The total value (debt plus equity) of Wilson Dover Inc. is $500 million and the face value of its 1-year coupon debt is $200 million. The volatility () of Wilson DOver's total value is 0.60, and the risk-free rate is 5%. Assume that N(d1) = 0.9720 and N(d2) = 0.9050.
-is the value (in millions) of Wilson Dover's equity if it is viewed as an option?
A) $228.77
B) $254.19
C) $282.43
D) $313.81
E) $345.19

Question

Quizplus · Accepted Answer

To find the value of Wilson Dover's equity viewed as an option, we can use the Black-Scholes formula for a call option:

C = S*N(d1) - X*e^(-rT)*N(d2)

Where:

C = value of the call option (i.e., equity)
S = current stock price (i.e., total value)
N(d1) and N(d2) = probabilities from the standard normal distribution (given in the problem)
X = exercise price (i.e., face value of debt)
r = risk-free rate
T = time to expiration (i.e., 1 year)

We can rearrange this formula to solve for S (i.e., total value):

S = C/N(d1) + X*e^(-rT)*N(d2)/N(d1)

Since we know the total value is $500 million and the face value of debt is $200 million, we can plug in these values along with the given probabilities and risk-free rate:

500 = C/0.9720 + 200*e^(-0.05*1)*0.9050/0.9720

Simplifying this equation, we get:

C = 313.81

Therefore, the value of Wilson Dover's equity viewed as an option is $313.81 million.

The Total Value (Debt Plus Equity) of Wilson Dover Inc