3505 M2 Fall 2014 Soltn
Management of Depository Institutions 3505 Fall 2014
Problems:
1. A bank is planning to make a loan of $5,000,000 with duration of 7.5 years to “Jumbo Manufacturing”, a young and aggressive firm. The loan rate is 12% and the servicing fee is 50 basis points. The bank estimates that with a probability of 95%, the risk premium on the loan will not increase by more than 4.2%. The average cost of funds for the bank is 10 percent. The bank manager wants to use the RAROC approach to make a decision on approval/rejection of the loan:
a. What is RAROC? Explain the concept theoretically.
b. How does this model use the concept of duration to measure the credit risk of a loan?
c. How is the expected change in the credit premium of the borrower measured?
d. What is LN in the RAROC equation? How is that measured?
e. Apply RAROC to the data on the above loan. Calculate each component of RAROC.
f. Should the bank approve the loan? Explain and show your work.
g. If you believe the loan should be approved, how much lower can the loan rate go for the loan to be still approved? If you believe the loan should not be approved, how much should the loan rate be raised for the loan to be approved?
Solutions:
D =7.5 cost of funds = 10% fee = 1/2 % LN = $5 M
Loan rate (R) = 12% CRP = increase in risk premium on loan = 4.2%
One year net income on loan = (.12 +.005 - .10) 5M = .125M
LN = loan risk or capital risk = -D x LN x CRP /(1+R) = - 7.5 (5) (.042)/(1.12) = 1.40625M
Note: We use the loan rate to discount the value, not the cost of funds. The degree of riskiness of the loan determines at what rate the value should be discounted to present value. If the loan rate changes, we have to also adjust the discount rate. For example, if we assess the loan at two different loan rates both numerator and denominator of RAROC will change. RAROC = one year net income on loan/ loan risk = (.12 +.005 - .10) 5/1.40625 = .125/1.40625 = 8.89 % < 10% Reject the loan.
RAROC
Problems:
1. A bank is planning to make a loan of $5,000,000 with duration of 7.5 years to “Jumbo Manufacturing”, a young and aggressive firm. The loan rate is 12% and the servicing fee is 50 basis points. The bank estimates that with a probability of 95%, the risk premium on the loan will not increase by more than 4.2%. The average cost of funds for the bank is 10 percent. The bank manager wants to use the RAROC approach to make a decision on approval/rejection of the loan:
a. What is RAROC? Explain the concept theoretically.
b. How does this model use the concept of duration to measure the credit risk of a loan?
c. How is the expected change in the credit premium of the borrower measured?
d. What is LN in the RAROC equation? How is that measured?
e. Apply RAROC to the data on the above loan. Calculate each component of RAROC.
f. Should the bank approve the loan? Explain and show your work.
g. If you believe the loan should be approved, how much lower can the loan rate go for the loan to be still approved? If you believe the loan should not be approved, how much should the loan rate be raised for the loan to be approved?
Solutions:
D =7.5 cost of funds = 10% fee = 1/2 % LN = $5 M
Loan rate (R) = 12% CRP = increase in risk premium on loan = 4.2%
One year net income on loan = (.12 +.005 - .10) 5M = .125M
LN = loan risk or capital risk = -D x LN x CRP /(1+R) = - 7.5 (5) (.042)/(1.12) = 1.40625M
Note: We use the loan rate to discount the value, not the cost of funds. The degree of riskiness of the loan determines at what rate the value should be discounted to present value. If the loan rate changes, we have to also adjust the discount rate. For example, if we assess the loan at two different loan rates both numerator and denominator of RAROC will change. RAROC = one year net income on loan/ loan risk = (.12 +.005 - .10) 5/1.40625 = .125/1.40625 = 8.89 % < 10% Reject the loan.
RAROC