1. Engineering Economic Analysis
Chapter 15
Selection of a Minimum Attractive Rate of Return
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 MARR for Individuals Sources of Capital Cost of Funds
Investment Opportunities
Selecting a Minimum Attractive Rate of Return
Adjusting MARR for Risk & Uncertainty
Representative Values of MARR Used in Industry
Capital Budgeting or Selecting the Best Projects
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3. Learning Objectives
Define sources of capital & the costs of those funds
Understand the impact of inflation & the cost of borrowed money
Select MARR based on opportunity cost approach
Adjust MARR for risk & uncertainty
Use spreadsheets for investing & opportunity cost of capital
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4. Vignette: What’s the Rate of Return on a Dam?
Tajikistan with 8 million people supplies over 40% of Central Asia’s water
Construction of Rogun Dam began in 1976 & halted after collapse of Soviet Union
The dam across Vakhsh River in southern Tajikistan has a planned capacity of 3600 megawatts.
Tajikistan re-started work after offering $1.4 billion in bonds
Construction halted again in 2012
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5. Vignette: Rogun Dam: Green Solution?
What are advantages & disadvantages of hydroelectric power in a country such as Tajikistan?
What are consequences of new dam construction?
How would you balance benefits against costs to decide whether a new hydroelectric facility should be built?
What ethical issues arise when investing in foreign countries?
What risks are associated with the Rogun dam for Tajikistan? For its neighboring countries downstream? For foreign investors?
How would a private firm determine the MARR to be used?
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6. MARR for Individuals Minimum attractive rate of return
Applies to firms
Applies to individuals
For individuals MARR = highest of …
Rate on highest interest rate loan
Credit card interest may be quite high or low if balance paid off each month
Opportunity cost for investing is expected return on investment portfolio (see Appendix 10A)
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7. Sources of Capital Internal funds are monies generated by firm
Retained earnings (profits kept in firm)
Depreciation charges
External funds
Short term: banks loans (usually unsecured)
Long term: selling bonds (10-30 years)
Sale of company stock—new stock or treasury stock ≡ shares previously repurchased by firm
Need to maintain balance between debt & equity
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8. Cost of Funds
Cost of borrowed money depends on firm’s financial strength, ability to repay, debt’s duration, whether debt is secured by collateral
Cost of capital ≡ weighted average cost of capital (WACC) is based on all sources of the firm’s capital
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9. Example 15-1 Weighted Average Cost of Capital
Source of Fund
Amount
Before-Tax
Interest Rate
Bank loan
$20 M 9%
Bonds 7%
Common Stock & Ret. Earnings
$60 M
11%
Total
$100 M
After-Tax
Interest Rate
9%(1 − 0.4) = 5.4%
7%(1 − 0.4) = 4.2%
11%
After-tax interest cost = (Before-tax interest cost) x (1 – Tax rate)
Only interest is tax deductible. Both loans & bonds are 20% of total.
The other 60% is equity.
WACC = (0.2)(9%)(1 − 0.4) + (0.2)(7%)(1 − 0.4) + (0.6)(11%) = 8.52%
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10. Inflation & the Cost of Borrowed Money: The Real Interest Rate
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11. Investment Opportunities and Opportunity Cost
Firms have a wide variety of investment options
Both internal & external
What is source & amount of money available?
What are investment opportunities?
What is the opportunity cost?
All selected projects should be better than the best rejected project
Opportunity cost = Cost of best opportunity forgone
= Rate of return on best rejected project
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12. If you can’t fund all projects,
Fund those with smallest cost
Fund the most politically popular
Fund those with largest NPV
Fund those with largest IRR
Use Dynamic Programming to optimize
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13. If you can’t fund all projects,
Fund those with smallest cost
Fund the most politically popular
Fund those with largest NPV
Fund those with largest IRR
Use Dynamic Programming to optimize
While companies use a variety of techniques, ranking by IRR is the most common.
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14. Investment Opportunities
Project
Project Description
Cost(x103)
Estimated RoR
Investment Related to Current Operations 1
New equipment to reduce labor costs
$150
30% 2
Other equipment to reduce labor costs 50 45 3
Overhaul of machines 38 4
New test equipment
100 40
New Operations 5
Manufacture parts
200 35 6
Further processing of products 28 7
Further processing of other products 18
New Production Facilities 8
Relocation of production to new plant
250 25
External Investments 9
Investment in a different industry
300 20 10
Other investment in a different industry 11
Overseas investment
400 15 12
Purchase of Treasury bills
Unlimited
0.8
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15. Investment Opportunities
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16. Investment Opportunities
Budget Limit = $1.2 million
Opportunity cost of capital = 18%
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17. Example 15-3 Investment Opportunities; Capital Budget = $650,000
Rank projects by rate of return:
Project
Cost
(x1000)
Rate of Return
Cumulative Cost (x1000) 3
$50
25% 1
100 20
150 4
250 5
350 6 18
450 2
200 15
650 9 50 14
700 8
300 12
1000 7 10
1300
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18. Example 15-3 Investment Opportunities
Budget Limit = $650,000
Opportunity cost of capital = 14%
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19. Multiple projects, budget = $250,000
Project IRR 1st Cost % 100k k k k k
Which get funded? #1
#1 & 2
#1, 2, & 3
#1, 2, 3, & 4
All five
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20. Multiple projects, budget = $250,000
Project IRR 1st Cost % 100k k k k k
Which get funded? #1
#1 & 2
#1, 2, & 3
#1, 2, 3, & 4
All five
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21. Multiple projects, budget = $200,000
Project IRR 1st Cost % 70k k k k k
Which get funded? #5
#2 & 5
#2, 4, & 5
#1, 2, & 5
None of these
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22. Multiple projects, budget = $200,000
Project IRR 1st Cost % 70k k k k k
Which get funded? #5
#2 & 5
#2, 4, & 5
#1, 2, & 5
None of these
Totals of 1st costs do not always exactly equal the capital budget!
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23. Example 15-4 Capital budget = $800,000
Sort by IRR
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24. Example 15-4 Capital budget = $800,000
Fund Projects D, I, B, G
Opportunity cost of capital = 10.6%
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25. Example 15-5 Capital Budgeting Incremental Rate of Return
For proposals with 2 or more alternatives, incremental ROR is required.
Budget = $250,000
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26. Example 15-5 Capital Budgeting Incremental Rate of Return
Incremental Analysis:
Project
Cost
($1000)
Benefit
Salvage
Uniform Annual Benefit
Salvage ($1000)
ROR
Proposal 1
Alt. A
100
$23.85
B – A 50
8.35
10.6%
Alt. B
150
32.20
C – B
7.65
8.6
C – A
16.00
9.6
Alt. C
200
39.85
Proposal 2
14.92
Proposal 3
18.69 25
0.73
8.3
19.42
125
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27. Example 15-5 Capital Budgeting Incremental Rate of Return
Budget Limit = $250,000
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28. Example 15-5 Capital Budgeting Incremental Rate of Return
Project Ranking
Project
Cost
($1000)
Computed
Rate of
Return
Cumulative 1A
100
20.0% 2A 50
15.0
150 3A
250
1B-1A
10.6
300
1C-1B
8.6
350
3B-3A
8.3
400
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29. Selecting a Minimum Attractive Rate of Return
Minimum Attractive Rate of Return (MARR) should be equal to the largest of:
Cost of borrowed money
Cost of capital
Opportunity cost
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30. Adjusting MARR to Account for Risk & Uncertainty
Risk: Probabilities can be assigned to possible future outcomes
Uncertainty: Probabilities are unknown
Projects with normal business risk, no need to adjust MARR
Projects with greater risk, increase MARR
Most companies use risk-adjusted rates
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31. Example Risk-Adjusted Interest Rates for Manufacturing
6% Equipment replacement
8% New equipment
10% New product in normal market
12% New product in related market
16% New product in new market
20% New product in foreign market
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32. Example 15-6 Adjusting MARR for Risk & Uncertainty
Alternative B is riskier than Alternative A.
Year
Alt. B
Alt. A
Alt. A - Alt. B
-$80.00
$0.00
1-10
13.86
10.00
-3.86
11-20
20.00
IRR
15.48%
14.05%
10.00%
$28.83
$1.97
-$5.00
-$6.97
If MARR = 10%, Alternative A is selected since Alt. B is riskier.
If MARR = 15%, Alternative B is selected.
Increasing MARR due to risk is only an approximate technique; may result on increased focus on short-term results
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33. Representative Values of MARR
MARR should equal the largest of
Cost of borrowed money
Cost of capital
Composite value of the capital structure
After-tax return, 0% – 40%, average 8%
After-tax return on common stock & retained earnings, 0% – 65%, average 14%
Opportunity cost
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34. Representative Values of MARR
MARR used by enterprises
25 – 30% for high-tech start-ups, petroleum & mining
12 – 15% for companies with normal risk level
Usually decided by opportunity cost
Much higher than MARR by individuals
Better opportunities
Diminished competition
Higher risk
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35. Capital Budgeting Capital budgeting: selecting best projects
Opportunity cost of capital approach: rank projects by ROR
Management consensus
May rank projects by B/C ratios or present worth index
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36. Example 15-7 Present Worth Index
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37. Example 15-7 Present Worth Index
Project
Cost
($1000)
Computed
Rate of Return
Ranking by
ROR
NPW
Present
Worth
Index
PW Index 1
100
20% 2
22.01
0.2201
200 15 6
3.87
0.0194 3 50 25
6.81
0.1362 5 4 20
21.10
0.2110
28.14
0.2814 18
17.91
0.1791 7
300 10 9
-27.05 8 12
-31.69 14
-1.28
Ranking is different between ROR & PW Index
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