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Unformatted text preview: Doing so, we find: VL = $6,936,000 / .1524 VL = $45,520,661.16 Now we can use the debt-value ratio and equity-value ratio to find the value of debt and equity, which are: B = VL(Debt-value) B = $45,520,661.16(.26) B = $11,801,652.89 S = VL(Equity-value) S = $45,520,661.16(.74) S = $33,719,008.26 d. In order to value a firm’s equity using the flow-to-equity approach, we can discount the cash flows available to equity holders at the cost of the firm’s levered equity. First, we need to calculate the levered cash flows available to shareholders, which are: Sales Variable costs EBIT Interest EBT Tax Net income $28,900,000 17,340,000 $11,560,000 1,062,149 $10,497,851 4,199,140 $6,298,711 So, the value of equity with the flow-to-equity method is: S = Cash flows available to equity holders / RS S = $6,298,711 / .1868 S = $33,719,008.26 390 16. a. Since the company is currently an all-equity firm, its value equals the present value of its unlevered after-tax earnings, discounted at its unlevered cost of capital. The cash flows to shareholders for the unlevered firm are: EBIT Tax Net income $83,000 33,200 $49,800 So, the value of the company is: VU = $49,800 / .15 VU = $332,000 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 after-tax present value of cash flows resulting from debt. Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt, so: NPV = Proceeds – Aftertax PV(Interest payments) NPV = $195,000 – (1 – .40)(.09)($195,000) / 0.09 NPV = $78,000 So, using the APV method, the value of the company is: APV = VU + NPV(Financing side effects) APV = $332,000 + 78,000 APV = $410,000 The value of the debt is given, so the value of equity is the value of the company minus the value of the debt, or: S=V–B S = $410,000 – 195,000 S = $215,000 c. 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 = .15 + ($195,000 / $215,000)(.15 – .09)(1 – .40) RS = .1827 or 18.27% 391 d. In order to value a firm’s equity using the flow-to-equity approach, we can discount the cash flows available to equity holders at the cost of the firm’s levered equity. First, we need to calculate the levered cash flows available to shareholders, which are: EBIT Interest EBT Tax Net income $83,000 17,550 $65,450 26,180 $39,270 So, the value of equity with the flow-to-equity method is: S = Cash flows available to equity holders / RS S = $39,270 / .1827 S = $215,000 17. Since the company is not publicly traded, we need to use the industry numbers to calculate the industry levered return on equity. We can then find the industry unlevered return on equity, and relever the industry return on equity to account for the different use of leverage. So, using the CAPM to calculate the industry levered return on equity, we find: RS = RF + β(MRP) RS = 5% + 1.2(7%) RS = 13.40% Next, to find the average cost of unlevered equity in the holiday gift industry we can use ModiglianiMiller Proposition II with corporate taxes, so: RS = R0 + (B/S)(R0 – RB)(1 – tC) .1340 = R0 + (.35)(R0 – .05)(1 – .40) R0 = .1194 or 11.94% Now, we can use the Modigliani-Miller Proposition II with corporate taxes to re-lever the return on equity to account for this company’s debt-equity ratio. Doing so, we find: RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .1194 + (.40)(.1194 – .05)(1 – .40) RS = .1361 or 13.61% Since the project is financed at the firm’s target debt-equity ratio, it must be discounted at the company’s weighted average cost of capital. 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 392 So, we need the debt-value and equity-value ratios for the company. The debt-equity ratio for the company is: B/S = 0.40 B = 0.40S Substituting this in the debt-value ratio, we get: B/V = .40S / (.40S + S) B/V = .40 / 1.40 B/V = .29 And the equity-value ratio is one minus the debt-value ratio, or: S/V = 1 – .29 S/V = .71 So, using the capital structure weights, the company’s WACC is: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS RWACC = .29(1 – .40)(.05) + .71(.1361) RWACC = .1058 or 10.58% Now we need the project’s cash flows. The cash flows increase for the first five years before leveling off into perpetuity. So, the cash flows from the project for the next six years are: Year 1 cash flow Year 2 cash flow Year 3 cash flow Year 4 cash flow Year 5 cash flow Year 6 cash flow So, the NPV of the project is: NPV = –$475,000 + $80,000/1.1058 + $84,000/1.10582 + $88,200/1.10583 + $92,610/1.10584 + $97,240.50/1.10585 + ($97,240.50/.1058)/1.10585 NPV = $408,125.67 $80,000.00 $84,000.00 $88,200.00 $92,610.00 $97,240.50 $97,240.50 393 CHAPTER 19 DIVIDENDS AND OTHER PAYOUTS
Answers to Concepts Review and Critical Thinking Questions 1. Dividend policy deals with the timing of dividend payments, not the amounts ultimately paid. Dividend policy is irrelevant when the timing of dividend payments doesn’t affect the present value of all future dividends. A stock repurchase reduces equity while leaving debt...
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