Young Corporation expects an EBIT of $ 16,000 every year forever. The company cu

Question

Young Corporation expects an EBIT of $ 16,000 every year forever. The company currently has no debt, and its cost of equity is 15 percent.
a. What is the current value of the company?
b. Suppose the company can borrow at 10 percent. If the corporate tax rate is 35 percent, what will the value of the firm be if the company takes on debt equal to 50 percent of its unlevered value? What if it takes on debt equal to 100 percent of its unlevered value?
c. What will the value of the firm be if the company takes on debt equal to 50 percent of its levered value? What if the company takes on debt equal to 100 percent of its levered value?

Explanation / Answer

a) The value of the company is nothing but the value of the unlevered firm. Since there is no use of debt, the firm is unlevered. Calculating the value of the unlevered firm: To calculate the value of unlvered firm, we have to find out the value of unlevered cost of capital. Since there is no use of debt, the capital structure consists of only equity. Therefore, the weight of equity is 100% which is equal to 1.0 WACC = Cost of debt * Weight of debt (1-Tax rate) + Cost of equity * Weight of equity              = 0 + 0.15 * 1.0              = 0.15 or 15% Therfore, the unlevered cost of capital is 15% Value of Unlevered company = EBIT (1-TC) / Ru Where EBIT is the Earnings before interest and tax rate            Tc is the tax rate             Ru is the Cost of unlevered capital                                              = $16,000 / 0.15                                              = $106,667 b) Calculating the cost of capital : WACC = Cost of debt * Weight of debt (1-Tax rate) + Cost of equity * Weight of equity              = 0.10 * 0.50 * (1-0.35) + 0.15 * 0.50              = 0.325 + 0.075              = 0.1075 or 10.75% Value of the firm = EBIT(1-Tc) / Ru                           = $16,000 (1-0.35) / 0.1075                           = $10,400 / 0.1075                           = $96,744 Therefore, the firm is worth $96,744 Calculating the value of Levered firm: Value of levered firm = Value of Unlevered firm + Tax rate * Debt                                  = $106,667 + 0.35 * $106,667                                  = $106,667 + $37,333                                  = $144,000 Therefore, the total value of the firm is $144,000 of which $106,667 is debt and $37,333 is equity. c) Calculating the levered cost of capital: WACC = Cost of debt * Weight of debt (1-Tax rate) + Cost of equity * Weight of equity              = 0.10 * 0.50 * (1-0.35) + 0.15 * 0.50              = 0.325 + 0.075              = 0.1075 or 10.75% Value of the firm = EBIT(1-Tc) / Ru                           = $16,000 (1-0.35) / 0.1075                           = $10,400 / 0.1075                           = $96,744 WACC = Cost of debt * Weight of debt (1-Tax rate) + Cost of equity * Weight of equity              = 0.10 * 1.0 * (1-0.35) + 0.15 * 0.0              = 0.065 or 6.5% Value of Levered firm = Value of Unlevered firm + Tax rate * Debt]                                   = $96,744 + 0.35 * $96,744                                   = $130,604              = 0.10 * 0.50 * (1-0.35) + 0.15 * 0.50              = 0.325 + 0.075              = 0.1075 or 10.75% Value of the firm = EBIT(1-Tc) / Ru                           = $16,000 (1-0.35) / 0.1075                           = $10,400 / 0.1075                           = $96,744 Therefore, the firm is worth $96,744 Calculating the value of Levered firm: Value of levered firm = Value of Unlevered firm + Tax rate * Debt                                  = $106,667 + 0.35 * $106,667                                  = $106,667 + $37,333                                  = $144,000 Therefore, the total value of the firm is $144,000 of which $106,667 is debt and $37,333 is equity. c) Calculating the levered cost of capital: WACC = Cost of debt * Weight of debt (1-Tax rate) + Cost of equity * Weight of equity              = 0.10 * 0.50 * (1-0.35) + 0.15 * 0.50              = 0.325 + 0.075              = 0.1075 or 10.75%              = 0.10 * 0.50 * (1-0.35) + 0.15 * 0.50              = 0.325 + 0.075              = 0.1075 or 10.75% Value of the firm = EBIT(1-Tc) / Ru                           = $16,000 (1-0.35) / 0.1075                           = $10,400 / 0.1075                           = $96,744 Value of the firm = EBIT(1-Tc) / Ru                           = $16,000 (1-0.35) / 0.1075                           = $10,400 / 0.1075                           = $96,744 WACC = Cost of debt * Weight of debt (1-Tax rate) + Cost of equity * Weight of equity              = 0.10 * 1.0 * (1-0.35) + 0.15 * 0.0              = 0.065 or 6.5% Value of Levered firm = Value of Unlevered firm + Tax rate * Debt]                                   = $96,744 + 0.35 * $96,744                                   = $130,604              = 0.10 * 1.0 * (1-0.35) + 0.15 * 0.0              = 0.065 or 6.5% Value of Levered firm = Value of Unlevered firm + Tax rate * Debt]                                   = $96,744 + 0.35 * $96,744                                   = $130,604

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