Onyx Corporation has a $200,000 loan that will mature in one year.The risk free interest rate is 6 percent.The standard deviation in the rate of change in the underlying asset's value is 12 percent, and the leverage ratio for Onyx is 0.8 (80 percent).The value for N(h1) is 0.02743, and the value for N(h2) is 0.96406. What is the current market value of the loan?

Question

Quizplus · Accepted Answer

Using the Black-Scholes-Merton model, we can calculate the current market value of the loan as:
V = K*N(-h2) - S0*N(-h1)
where:
K = $200,000 (the face value of the loan)
S0 = ? (unknown market value of the loan)
h1 = (ln(S0/K) + (r + 0.5*sigma^2)*T) / (sigma*sqrt(T)) = (ln(S0/$200,000) + (0.06 + 0.5*0.12^2)*1) / (0.12*sqrt(1)) = 1.676
h2 = h1 - sigma*sqrt(T) = 1.176

Plugging in the given values, we get:
V = $200,000*0.96406 - S0*0.02743
Simplifying, we get:
V = $192,812.02 - 0.02743S0

To solve for S0, we rearrange the equation:
S0 = ($192,812.02 - V) / 0.02743

Substituting V = $200,000 (the face value of the loan), we get:
S0 = ($192,812.02 - $200,000) / 0.02743 = $189,932.07

Therefore, the current market value of the loan is approximately $189,932.07, which corresponds to answer choice B.

Onyx Corporation Has a $200,000 Loan That Will Mature in One