Engineering Economic Analysis

1. Engineering Economic Analysis Chapter 15  Selection of a MARR rd

2. Sources of Capital Money Generated from the Operations of the Firm Profit Depreciation External Sources of Money Loans Mortgage Bonds Choice of Source of Funds rd

3. Preference of Capital Companies prefer Internal to External financing and debt to equity when external financing. You need to raise $1M. Debt or Equity or does it matter? Doesn't matter for fair valued assets. rd

4. Equity Financing Equity financing uses retained earnings raised from issuance of stock to finance capital investments. A company needs $10M and decides to sell its common stock. Current price is $30/share, but investment bankers feel the price of $28/share is better because of decreasing demand. Flotation costs (banker's fee, etching fee, lawyers’ fee) is 6% of selling price; thus $26.32 How many shares to sell to raise $10M? Let X be the number of shares sold. Flotation cost is 0.06 * 28 * X = 1.68X Sales proceeds – flotation cost = Net proceeds 28X – 1.68X = $10M => X = 379,940 shares Flotation cost for issuing common stock is 1.68 * 379,940 = $638,300. rd

5. Debt Financing Debt financing uses money raised through loans by an issuance of bonds to finance a capital investment. Task is to raise $10M by debt financing. Bond financing ~ floatation cost is 1.8% of the $10M issue with face value of $1000 sold at discount $985. Bond pays annual interest of 12%. Term loan ~ $10M bank loan secured at 11%/year for 5 years. How many $1000 par value bonds to raise $10M? 10,338.38 What is annual payments on bond and what is annual payment on loan? $1,240,605.60 To net $10M; $10M/(1 – 0.018) = $10,183,300 paying $183,300 in floatation costs. But bond sold at 1.5% discount, for bond financing Total number of bonds sold $10,183,300/$985 = 10,338.38 bonds Annual interest is $10,338,380 * 0.12 = $1,240,605.60 paid each year. Term loan ~ $10M(A/P, 11%, 5) = $2,705,703.10 annual payment. rd

6. MARR Factors Project risk ~ higher perceived risk, higher MARR Investment opportunity ~ MARR may be lowered to encourage investment. Flexibility is important. Tax structure ~ higher corporate taxes => higher MARR Limited capital ~ tends to increase MARR. Opportunity cost Market rates at other corporations ~ Keep in step. Before-tax MARR = (1 – tax rate) * after-tax MARR rd

7. Cost of Borrowed Money Interest Rate Prime Financial strength of borrower Duration Cost of Capital Common stock RoR Mortgage bonds Bank loans rd

8. Weighted Average Cost of Capital WACC= (equity fraction)(cost of equity capital) + (debt fraction)(cost of debt capital) where equity capital can be preferred stock, common stock, or retained earnings. rd

9. Example 15-1 ROR Annual $20 million Bank loan 9% $1.8M 20 Mortgage bonds 7 1.4 60 Common stock 11 6.6 $100 million raised $9.8 M After Tax analysis: Assume tax rate at 40% Bank loan  0.09(1 – 0.4) = 5.4% Mortgage bonds  0.07(1 – 0.4) = 4.2% Dividends and retained earnings are not tax deductible. $20M(5.4%) + 20M(4.2%) + 60M(11%) = $8.52M Cost of capital = 8.52M/100M = 8.52% rd

10. Table 15-1 Budget $1.2M Opportunity Cost rd

11. Selecting a MARR Cost of Borrowed Money Cost of Capital Opportunity Cost MARR should be the largest rate of the above costs. Now we need to hedge for uncertainty in the estimates. Probability => Risk rd

12. Problem 15-2 A B C First cost $100 $50 $25UAB 16.27 9.96 5.96 IRR 10% 15% 20% Express the three mutually exclusive alternatives with10-year lives over an unspecified MARR. B-C (UIRR 25 4 10) 9.61% A-B  (UIRR 50 6.31 10)  4.47% A-C  (UIRR 75 10.31 10)  6.25% 0 < MARR < 4.47 Choose A4.47 < MARR < 9.61 Choose B9.61 < MARR < 20 Choose CMARR > 20% Choose Do Nothing rd

13. Example 15-3 n 0 1-10 11-2014.05% 10% 15%A -80 10 20 0 28.83 -5 NPWB -80 13.86 10 0 28.83 1.97 NPW 15.48% B – A $6.97 At a MARR of 10% both are 28.83, both equally desirable, but B is believed to have greater risk. Thus choose A. At MARR 15%, A has negative return, but B is positive; thus choose B. rd

14. Problem 15-7 Budget = $70K Project First Cost Benefit IRR (%)1 $20K $11K (UIRR 20 11 3 0)  29.922 30K 14K (UIRR 30 14 3 0)  18.913 10K 6K (UIRR 10 6 3 0)  36.314 5K 2.4K (UIRR 5 2.4 3 0)  20.715 25K 13K (UIRR 25 13 3 0)  26.016 15K 7K (UIRR 15 7 3 0)  18.917 40K 21K (UIRR 40 21 3 0)  26.67 3 1 7 5 4 2 6 10 20 40 25 5 30 15 The opportunity cost of capital is (first reject project 5) at 26.1% rd

15. Problem 15-8 with $500K Budget rd

16. Problem 15-9 rd

17. Problem 16-11 Parabolic Benefit/Cost equation: PWB2 – 22PWC + 44 = 0; find PWC for optimal size project. Let y = PWB and x = PWC. Then y2 - 22x + 44 = 0; Solve for slope and set slope to 1. 2yy' - 22 = 0; y' = 11/y = 1 => y = 11 and x = 7.5 112 -22x +44 = 0 => x = 7.5 = PWC rd

18. Problem 16-26 Conventional B/C and incremental analysis C-A rd

19. Determining the MARR Suppose cost of capital is 10% (borrowing rate) and lending rate is 6% (opportunity cost) with budget at) $40K b) $60K and c) $0K, determine MARR using ranked projects by their IRR. a) With $40K budget, invest in 1,2,3,4. MARR = 8%. b) With $60K, invest in projects 1,2,3,4,5. Lend $10K at 6%. MARR = 6%. c) Borrow for projects 1 & 2. MARR = 10% lending < MARR < borrowing rd

20. Example Calculate the after-tax cost of debt for the following: • Interest rate is 12%; tax rate is 25% ¾ * 12 = 9% • Interest rate is 14%; tax rate is 34% 0.66 *14 = 9.24% c) Interest rate is 15%; tax rate is 40% 0.6 * 15 = 9% rd

21. Example With budget at $3500 and lend out remaining funds at 10%, and goal is to maximize future worth at n = 3. FWA(10%) = $648, FWB(10%) = $847; FWC(10%) = $190.08; FWD(10%) = -$11 A & C for $838 + 500(F/P, 10%, 3) = $1503.58 B  847 + 500(F/P, 10%, 3) = $1512.50 rd

22. Example You need $10M in capital. Capital stock sales  $5M at 13.7% Use of retained earnings  $2M at 8.9% Debt financing with bonds  $3M at 7.5%. Historical D-E mix of 40% from debt costing 7.5% and 60% from equity costing 10%. Calculate historical WACC and current WACC. Historical: 0.6(10) + 0.4(7.5) = 9% Current: (5/10)(13.7) + (2/10)(8.9) + (3/10)(7.5) = 10.88%. After-tax analysis is appropriate. rd

23. Example Debt Capital You need $10M in debt capital by issuing 5,000 $1K 10-year bonds paying 8%/year with 50% tax rate. Bonds are discounted 2% for quick sale. Ignore flotation costs. Compute cost of debt capital before and after taxes. 980 = 80(P/A, i%, 10) + 1000(P/F, i%, 10) (UIRR 980 80 10 1000)  8.3% Before tax (UIRR 980 40 10 1000)  4.24% After-tax rd

24. Debt Capital You buy a $20K 10-year asset by putting $10K down and borrowing $10K at 6%/year by paying the interest each year and the $10K in year 10. Tax rate is 42%. Compute after tax cost of debt capital. Deduction for interest is $600 at tax rate 42% leaving ATCF 600(1 – 0.42) = $348 (UIRR 10000 348 10 10000) 3.48%. rd

25. Inflation • A machine costing $2550 4 years ago now costs $3930with general inflation at 7% per year. Calculate the true percentage increase in the cost of the machine. a) 14.95% b) 54.12% c) 35.11% d) 7% e) 17.58% • If you want a 7% inflation-free return on your investment with f = 9% per year, your actual interest rate must be • 16% b) 20% c) 12% d) 15% e) 14% • I want $25K per year forever in R$ when I die for my family. Insurer offers 7% per year while inflation is expected to be 4% per year. First payment is 1 year after my death. How much insurance do I need? a) $866K b) $357K c) $625K d) $841K rd

26. Cost of Capital 250M shares priced at $29.30 20M preferred stock priced at $40.50 150M selling at $101.75 per 100 500M loan at 4.5% interest. rd