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 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

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? Copyright Oxford University Press 2017

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) Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

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% Copyright Oxford University Press 2017

Inflation & the Cost of Borrowed Money: The Real Interest Rate Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

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. Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

Investment Opportunities Copyright Oxford University Press 2017

Investment Opportunities Budget Limit = $1.2 million Opportunity cost of capital = 18% Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

Example 15-3 Investment Opportunities Budget Limit = $650,000 Opportunity cost of capital = 14% Copyright Oxford University Press 2017

Multiple projects, budget = $250,000 Project IRR 1st Cost 1 20.0% 100k 2 15.0 50k 3 15.0 100k 4 10.6 50k 5 8.6 50k Which get funded? #1 #1 & 2 #1, 2, & 3 #1, 2, 3, & 4 All five Copyright Oxford University Press 2017

Multiple projects, budget = $250,000 Project IRR 1st Cost 1 20.0% 100k 2 15.0 50k 3 15.0 100k 4 10.6 50k 5 8.6 50k Which get funded? #1 #1 & 2 #1, 2, & 3 #1, 2, 3, & 4 All five Copyright Oxford University Press 2017

Multiple projects, budget = $200,000 Project IRR 1st Cost 1 15.6% 70k 2 18.2 40k 3 11.4 20k 4 15.8 100k 5 18.6 90k Which get funded? #5 #2 & 5 #2, 4, & 5 #1, 2, & 5 None of these Copyright Oxford University Press 2017

Multiple projects, budget = $200,000 Project IRR 1st Cost 1 15.6% 70k 2 18.2 40k 3 11.4 20k 4 15.8 100k 5 18.6 90k 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! Copyright Oxford University Press 2017

Example 15-4 Capital budget = $800,000 Sort by IRR Copyright Oxford University Press 2017

Example 15-4 Capital budget = $800,000 Fund Projects D, I, B, G Opportunity cost of capital = 10.6% Copyright Oxford University Press 2017

Example 15-5 Capital Budgeting Incremental Rate of Return For proposals with 2 or more alternatives, incremental ROR is required. Budget = $250,000 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

Example 15-5 Capital Budgeting Incremental Rate of Return Budget Limit = $250,000 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

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% NPW@10% $28.83 NPW@15% $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 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

Example 15-7 Present Worth Index Copyright Oxford University Press 2017

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 -0.0902 8 12 -31.69 -0.1056 14 -1.28 -0.0256 Ranking is different between ROR & PW Index Copyright Oxford University Press 2017