A company has a single zero coupon bond outstanding which matures in 10 years wi

Question

A company has a single zero coupon bond outstanding which matures in 10 years with a face value of $15 million. The current value of the company’s assets is $13.2 million, and the standard deviation of the return on the firm’s assets is 47 percent per year. The risk-free rate is 6 percent per year, compounded continuously. a. What is the current market value of the company’s equity? b. What is the current market value of the company’s debt? c. What is the company’s continuously compounded cost of debt? d. The company has a new project available. The project has an NPV of $1.8 million. If the com- pany undertakes the project, what will be the new market value of equity? Assume volatility is unchanged.

Explanation / Answer

Answer:

1. Calculating the Equity value of the firm in the form of call options as under:

Current Value of Firm: $ 13.2 Million.

Outstanding Debt: $ 15.0 Million.

   Cost of Debt:    6%

Using Black Scholes Model:

   d1 = (ln(13.2/15)+ (0.06+((0.47)^2)/2)*10)/0.47*sqrt(10) = 1.060

d2 = 1.060 - 0.47*sqrt(10) = -0.426.

N(d1) = 0.8554. Log Normal Probability.

N(d2) = 0.3336

C (value of equity) = 13.2*0.8554 - 15*0.3336*exp(-0.06*10) = $ 8.55 million.

Market Value of Debt = 13.2 - 8.55 = $4.654 Million.

2. NPV of Project : $ 1.8 Million.

   Current Firm Value = 13.2 + 1.8 = $ 15 Million.

Debt Outstanding: $ 15 Million.

Risk Free Rate : 6%.

Using Balck Scholes Model:

d1 = (ln(15/15)+(0.06+ ((0.47^2)/2))))*10/0.47*sqrt(10) = 1.146

d2 = -0.3394

N(d1) = 0.8729

N(d2) = 0.3669

Market Value of Equity = 15*0.8729 - 15*0.3669*exp(-0.06*10) = $ 10.07 Million.

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