(P/F,6%,4)=

-$4,572

5 $9,000-$4,572+$9,000*(P/F,6%,5)=

+$2,153Simple Payback Period=4

Discounted Payback Period=5

engineering economy - cloudecampus.org · engineering economy lecture 8 evaluating a single project...

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