Mojito Mint Company has a debt–equity ratio of .35. The required return on the c

Question

Mojito Mint Company has a debt–equity ratio of .35. The required return on the company’s unlevered equity is 11 percent, and the pretax cost of the firm’s debt is 7.6 percent. Sales revenue for the company is expected to remain stable indefinitely at last year’s level of $18,100,000. Variable costs amount to 75 percent of sales. The tax rate is 40 percent, and the company distributes all its earnings as dividends at the end of each year.

A. If the company were financed entirely by equity, how much would it be worth? (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

B. What is the required return on the firm’s levered equity? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

C. Use the weighted average cost of capital method to calculate the value of the company. (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

D. What is the value of the company’s equity? (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

E. What is the value of the company’s debt? (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

F. Use the flow to equity method to calculate the value of the company’s equity. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

Sales Revenue 18100000 Variable costs 18100000*.75 13575000 EBIT 4525000 Taxes at 40% 1810000 Unlevered After Tax Earning 2715000 VU = 2715000/ 0.11 =24681818 Therefore, Mojito Mint Company would be worth $24681818 as an unlevered firm. According to Modigliani-Miller Proposition II with corporate taxes: rS = r0 + (B/S)(r0 – rB)(1 – TC) where r0 = the required return on the equity of an unlevered firm rS = the required return on the equity of a levered firm rB = the pre-tax cost of debt TC = the corporate tax rate    B/S = the firm’s debt-to-equity ratio r0 = 0.11 rB = 0.076 TC = 0.40 B/S = .35 The required return on Mojito’s levered equity is rS = r0 + (B/S)(r0 – rB)(1 – TC) =0.11+(0.35)*(0.11-0.076)*(1-0.4)=11.71% The required return on Mojito’s levered equity (rS) is 11.71% In a world with corporate taxes, a firm’s weighted average cost of capital (rwacc) equals: rwacc = {B / (B+S)}(1 – TC) rB + {S / (B+S)}rS B / (B+S) = the firm’s debt-to-value ratio S / (B+S) = the firm’s equity-to-value ratio rB = the pre-tax cost of debt rS   = the cost of equity TC    = the corporate tax rate Mojito’s debt-to-value ratio = (.35)(S) / { (.35)(S) + S} =.25925 Mojito’s equity-to-value ratio =S / {(.35)(S) + S}=.740741 The inputs to the WACC calculation are: B / (B+S) = .25925 S / (B+S) = .740741 rB    = 0.076 rS    = 0.117 TC    = 0.40 rwacc = {B / (B+S)}(1 – TC) rB + {S / (B+S)}rS =(0.25925)*(1-0.4)*(0.1)+(0.740741)*(0.117)=10.22% Mojito’s weighted average cost of capital is 10.22% Use the weighted average cost of capital to discount the firm’s unlevered after-tax earnings. VL = $2715000 / 0.1022 =26565558 Therefore, the value of Mojito Mint Company is $26565558 Since the firm’s equity-to-value ratio is 3/5, the value of Mojito’s equity is .740741*26565558 =19678198 Since the firm’s debt-to-value ratio is 2/5, the value of Mojito’s debt is .25925*26565558=6887121 In order to value a firm’s equity using the Flow-to-Equity approach, discount the cash flows available to equity holders at the cost of the firm’s levered equity (rS).   Since the pre-tax cost of the firm’s debt is 7.6%, and the firm has $6887121of debt outstanding, Mojito must pay $523421 (= 0.076 * $6887121) in interest at the end of each year. Sales Revenue 18100000 Variable costs 18100000*.75 13575000 EBIT 4525000 Interest 523421 Pre Tax earning 4001579 Taxes at 40% 1600632 Unlevered After Tax Earning 2400947 Since the firm pays all of its after-tax earnings out as dividends at the end of each year, equity holders will receive $2400947 of cash flow per year in perpetuity S = Cash Flows Available to Equity Holders / rS = $2400947 / 0.117 =20520914.53 The value of Mojito’s equity is =20520914.53

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