Question

2. What risk premium will a financial institution require on a $25 million loan given the following information:

the financial institution needs an expected return of 6.75% in order to generate the desired profit for its investors;

the expected default rate on loans of this type is 3%;

if the borrower defaults on the loan, the financial institution expects to recover 70% of the total return;

the financial institution’s base rate covers its costs of funds (2.5%) and overhead (2%); and

the lender charges an origination fee of 0.375% of the loan amount.

Answer 1

Answer:

Given, Expected return = 6.750%, and expected default rate (probability of default) on such loans is 3%.

Let the interest rate quoted for this loan is R%, then recovery in case of default will be R * 70%

Expected return = Expected return in case of no default + Expected return in case of default + Origination fee

=> 6.750% = (R * 97% + (R * 70%) * 3%) + 0.375%

=> R = 6.433%

Now, R = Base rate + Risk premium

=> Risk premium = 6.433% - (2.5% + 2%) = 1.933%

In amount, risk premium = 1.933% of $25 million = $0.483 million.