1.The current market value of the assets of Bigelow, Inc. is $91 million, with a

Question

1.The current market value of the assets of Bigelow, Inc. is $91 million, with a standard deviation of 19 percent per year. The firm has zero-coupon bonds outstanding with a total face value of $45 million. These bonds mature in 2 years. The risk-free rate is 4 percent per year compounded continuously. What is the value of d1?

2.Assume you are being granted at-the-money stock options today when the stock is trading at $32 a share. These options mature in one year, the continuously compounded risk-free rate is 4.2 percent, and the volatility of the stock’s returns is 22 percent. What is the value of d2 as it is used in the Black-Scholes model?

3.Sam has been granted options on 50,000 shares. The stock is currently trading at $17 a share and the options are at the money. The volatility of the stock returns averages 16 percent. The options mature in 2 years and the risk-free rate is 3.45 percent. N(d1) is .662055 and N(d2) is .576052. Given this information, what is the value of a call option on one share of this stock?

Explanation / Answer

1)

d1 = (LN(91 ÷ 45) + (4% + (19%2 ÷ 2)) * 2) ÷ (19% * Sqrt(2)) = 3.0528

2)

d1 = (LN(32 ÷32) + (4.2% + (22%2 ÷ 2)) * 1) ÷ (22% * Sqrt(1)) = 0.3009

d2 = 0.3009 - 22%*Sqrt(1) = 0.0809

3)

Call = stock price * N(d1) - N(d2)*strike price*EXP(-r*T)

Call = 17*0.662055 - 0.576052*17*EXP(-3.45%*2)

   = 2.115

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