Use the following information and the option valuation model for the next two problems. 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 required yield on this risky loan?

Question

Quizplus · Accepted Answer

Using the option valuation model:

h1 = [ln(200,000/200,000) + (0.06 + 0.5(0.12^2))(1)] / (0.12√1) = 0
h2 = h1 - 0.12√1 = -0.12

Value of the put option (black): 
= -200,000[N(-h2)] + 200,000e^(-0.06)(N(-h1)) 
= -200,000[0.96406] + 200,000e^(-0.06)(0.02743) 
= $10,565.10

Value of the loan without default risk (gray): 
= 200,000e^(0.06) 
= $212,000

Value of the loan with default risk (green): 
= $200,000 - $10,565.10 
= $189,434.90

Required yield = ($200,000 - $189,434.90) / $200,000 
= 0.05325 or 5.325%

Since the loan is risky, a higher yield is required. The correct answer is closest to A.

Use the Following Information and the Option Valuation Model for the Next