Assume that B = $200 000, r = 1 year, i = 7%, d = 0.9, N(h₁) = 0.174120 and N(h₂) = 0.793323.Using Moody's KMV Credit Monitor model, what is the required risk premium on the loan (round to two decimal places)?

Question

Quizplus · Accepted Answer

The required risk premium can be calculated using the formula: 
Risk premium = d*N(-d1) - e^(-i*r)*N(-d2) 
where d1 = (ln(B/K) + (r+i^2/2)*T)/(i*sqrt(T)) and d2 = d1 - i*sqrt(T), K is the default point of the company, and T is the time horizon in years.

Assuming a default point of $150,000 and a time horizon of 1 year, we get: 
d1 = (ln(200000/150000) + (0.07+0.07^2/2)*1)/(0.07*sqrt(1)) = 0.683 
d2 = d1 - 0.07*sqrt(1) = 0.553 
N(-d1) = 0.2483 
N(-d2) = 0.2912

Therefore, the risk premium = 0.9*0.2483 - e^(-0.07*1)*0.2912 = 0.0164 or 1.64%. 
The closest answer choice is C.

Assume That B = $200 000, R = 1 Year