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Chapter 16 (2): Capital Structure 16.12 a. The expected return on a firm’s equity is the ratio of annual after–tax earnings to the market value of the firm’s equity. Green expects $1,500,000 of pre–tax earnings per year. Because the firm is subject to a corporate tax rate of 36%, it must pay $540,000 worth of taxes every year. Since the firm has no debt in its capital structure and makes no interest payments, Green’s annual after–tax expected earnings are $960,000 (= $1,500,000 – $540,000). The market value of Green’s equity is $14,000,000. Therefore, the expected return on Green’s unlevered equity is 6.857% (= $960,000 / $14,000,000). b. Green is an all–equity firm. The present value of the firm’s after–tax earnings is $14,000,000 (= $960,000 / 0.06875). Green’s market–value balance sheet before the announcement of the debt issue is: Green Manufacturing Assets = $ 14,000,000 $ - Equity = $ 14,000,000 Total Assets = $ 14,000,000 Total D + E = $ 14,000,000 Since the market value of Green’s equity is $14,000,000 and the firm has 750,000 shares of common stock outstanding, the price of Green’s stock is $18.666 per share (= $14,000,000 / 750,000 shares) before the announcement of the debt issue. c. When Green announces the debt issue, the value of the firm will increase by the present value of the tax shield on the debt. Since Green plans to issue $3,000,000 of debt and the firm is subject to a corporate tax rate of 36%, the present value of the firm’s tax shield is: PV(Tax Shield) = TCB = (0.36)($3,000,000) = $1,080,000 Therefore, the value of Green Manufacturing will increase by $1,080,000 as a result of the debt issue. The value of Green Manufacturing after the repurchase announcement is: V L = V U + T CB = $14,000,000 + (0.36)($3,000,000) = $15,080,000 Since the firm has not yet issued any debt, Green’s equity is also worth $15,080,000. Answers to End-of-Chapter Problems B- 214 Green’s market–value balance sheet after the announcement of the debt issue is: Green Manufacturing Old Assets = $ 14,000,000 Debt = $ - PV(Tax Shield) = $ 1,080,000 Equity = $ 15,080,000 Total Assets = $ 15,080,000 Total D + E = $ 15,080,000 d. Since the market value of Green’s equity after the announcement of the debt issue is $15,080,000 and the firm has 750,000 shares of common stock outstanding, the price of Green’s stock is $20.1066 per share (=$15,080,000 / 750,000 shares) after the announcement of the debt issue. Therefore, immediately after the repurchase announcement, Green’s stock price will rise to $20.1066 per share. e. Green will issue $3,000,000 worth of debt and use the proceeds to repurchase shares of common stock. Since the price of Green’s stock after the announcement will be $20.1066 per share, Green can repurchase 149,204.7387 shares (= $3,000,000 / $20.1066 per share) as a result of the debt issue. Green will repurchase 149,204.7387 shares with the proceeds from the debt issue. Since Green had 750,000 shares of common stock outstanding and repurchased 149,204.7387 shares as a result of the debt issue, the firm will have 600,795.2613 (= 750,000 – 149,204.7387 shares) shares of common stock outstanding after the repurchase. Green will have 600,795.2613 shares of common stock outstanding after the repurchase. f. After the restructuring has taken place, Green will have $3,000,000 worth of debt in its capital structure. The value of Green after the restructuring is $15,080,000. The value of a levered firm is equal to the sum of the market value of its debt and the market value of its equity. That is, the value of a levered firm is: VL = S + B Rearranging this equation, the market value of the Green’s levered equity after the announcement of the debt issue is: S = VL – B = $15,080,000 – $3,000,000 = $12,080,000 Green’s market–value balance sheet after the restructuring is: Green Manufacturing Old Assets = $ 14,000,000 Debt = $ 3,000,000 PV(Tax Shield) = $ 1,080,000 Equity = $ 12,080,000 Total Assets = $ 15,080,000 Total D + E = $ 15,080,000 Answers to End-of-Chapter Problems B- 215 Since the market value of Green’s equity after the restructuring is $12,080,000 and the firm has 600,795.2613 shares of common stock outstanding, the price of Green’s stock will be $20.1066 per share (=$12,080,000/ 600,795.2613 shares) after the restructuring. Therefore, Green’s stock price will remain at $20.1066 per share after the restructuring has taken place. g. The required return on Green’s levered equity after the restructuring is: rS = r0 + (B/S)(r0 – rB)(1 – TC) = 0.06857+ ($3,000,000 / $12,080,000)( 0.06875 – 0.0465)(1 – 0.36) = 0.0721 Therefore, the required return on Green’s levered equity after the restructuring is 7.21%. 16.15 a. The value of Strider Publishing is: VU = [(EBIT)(1–TC)] / r0 = [($1,800,000)(1 – 0.36)] / 0.18 = $6,400,000 Therefore, the value of Strider Publishing as an all–equity firm is $6,400,000. b. The value of Strider Publishing will be: V L = V U + T CB = $6,400,000 + (0.36)($750,000) = $6,670,000 Therefore, the value of Strider Publishing Company will be $6,670,000if it issues $750,000 of debt and repurchases stock. c. Since interest payments are tax deductible, debt lowers the firm’s taxable income and creates a tax shield for the firm. This tax shield increases the value of the firm. d. The Modigliani–Miller assumptions in a world with corporate taxes are: – There are no personal taxes. – There are no costs of financial distress. – Perpetual cash flow – No transaction costs – Individuals and corporations can borrow at the same rate – Complete information Both personal taxes and costs of financial distress will be covered in more detail in a later chapter. Answers to End-of-Chapter Problems B- 216 16.17 a. The value of Appalachian if it were unlevered is: VU = [(EBIT)(1–TC)] / r0 = [($6,000,000)(1 – 0.35)] / 0.14 = $27, 857, 142.86 The value of Appalachian if it were an all–equity firm is $27, 857, 142.86. Appalachian currently has $9,000,000 of debt in its capital structure and is subject to a corporate tax rate of 35%. The value of Appalachian is: V L = V U + T CB = $27, 857, 142.86+ (0.35)($9,000,000) = $31,007,142.86 Therefore, the value of Appalachian is $31,007,142.86. b. The required return on Appalachian’s levered equity is: rS = r0 + (B/S)(r0 – rB)(1 – TC) = 0.14 + ($9,000,000 / $22,007,142.86)(0.14 – 0.11)(1 – 0.35) = 0.148 Therefore, the cost of Appalachian’s levered equity is 14.8%. c. Appalachian’s weighted average cost of capital is: rwacc= {B / (B+S)}(1 – TC) rB + {S / (B+S)}rS = ($9,000,000 / $31,007,142.86)(1 – 0.35)(0.11) + ($22,007,142.86/ $31,007,142.86)(0.148) = 0.1258 Therefore, Appalachian’s weighted average cost of capital is 12.58%. 16.18 a. If Williamson’s debt–to–equity ratio is 3.5: B / S = 3.5 Solving for B: B = (3.5 * S) The above formula for rwacc uses the following ratio: B / (B+S) Since B = (3.5 * S): B/ (B+S) = (3.5 * S) / { (3.5 * S) + S} = (3.5 * S) / (4.5 * S) = (3.5 / 4.5) = 0.778 Answers to End-of-Chapter Problems B- 217 Williamson’s debt–to–value ratio is 77.8% The above formula for rwacc also uses the following ratio: S / (B+S) Since B = (3.5 * S): Williamson’s equity–to–value ratio = 1 – B/(B+S) = 1 – 0.778 = 0.222 Williamson’s equity–to–value ratio is 22.2%. In order to solve for the cost of Williamson’s equity capital (rS), set up the following equation: rwacc = {B / (B+S)}(1 – TC) rB + {S / (B+S)}rS 0.146 = (0.778)(1 – 0.35)(0.098) + (0.222)(rS) rS = 0.4344 Therefore, the cost of Williamson’s equity capital is 43.44%. b. In order to solve for the cost of Williamson’s unlevered equity (r0), set up the following equation: rS = r0 + (B/S)(r0 – rB)(1 – TC) 0.4344= r0 + (3.5)(r0 – 0.098)(1 – 0.35) r0 = 0.2007 Therefore, Williamson’s unlevered cost of equity is 20.07%. c. If Williamson’s debt–to–equity ratio is 0.75, the cost of the firm’s equity capital (rS) will be: rS = r0 + (B/S)(r0 – rB)(1 – TC) = 0.2007+ (0.75)( 0.2007– 0.098)(1 – 0.35) = 0.2508 If Williamson’s debt–to–equity ratio is 0.75: B / S = 0.75 Solving for B: B = (0.75 * S) A firm’s debt–to–value ratio is: B / (B+S) Since B = (0.75 * S): Williamson’s debt–to–value ratio = (0.75 * S) / { (0.75 * S) + S} = (0.75 * S) / (1.75 * S) Answers to End-of-Chapter Problems B- 218 = (0.75 / 1.75) = 0.4286 Williamson’s debt–to–value ratio is 42.86% A firm’s equity–to–value ratio is: S / (B+S) Since B = (0.75 * S): Williamson’s equity–to–value ratio = 1- 0.4286 = 0.5714 Williamson’s equity–to–value ratio is 57.14%. Williamson’s weighted average cost of capital (rwacc) is: rwacc= {B / (B+S)}(1 – TC) rB + {S / (B+S)}rS = (0.4286)(1 – 0.35)(0.098) + (0.5714)( 0.2508) = 0.1706 Therefore, Williamson’s weighted average cost of capital (rwacc) is 17.06% if the firm’s debt– to–equity ratio is 0.75. If Williamson’s debt–to–equity ratio is 1.5, then the cost of the firm’s equity capital (rS) will be: rS = r0 + (B/S)(r0 – rB)(1 – TC) = 0.2007 + (1.5)(0.2007 – 0.098)(1 – 0.35) = 0.3008 If Williamson’s debt–equity ratio is 1.5: B / S = 1.5 Solving for B: B = (1.5 * S) A firm’s debt–to–value ratio is: B / (B+S) Since B = (1.5 * S): Williamson’s debt–to–value ratio = (1.5 * S) / { (1.5 * S) + S} = (1.5 * S) / (2.5 * S) = (1.5 / 2.5) = 0.60 Williamson’s debt–to–value ratio is 60% A firm’s equity–to–value ratio is: S / (B+S) Since B = (1.5 * S): Answers to End-of-Chapter Problems B- 219 Williamson’s equity–to–value ratio = 1- 0.6 = 0.40 Williamson’s equity–to–value ratio is 40%. Williamson’s weighted average cost of capital (rwacc) is: rwacc= {B / (B+S)}(1 – TC) rB + {S / (B+S)}rS = (0.60)(1 – 0.35)(0.098) + (0.40)(0.3008) = 0.1585 Therefore, Williamson’s weighted average cost of capital (rwacc) is 15.85% if the firm’s debt– to–equity ratio is 1.5. Answers to End-of-Chapter Problems B- 220