Summer CH5 Solutions

# Summer CH5 Solutions - MIME 310 ENGINEERING ECONOMY...

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1 M I M E 3 1 0 E N G I N E E R I N G E C O N O M Y SOLUTIONS TO PROBLEM EXERCISES – SOURCES OF FUNDS AND THE COST OF CAPITAL 1. Equity sources of funds comprise shares and retained earnings. Thus, for the current capi- tal funding of a firm, the cost of equity as given applies to both common shares and retained earnings. The weighted-average after-tax cost of capital (WACC) is determined from the follow- ing relationship: WACC = K d (1 - t) d + K e (1 - d) in which K d and K e are the before-tax costs of debt and equity capital, respectively, t is the tax rate, and d is the proportion of debt in the capital structure. Therefore, WACC = 10% (1 - 0.45) 0.3 + 15% (1 - 0.3) = 12.2% 2. The cost of debt is the discount rate that equates the present value of all future disburse- ments to the net proceeds. Using the values associated with the issue of one bond, and semi- annual periods, Net proceeds: 90 Semi-annual interest payment and administrative costs: 100 (0.1 / 2) + 0.25 = 5.25 Number of periods: 24 Repayment at maturity: 100 Therefore, the semi-annual cost of debt is determined by finding the discount rate in the follow- ing relationship: 90 = 5.25 (P/A,i,24) + 100 (P/F,i,24) Clearly, the required discount rate is above 5 percent, the semi-annual coupon rate. Solving by trial and error, a semi-annual interest rate of 6.05 percent is obtained. Using a financial calculator with N=24, PV=90, PMT= -5.25 and FV= -100, compute I/Y to ob- tain 6.051%. On an annual basis, this is equivalent to: (1 + 0.06051) 2 - 1 = 0.1247 Therefore, the before-tax cost of the debt issue is 12.5% . 3. The after-tax cost of the debt issue is determined with the same relationship as that used in problem 2 above, but with the net after-tax proceeds and after-tax disbursements.

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