1. Engineering Economic Analysis
Chapter 7
Rate of Return Analysis
Donald G. Newnan
San Jose State University
Ted G. Eschenbach
University of Alaska Anchorage
Jerome P. Lavelle
North Carolina State University
Neal A. Lewis
University of New Haven
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2. Chapter Outline Internal Rate of Return Calculating Rate of Return
Interest Rates When There Are Fees or Discounts
Loans & Investments
Incremental Analysis
Analysis Period
XIRR
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3. Learning Objectives Evaluate cash flows with internal rate of return
Plot PW vs. interest rate to find IRR
Use incremental rate of return to evaluate alternatives
Develop & use spreadsheet in solving rate of returns
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4. Vignette: Barcodes Give a Number; RFID Codes Tell a Story!
Radio Frequency Identification (RFID) revolutionizes operations
RFID tag costs are dropping significantly
RFID tags can track & trace goods from manufacturing to consumers
Real cost & benefit to track items is?
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5. Vignette: Barcodes Give a Number; RFID Codes Tell a Story!
A clothing manufacturer may use RFID tags on new season’s line. What costs & benefits should be considered?
How would costs & benefits differ for those already using RFID vs. those who aren’t yet?
How do military costs & benefits differ from commercial companies?
Can RFID tags invade privacy? What are the ethical & social costs for a retail company?
“Kill“ technologies allow consumers to disable RFID tags after purchase. How might this affect consumer attitudes & company costs?
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6. Rate of Return Analysis
Rate of return is most frequently used measure
Major advantages
Single figure of merit that is readily understood
Calculating rate of return independent from minimum attractive rate of return (MARR)
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7. Internal Rate of Return
Interest rate at which PW = 0 = EUAW
On a loan it is interest rate paid on unpaid balance so balance = 0 after final payment
On an investment it is interest rate earned on the un- recovered investment so un-recovered investment = 0 after last cash flow
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8. Rate of Return in Investment
$5000 investment in 5 yrs at rate of return of 8% Yr
Cash Flow
Unrecovered Investment at Beginning of Year
8% Return on Unrecovered Investment
Investment Repayment at End of Year
Unrecovered Investment at End of Year
−$5000
$5000 1
$1252
$400
$ 852
$4148 2
$331
$ 921
$3227 3
$258
$ 994
$2233 4
$178
$1074
$1159 5
$ 93 $
Subtotal
$1260
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9. Calculating rate of return
Internal rate of return is interest rate where:
NPV = 0
PV of benefits = PV of costs
Annual benefits = annual costs
All of the above
None of the above
E All of the above
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10. Calculating rate of return
Internal rate of return is interest rate where:
NPV = 0
PV of benefits = PV of costs
Annual benefits = annual costs
All of the above
None of the above
E All of the above
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11. Example 7-1 Rate of Return Calculation
Engineer invests $5000 annually at year-end for 40 years. For $1 million at retirement, what interest must be earned?
Look in compound interest tables for rate where true.
The interest is 7%.
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12. Firm invests $75,000 to save $9000/year in energy costs for 15 years.
What is project’s rate of return?
8.44%
10.08%
12.38%
14.65%
None of the above
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13. Firm invests $75,000 to save $9000/year in energy costs for 15 years.
What is project’s rate of return?
8.44%
10.08%
12.38%
14.65%
None of the above
=RATE(15,9000,−75000)
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14. What is project’s rate of return? -3.68% 8.22% 8.75% 11.38%
A small restaurant costs $350,000. Expected profits equal $22,000/year for 6 years when value is $400,000.
What is project’s rate of return?
-3.68%
8.22%
8.75%
11.38%
None of the above
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15. What is project’s rate of return? -3.68% 8.22% 8.75% 11.38%
A small restaurant costs $350,000. Expected profits equal $22,000/year for 6 years when value is $400,000.
What is project’s rate of return?
-3.68%
8.22%
8.75%
11.38%
None of the above
=RATE(6,22000,−350000,400000)
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16. Example 7-2 Rate of Return Calculation
Year
Cash Flow
−$700 1
+100 2
+175 3
+250 4
+325
175
100
250
325 4 1 2 3
700
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17. Example 7-2 Rate of Return Calculation
Year
Cash Flow
−$700 1
+100 2
+175 3
+250 4
+325
175
100
250
325 4 1 2 3
700
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18. Example 7-3 Rate of Return Calculation
Year
Cash Flow
+$300,000 1
−45,000 2 3 4 5
−45,000 − 170,000
This can be solved in one step with the annuity function
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19. Example 7-3 Rate of Return Calculation
Year
Cash Flow
+$300,000 1
−45,000 2 3 4 5
−45,000 − 170,000
At i = 7%, PW = -$ At i = 8%, PW = $4629. Interpolating,
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20. Example 7-4 Rate of Return Calculation
Maria borrowed $9000 yearly for 4 years. No interest was charged until graduation, then rate = 5%. Maria makes 5 equal annual payments of? Rate of return for Maria’s loan = ?
9000 4 1 2 3 5 8 6 7 9 A
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21. Example 7-4 Spreadsheet solution
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22. Example 7-4 Rate of Return on Student LoanYr
Amount Owed at Start of Year
Interest at 2.66%
Cash Flow at End of Year
Amount Owed at End of Year
$9,000.00 1
$239.17
$18,239.17 2
$484.69
$27,723.86 3
$736.74
$37,460.59 4
$995.48
$38,456.07 5
$1,021.93
-$8,315.09
$31,162.91 6
$828.13
$23,675.95 7
$629.17
$15,990.02 8
$424.92
$8,099.85 9
$215.25
$0.00
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23. Example 7-4 Rate of Return on Student Loan
$(6,000) $-
$6,000
$12,000
$18,000 0% 5%
10%
15%
20%
Interest Rate
Net Present Worth
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24. Plot of NPW versus Interest Rate for Borrowed Money
Year
Cash Flow +P 1 -A 2 3 4 :
NPW  + i
IRR
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25. Plot of NPW versus Interest Rate for Invested Money
Year
Cash Flow -P 1 +A 2 3 4 :
NPW  + i
IRR
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26. Example 7-5
Corporate bond initially sold for $1000. Issuer will pay $40 interest every 6 months & repay $1000 face value after 10 years. After 1 year, bond was sold for $950.
(a) What rate of return did original buyer receive?
950 40 1 2
1000
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27. (b) What rate of return for new buyer if bond kept for remaining 9-year life?
Example 7-5
1000 40 4 1 2 3 17 18 4 1 2 3 17 18 1 2 3 4 17 18
950
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28. Example 7-5, Spreadsheet Solution
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29. =EFFECT() IRR = 1.66%/month APR = nominal rate = 19.9%
IRR = effective annual rate
= ( )12 – 1 = 21.8%
Or, =EFFECT(nominal_rate,npery)
=EFFECT(19.9%,12) = = 21.8%
The reverse is =NOMINAL(effect_rate,npery)
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30. Example 7-6, Fees or Discounts
If issuing firm paid a 1% fee to sell bond, what effective interest rate did firm pay on bond?
Example 7-6, Fees or Discounts
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31. Example 7-7 Two options to acquire a property priced at $300,000:
Finance through the seller with 20% down & the balance due in 5 annual payments at 12%
Pay cash with 10% discount
What is the IRR for the loan offered by the seller?
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32. Example 7-8 Two options for parking permit:
Buy annual parking permit on August 15th at $180; or
Buy semester permits on August & January 15th at $130 each
What is the IRR for annual permit?
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33. Example 7-9 Pay for liability insurance:
$10,000/quarter or $35,000/year
What is rate of return for paying annually?
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34. Example 7-10 Buy or lease options (for 2 years):
Buy for $40,000 with salvage value of $6000; or
Lease at $2500/month
What is IRR of lease?
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35. Incremental Analysis
With 2 or more alternatives, rate of return analysis must determine incremental rate of return, ΔIRR, on difference between alternatives
Incremental cash flow = higher initial-cost alternative minus lower initial-cost alternative
If ΔIRR≥MARR, choose higher-cost alternative
If ΔIRR<MARR, choose lower-cost alternative
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36. Example 7-11 Incremental ROR
Two mutually exclusive alternatives (MARR=6%):
Incremental
Year
Alt.1
Alt.2
Alt.2-Alt.1
−$1000
−$2000 1
IRR
50%
40%
ΔIRR=30%
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37. Example 7-13
A cost-saving device has no salvage value after 5 years. Two options:
Device A: Costs $10,000 & saves $3000 annually
Device B: Costs $13,500 & saves $3000 the 1st year & increases $500 annually
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38. Example 7-14 Machine X Machine Y Initial Cost $200 $700
Uniform annual benefit 95
120
Salvage value 50
150
Useful life, in years 6 12
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39. Example 7-15, Goal Seek Pump A Pump B Initial Cost $7000 $5000
End-of-useful-life salvage value
1500
1000
Useful life, in years 12 6
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40. Example 7-16, XIRR
A 401(k) is invested in stocks. On September 13, 2016 $1500 was deposited & another $2200 on June 7, If account worth $3840 on August 7, 2017, what annual rate of return has been earned?
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