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.