1. Engineering Economic Analysis
Chapter 7
RATE OF RETURN ANALYSIS
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

2. Three Major Methods of Economic Analysis
PW - Present Worth
AW - Annual Worth
IRR - Internal Rate of Return
If PW = A(P/A,i,n)
Then (P/A,i,n) = PW/A
Solve for (P/A,i,n) and look up interest in Compound Interest Tables
So far, we have talked about present worth analysis and annual cost analysis. We use the equivalent present worth to compare alternatives or the equivalent uniform annual cost. This can be confusing, to say things like:
Alternative A has a present worth of $32,000
Alternative A has equivalent uniform annual worth of $495
Alternative A has a rate of return of 25%
Present worth and annual cost depend on the interest rate chosen. Rate of return analysis finds the interest rate at which project costs equals project benefits, called the internal rate of return or i star.
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

3. Calculating Rate of Return
The IRR is the interest rate at which the benefits equal the costs. IRR = i*
PW Benefit - PW Cost = 0
PW Benefit/PW Cost = 1
NPW = 0
EUAB - EUAC = 0
PW Benefit = PW Cost
Most frequently used measure of merit in industry
More accurately called Internal Rate of Return (IRR)
For any single project, then, compare the internal rate of return to the MARR. The MARR is the interest rate used in present worth and annual cost analysis.
Find IRR by solving one of the following:
Present worth of benefits equals present worth of costs
Equivalent uniform annual benefits equals equivalent uniform annual costs
Where everything is known but i star
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

4. Example 1
Find the internal rate of return for the following set of cash flows:
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

5. Example 1
Since the benefits are in annual uniform series, use the EUAC = EUAB method. Need to find EUAC = 200 ( A/F, i, 2) or
Look at the tables, try i = 50%
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

6. Example 1: Excel In Excel, I find IRR to be the easiest to use
It works just like NPV: it operates on a set of cash flows, one per period, starting at time 1
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

7. Example 2 Find the rate of return on:
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

8. Example 2: Excel
Since we have a flow in Year 0, I use the idea of 1000 = NPV(rate, 0, 300, 300, 300, 300)
You could just try rates or use Goal Seek
Just by playing, I found 5.4%; Goal Seek found 5.399%
We can see here that i star, the internal rate of return is 5.4%.
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

9. Example 3
A bond costs $925, with a face value of $1000 and pays 4% of the face value each year. If the bond will be paid off at the end of 10 years and your MARR is 5%, should you buy the bond?
In a Bond
the cost is at year 0
the face value is at the end of the term
this term is 10 years
the yearly payment is a return
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

10. Example 3 Find the IRR and compare to MARR
If the IRR is greater than the MARR, buy the bond
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

11. Example 3: Excel Use the NPV method here again to find the IRR
Since we know we are comparing to 5%, we can actually just plug that in as the IRR
Since NPW < $925, we know IRR < 5% and we should NOT buy the bond
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

12. Calculating ROR
Where two mutually exclusive alternatives will provide the same benefit, ROR is performed using an incremental rate of return-ΔROR-on the difference between the alternatives.
Two-alternative situation
Decision
DROR ³ MARR
Choose higher-cost alternative
DROR < MARR
Choose lower-cost alternative
How do you compare alternatives?
2 alternatives only (3 or more, use incremental analysis, Chapter 8)
Assumes we spend money in year 0, investment
Find the incremental rate of return
ΔROR = higher initial cost alternative minus the lower initial cost alternative
Find i* for incremental difference
If ΔROR greater than or equal to the MARR choose the higher cost alternative
If ΔROR less than the MARR choose the lower cost alternative
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

13. Example 4 Consider these two alternatives with a MARR of 5%:
Year
Alt A
Alt B
-$2,000
-$2,800 1
$800
$1,100 2 3
Use ROR analysis to choose the better alternative.
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

14. Example 4
Since alternative B costs more than alternative A in year 0 we need to look at B - A
Year
B – A
$800 1
$300 2 3
Find ΔROR = i* for this flow
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

15. Example 4 We can use the NPW = 0 equation which gives us: i
(P/A, i, 3) 6%
2.673 7%
2.624
Therefore, i* is slightly greater than 6%.
Since ΔROR ≥ MARR we should choose the higher cost alternative
We should choose Alternative B
We could have just looked at the NPW with 5%
Use this method on the FE!!!!
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

16. Example 4: Excel I use If statements to tell me which way to subtract
Year 0 should always be negative
For Goal Seek, we can use the flow in year 0 plus the NPW to equal 0
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

17. Example 4: Excel We find i* is about 6.13%
Since ΔROR ≥ MARR (5%) we should choose the higher cost alternative
We should choose Alternative B
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

18. Analysis Period
Just as in PW and AW analysis, the analysis period must be considered:
Useful life of the alternative equals the analysis period
Alternatives have useful lives different from the analysis period
The analysis period is infinite, n = ∞
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

19. Example 5
Consider these 2 alternatives. Assume an analysis period of 8 years, MARR of 7%, and identical replacement. Which alternative should be bought? A B
Initial Cost
$9,200
$5,000
Uniform Annual Benefit
$1,850
$1,750
Useful Life (Years) 8 4
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

20. Example 5
Year A B
-$9,200
-$5,000 1
$1,850
$1,750 2 3 4
$1,750 - $5,000 = -$3,250 5 6 7 8
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

21. Example 5: Use IRR in Excel
Since alternative A costs more than alternative B in year 0 we need to look at A – B
Overall, I like IRR better because as your data changes, IRR will reflect those changes while the use of Goal Seek does not let the result change as you change your data
Same setup as Example 4, just use IRR
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

22. Example 5 We find i* is about 8.32%
Therefore ΔROR > MARR (7%) and we should pick the higher initial cost alternative
Therefore we should pick alternative A
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.

23. Borrowing Money
If 0th year is an inflow, as in a loan, treat it like an investment
Change all of the signs, but choose the opposite alternative
Why?
Because, as a borrower, you want a lower rate, while as the investor, you want the higher rate
Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.