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

11efb888_dc9a_5779_ba2a_71e72d182f1f_TB1314_00 The current market value of the loan can be calculated using the Black-Scholes-Merton model:

V = D * N(h1) - X * e^(-rt) * N(h2)

where:
D = face value of the loan = $200,000
X = expected payoff of the loan = $200,000 + (1.12 - 1) * $200,000 = $224,000
r = risk-free interest rate = 6%
t = time to maturity = 1 year
h1 = (ln(D/X) + (r + 0.5 * sigma^2) * t) / (sigma * sqrt(t)) = -0.8758
h2 = h1 - sigma * sqrt(t) = -1.4129

Plugging in the values, we get:

V = $200,000 * 0.02743 - $224,000 * e^(-0.06 * 1) * 0.96406
V = $5,488.60 - $189,932.00
V = -$184,443.40

Since the loan has a face value of $200,000, this means that the current market value is lower than the face value. The best choice is therefore B, which is the closest option to the calculated market value of -$184,443.40.

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