The current market value of the assets of AMN Co. is $47 million, with a standard deviation of 21 percent per year. The firm has zero-coupon bonds outstanding with a total face value of $35 million. These bonds mature in two years. The risk-free rate is 3.6 percent per year, compounded continuously. What is the value of d₁ as it applies to the Black-Scholes option pricing model?
A) 1.32471
B) 1.48002
C) 1.60067
D) 1.38357
E) 0.89006

Question

Quizplus · Accepted Answer

To calculate d₁, we need to first calculate the value of the firm's assets in two years, which is:

V₂ = $47 million × e^(0.21^2 × 0.5) = $70.06 million

Next, we need to calculate the value of the firm's equity in two years, which is:

E₂ = $70.06 million - $35 million = $35.06 million

Using the Black-Scholes formula, we can then calculate d₁ as:

d₁ = [ln($35.06 million / $47 million) + (0.036 + 0.5 × 0.21^2) × 2] / (0.21 × sqrt(2)) = 1.38357

Therefore, the answer is (D).

The Current Market Value of the Assets of AMN Co