HW8 Soln 10 - 10.25 Given: two M.E. projects, lives of 1...

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Eng 106 Homework #8 Solution Winter 2010 9.47 Given: Beta = 1.7, market return r m = 14%, risk-free rate r f = 7%. Find: cost of equity, i e . Cost of equity , i e = r f + Beta(r m – r f ) = 7% + 1.7(14% - 7%) = 18.9% 9.48 Given: a.t. cost of equity i e = 25%, b.t. cost of debt = 12%, marg tax rate t m = 40%, debt-to-equity ratio = 40%. Find: weighted (after-tax) cost of capital, k. k = i e * fraction of capital from equity + (b.t. cost of debt)(1 - t m ) * fraction of capital from debt (1) fraction from debt + fraction from equity = 1 (2) debt-to-equity ratio = fraction from debt/fraction from equity (3) combine (2) and (3) then solve for fraction from equity: debt-to-equity ratio = (1 - fraction from equity)/fraction from equity (1 + debt-to-equity ratio) * fraction from equity = 1 fraction from equity = 1/(1 + debt-to-equity ratio) Plug in given debt-to-equity ratio: fraction from equity = 1/1.4 Use this and (2) to find: fraction from debt = 0.4/1.4 Plug all values into (1): Cost of capital, k = 25% (1/1.4) + 12% (1 – 0.4)(0.4/1.4) = 19.9%
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Unformatted text preview: 10.25 Given: two M.E. projects, lives of 1 yr, zero salvage values, following PW of cash flows: Project 1 Project 2 Prob Value Prob Value Initial cost (certain): 1.0 $1000 1.0 $800 0.2 $2000 0.3 $1000 0.6 $3000 0.4 $2500 PW of year-end revenue: 0.2 $3500 0.3 $4500 a) Find: which project to select based on maximizing expected NPW E[NPW] for project 1 = -1000 + 0.2*2000 + 0.6*3000 + 0.2*3500 = 1900 E[NPW] for project 2 = -800 + 0.3*1000 + 0.4*2500 + 0.3*4500 = 1850 Select Project 1 because it has a the larger expected net worth. b) Find: which project to select if you also consider the variance Var[NPW] for project 1 = 0.2*((2k-1k)-1.9k) 2 + 0.6*((3k-1k)-1.9k) 2 + 0.2*((3.5k-1k)-1.9k) 2 = 240k Var[NPW] for project 2 = 0.3*((1k-0.8k)-1.85k) 2 + 0.4*((2.5k-0.8k)-1.85k) 2 + 0.3*((4.5k-0.8k)-1.85k) 2 = 1852k Project 1 has a smaller variance as well as a higher expected worth, so it is better than Project 2 on both measures....
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This note was uploaded on 04/09/2010 for the course ENGR ENG106 taught by Professor Hartsrough during the Winter '10 term at UC Davis.

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