Chapter 16 Solutions

Chapter 16 Solutions - Chapter 16: Capital Structure: Basic...

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Chapter 16: Capital Structure: Basic Concepts 16.2 a. A firm’s debt–equity ratio is the market value of the firm’s debt divided by the market value of a firm’s equity. The market value of Acetate’s debt $9 million, and the market value of Acetate’s equity is $30 million. Debt–Equity Ratio = Market Value of Debt / Market Value of Equity = $9 million / $30 million = 0.03 Therefore, Acetate’s Debt–Equity Ratio is 30 %. b. The cost of Acetate’s equity is: r S = r f + β S {E(r m ) – r f } = 0.07 + 0.85( 0.21 – 0.07) = 0.189 The cost of Acetate’s equity (r S ) is 18.9%.Assume a cost of debt of 14%(missing in the statement of the problem). Acetate’s weighted average cost of capital equals: r wacc = {B / (B+S)} r B + {S / (B+S)}r S = ($9 million / $39 million)(0.14) + ($30 million / $39 million)(0.189) = (0.23)(0.14) + (.77)(0.189) = 0.1777 Therefore, Acetate’s weighted average cost of capital is 17.77%. c. According to Modigliani–Miller Proposition II (No Taxes): r S = r 0 + (B/S)(r 0 – r B ) Thus: 0.189= r 0 + (9/30)(r 0 – 0.14) Solving for r 0: r 0 = 0.1777 Therefore, the cost of capital for an otherwise identical all–equity firm is 17.77%. This is consistent with Modigliani–Miller’s proposition that, in the absence of taxes, the cost of capital for an all–equity firm is equal to the weighted average cost of capital of an otherwise identical levered firm. Answers to End-of-Chapter Problems B- 214
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16.4 a. Plan I: The earnings after interest will be: $9,500 – $12,000(0.1) = $8,300 EPS = $8,300 / 900 shares = $9.22/share Plan II: The earnings after interest will be: $9,500 – $15,000(0.1) = $8,000 EPS = $8,000 / 650 shares = $12.31/share All equity: EPS = $9,500 / 1,100 shares = $8.63/share Plan II has the highest EPS. b. Plan I: The earnings after interest will be: ($9,500 – $12,000(0.1)) (1–.25) = $6,225 EPS = $6,225 / 900 shares = $6.91/share Plan II: The earnings after interest will be: ($9,500 – $15,000(0.1) )(1–.25) = $6,000 EPS = $6,000 / 650 shares = $9.23/share All equity: EPS = $95,000 (1–.25) / 1,100 shares = $6.47/share Plan II has the highest EPS. 16.6 Before the restructuring the market value of Grimsley’s equity was $6,750,000 (= 150,000 shares * $45 per share). Since Grimsley issues $900,000 worth of debt and uses the proceeds to repurchase shares, the market value of the firm’s equity after the restructuring is $5,850,000 (= $6,750,000 – $900,000). Because the firm used the $900,000 to repurchase 20,000 shares, the firm has 130,000 (150,000 – 20,000) shares outstanding after the restructuring. Note that the market value of Grimsley’s stock remains at $45 per share (= $5,850,000 / 130,000 shares). This is consistent with Modigliani and Miller’s theory. Since Ms. Cannon owned $13,500 worth of the firm’s stock, she owned 0.2% (= $13,500 / $6,750,000) of Grimsley’s equity before the restructuring. Ms. Cannon also borrowed $2,500 at 17% per annum, resulting in $425 (= 0.17 * $2,500) of interest payments at the end of the year. Let Y equal Grimsley’s earnings over the next year. Before the restructuring, Ms. Cannon’s payout, net of personal interest payments, at the end of the year was: (0.002)($Y) – $425 After the restructuring, the firm must pay $153,000 (= 0.17 * $900,000) in interest to debt holders at the end of the year before it can distribute any of its earnings to equity holders. Also, since the market value of Grimsley’s equity dropped from $6,750,000 to $5,850,000, Ms. Cannon’s $10,000 holding of stock Answers to End-of-Chapter Problems B- 215
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now represents 0.231% (= $13,500 / $5,850,000) of the firm’s equity. For these two reasons, Ms.
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Chapter 16 Solutions - Chapter 16: Capital Structure: Basic...

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