1. Assume that there are two factors influencing the past default behaviour of b
ID: 1171739 • Letter: 1
Question
1. Assume that there are two factors influencing the past default behaviour of borrowers, these being the debt to equity ratio and the sales to assets ratio. Based on past default (repayment) experience, the linear probability model is estimated as Zi = 0.3(D/Ei) + 0.15 (S/Ai).
Assume that a prospective borrower has a D/E ratio of 0.9 and a sales to assets ratio of 2.5.
What is the borrower's probability of default?
2. Consider the case of a simple one-period framework. If i = 12.50%, k = 14.85%, p = 0.98, and g = 0.85 what is the required risk premium (round to two decimals)?
3. 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)?
4. Assume that i1 = 11% and i2 = 12%, and that k1 = 14.50% and k2 = 16.50%.
What is the expected probability of repayment on the one-year corporate bonds in one year's time (round to two decimals)?
Explanation / Answer
(1) The probability of Default Equation = Zi = 0.3 x (D/E)i + 0.15 x (S/A)i
Borrower's D/E = 0.9 and S/A = 2.5
Therefore, Borrower's probability of default = Zi = 0.3 x 0.9 + 0.15 x 2.5 = 0.645
NOTE: Please raise separate queries for solutions to the remaining unrelated sub-parts.
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