Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

The debt equity ratio for the company is bs 040 b 040s

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Unformatted text preview: 75) RWACC = .1105 or 11.05% Finally, we can use the WACC to discount the unlevered cash flows, which gives us an NPV of: NPV = –$45,000,000 + $13,500,000(PVIFA11.05%,5) NPV = $4,837,978.59 b. The weighted average cost of capital used in part a will not change if the firm chooses to fund the project entirely with debt. The weighted average cost of capital is based on optimal capital structure weights. Since the current capital structure is optimal, all-debt funding for the project simply implies that the firm will have to use more equity in the future to bring the capital structure back towards the target. Challenge 14. a. The company is currently an all-equity firm, so the value as an all-equity firm equals the present value of aftertax cash flows, discounted at the cost of the firm’s unlevered cost of equity. So, the current value of the company is: VU = [(Pretax earnings)(1 – tC)] / R0 VU = [($28,000,000)(1 – .35)] / .20 VU = $91,000,000 The price per share is the total value of the company divided by the shares outstanding, or: Price per share = $91,000,000 / 1,500,000 Price per share = $60.67 b. The adjusted present value of a firm equals its value under all-equity financing plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the aftertax present value of cash flows resulting from the firm’s debt. Given a known level of debt, debt cash flows can be discounted at the pretax cost of debt, so the NPV of the financing effects are: NPV = Proceeds – Aftertax PV(Interest Payments) NPV = $35,000,000 – (1 – .35)(.09)($35,000,000) / .09 NPV = $12,250,000 So, the value of the company after the recapitalization using the APV approach is: V = $91,000,000 + 12,250,000 V = $103,250,000 387 Since the company has not yet issued the debt, this is also the value of equity after the announcement. So, the new price per share will be: New share price = $103,250,000 / 1,500,000 New share price = $68.83 c. The company will use the entire proceeds to repurchase equity. Using the share price we calculated in part b, the number of shares repurchased will be: Shares repurchased = $35,000,000 / $68.83 Shares repurchased = 508,475 And the new number of shares outstanding will be: New shares outstanding = 1,500,000 – 508,475 New shares outstanding = 991,525 The value of the company increased, but part of that increase will be funded by the new debt. The value of equity after recapitalization is the total value of the company minus the value of debt, or: New value of equity = $103,250,000 – 35,000,000 New value of equity = $68,250,000 So, the price per share of the company after recapitalization will be: New share price = $68,250,000 / 991,525 New share price = $68.83 The price per share is unchanged. d. In order to value a firm’s equity using the flow-to-equity approach, we must discount the cash flows available to equity holders at the cost of the firm’s levered equity. According to Modigliani-Miller Proposition II with corporate taxes, the required return of levered equity is: RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .20 + ($35,000,000 / $68,250,000)(.20 – .09)(1 – .35) RS = .2367 or 23.67% After the recapitalization, the net income of the company will be: EBIT Interest EBT Taxes Net income $28,000,000 3,150,000 $24,850,000 8,697,500 $16,152,500 388 The firm pays all of its earnings as dividends, so the entire net income is available to shareholders. Using the flow-to-equity approach, the value of the equity is: S = Cash flows available to equity holders / RS S = $16,152,500 / .2367 S = $68,250,000 15. a. If the company were financed entirely by equity, the value of the firm would be equal to the present value of its unlevered after-tax earnings, discounted at its unlevered cost of capital. First, we need to find the company’s unlevered cash flows, which are: Sales Variable costs EBT Tax Net income $28,900,000 17,340,000 $11,560,000 4,624,000 $6,936,000 So, the value of the unlevered company is: VU = $6,936,000 / .17 VU = $40,800,000 b. According to Modigliani-Miller Proposition II with corporate taxes, the value of levered equity is: RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .17 + (.35)(.17 – .09)(1 – .40) RS = .1868 or 18.68% c. In a world with corporate taxes, a firm’s weighted average cost of capital equals: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS So we need the debt-value and equity-value ratios for the company. The debt-equity ratio for the company is: B/S = 0.35 B = 0.35S Substituting this in the debt-value ratio, we get: B/V = .35S / (.35S + S) B/V = .35 / 1.35 B/V = .26 389 And the equity-value ratio is one minus the debt-value ratio, or: S/V = 1 – .26 S/V = .74 So, using the capital structure weights, the company’s WACC is: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS RWACC = .26(1 – .40)(.09) + .74(.1868) RWACC = .1524 or 15.24% We can use the weighted average cost of capital to discount the firm’s unlevered aftertax earnings to value the company....
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