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SOLUTIONS CHAPTER 11 - CHAPTER 11 COST OF CAPITAL 11.1 11-2...

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CHAPTER 11 COST OF CAPITAL 11.1 k D = Y (1 – t) k D = 0.124 (1 - 0.40) = 7.4% 11-2 K p = D p / (P p – F) Where: K p = Investor’s required return on preferred stock D p = Dividend in $ per share on preferred stock F = Flotation cost in $ per share K p = $4.20 / $40 = 10.5% 11-3 K e = D 1 /P 0 + g Where: K e = Investor’s required return on common stock D 1 = Expected dividend in $ per share next year P 0 = Current common stock price in $ per share g = Firm’s expected constant growth rate in earnings K e = ($ 4 / $54) + 0.09 = 16.4% 11-4 Component Weighted Capital Book Value Weight Cost Cost Debt $100,000 0.50 7.4% 3.700% Preferred stock 50,000 0.25 10.5 2.625 Common stock 50,000 0.25 16.4 4.100 Total $200,000 1.00 10.425% 11-5 Component Weighted Capital Market Value Weight Cost Cost Debt $ 90,000 0.30 7.4% 2.22% Preferred stock 60,000 0.20 10.5 2.10 Common stock 150,000 0.50 16.4 8.20 Total $300,000 1.00 12.52% 11-6 (a) To maintain its current capital structure, the firm must finance 50 percent of its $1 million expansion program through common equity. Because retained earnings are estimated to be $200,000, the firm must obtain an external equity of $300,000.
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(b) K D = 4.74% K p = 9.2% Cost of retained earnings or K e Or K e = D1/ P 0 + g = $2(1 + 0.05) / $50 + 0.05 = 9.2% Cost of new common stock or K n Or K n = $2(1 + 0.05) / ($50-$10) + 0.05 = 10.25% Component Weighted Capital Target Amount Weight Cost Cost Debt $ 300,000 0.3 4.74% 1.422% Preferred stock 200,000 0.2 9.20 1.840 Retained earnings 200,000 0.2 9.20 1.840 Common stock (new) 300,000 0.3 10.25 3.075 Total $1,000,000 1.0 8.177% 11-7 (a) To compute the annual growth rate of dividends, use PV = FV n x PVIF n,g , where g = i. 1999 dividend = 2004 dividend / (1 + g) 5 = 199 dividend x PVIF 5,g $1.50 = $2 x PVIF 5,g ; PVIF 5,g = $1.50 / $2 = 0.75 If you look across the five-year row in Table C at the end of this book, the discount factor 0.75 is approximately under the 6 percent column. This 6 percent is the growth rate of dividends. Or by financial calculator : PV = -1.50 N = 5 FV = 2.00 CPT; IY = 5.92% (b) K e = $2.10 / $25 + 0.0592 = 14.32% (c) Cost of New Common Stock = $2.10 / ($25 - $5) + 0.0592 = 16.35% Where F = Flotation cost in $ per share
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11-8 (a) EBIT $1,500 Less: interest (8% of $5,000) 400 Earnings before taxes $1,100 Less: taxes at 50% 550 Earnings after taxes $ 550 Market value of stock ($550/0.10) $ 5,500 Market value of debt 5,000 Total value of the firm$10,500 (b) Overall Cost of Capital = EAT + Interest / Value of Firm = $550 + $200 / $10,500 = 7.14% OR K w = Y(1-t) (W D ) + K e (W e ) K w = 8%(1-.5) (5,000/10500) + 10% (5,500/10,500) K w = 4% (.476) + 10% (.524) K w = 1.9% + 5.24% K w = 7.14% 11-9 R A = 0.05 + (0.10 - 0.05)(1.5) = 12.5% < 15% undervalued R B = 0.05 + (0.10 - 0.05)(1.3) = 11.5% < 20% undervalued R C = 0.05 + (0.10 - 0.05)(0.8) = 9.0% > 8% overvalued R D = 0.05 + (0.10 - 0.05)(0.7) = 8.5% < 10% undervalued R E = 0.05 + (0.10 - 0.05)(1.1) = 10.5% > 9% overvalued F 1. The capital structure consists of long-term debt, notes payable , preferred stock, common stock, and retained earnings.
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