Question

# A company has a single zero coupon bond outstanding that matures in five years with a...

 A company has a single zero coupon bond outstanding that matures in five years with a face value of \$42 million. The current value of the company’s assets is \$32 million and the standard deviation of the return on the firm’s assets is 38 percent per year. The risk-free rate is 4 percent per year, compounded continuously.

(a) The equity of the firm has a payoff structure similar to that of a call option, with the bond's face value being equivalent to the option's strike price, the firm's asset value being equivalent to the current price of the underlying asset, standard deviation of return on assets being equivalent to option volatility, bond maturity being equivalent to option tenure and risk-free rate being 4 %.

Therefore, Option Strike Price = \$ 42 million, Current Asset Price = \$ 32 million, Tenure = 5 years, Standard Deviation of Returns = 38 % and Risk-Free Rate = 4 %

Using an online calculator to solve the above equation, we get: Call Price = Equity Value = \$ 9.77 million

(b) Company's Debt Value = Asset Value of Firm - Market Value of Equity = 32 - 9.77 = \$ 22.23 million

(c) Face Value of Debt = \$ 42 million, Current Value = \$ 22.23 million and Tenure = 5 years

Let the continuously compounded debt value be r

Therefore, 22.23 = 42 / e^(5 x r)

5 x r = r = 0.12725 or 12.725 % ~ 12.72 %

(d) If the firm undertakes a project with NPV = \$ 3100000 or \$ 3.1 million, the firm's value goes up by this amount.

Therefore, New Value of Firm Assets = 32 + 3.1 = \$ 35.1 million Call Price = New Market Value of Equity = \$ 11.79 million

(e) New Debt Value = 35.1 - 11.79 = \$ 23.31 million

Let the new cpst of debt be s

therefore, 23.31 = 42 / e^(5 x s)

5 x s = s = 0.11776 or 11.776 % ~ 11.78 %