Question

XYZ Corporation has $500 million in zero coupon debt outstanding, due in five years. The firm had earnings before interest and taxes of $40 million in the most recent year (the tax rate is 40%). These earnings are expected to grow 5% a year in perpetuity, and the firm paid no dividends. The firm had a return on capital of 12% and a cost of capital of 10%. The annualized standard deviation in firm values of comparable firms is 12.5%. The five-year bond rate is 5%. a. Estimate the value of the firm. b. Estimate the value of equity, using an option pricing model. c. Estimate the market value of debt and the appropriate interest rate on the debt.

Answer 1

The firm's value is estimated to be $102 million. The value of equity is estimated to be -$398 million using an option pricing model. The market value of debt is $500 million with an appropriate interest rate of 5%.

Step-by-step explanation:

a. The value of the firm can be estimated using the Gordon Growth Model. The formula for calculating the value of the firm is:

Value of Firm = Earnings before interest and taxes (EBIT) * (1 - Tax Rate) / (Cost of Capital - Growth Rate)

Plugging in the given values: Value of Firm = $40 million * (1 - 0.4) / (0.10 - 0.05) = $102 million.

b. To estimate the value of equity using an option pricing model, the firm's value is adjusted for the risk associated with the firm compared to the market. The formula for equity value is:

Equity Value = Firm Value - Market Value of Debt

Given that the firm has no dividends and zero coupon debt, the market value of debt is equal to the face value, which is $500 million. Therefore, Equity Value = $102 million - $500 million = -$398 million.

c. The market value of debt is $500 million, as mentioned earlier. The appropriate interest rate on the debt is the five-year bond rate, which is given as 5%.