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 ✔
NE 364 Engineering Economy
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.
NE 364 Engineering Economy
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.
NE 364 Engineering Economy
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.
NE 364 Engineering Economy
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%?
NE 364 Engineering Economy
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.
NE 364 Engineering Economy
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
NE 364 Engineering Economy
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.
NE 364 Engineering Economy
NE 364 Engineering Economy
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