Assume a bank grants a loan commitment at an interest rate of 10% per annum and the risk premium on the loan is 2%.The bank charges borrowers an upfront fee on the whole commitment of 0.25% and a back-end fee on any unused proportion of the loan of 0.5%.The compensating balance is 10% and so are reserve requirements.Assume that the average draw-down of the loan is 80% over the time of the loan commitment.What is the promised return on the loan commitment (round to two decimals)?

Question

Quizplus · Accepted Answer

To calculate the promised return on the loan commitment, we need to take into account all the fees and requirements mentioned in the question. Here are the steps to follow:

1. Calculate the effective interest rate:
- Interest rate: 10%
- Risk premium: 2%
- Effective interest rate = 10% + 2% = 12%

2. Calculate the amount of compensating balance required:
- Loan commitment: the amount is not given in the question, so let's assume $100.
- Compensating balance: 10%
- Amount of compensating balance required = Loan commitment x Compensating balance = $100 x 10% = $10

3. Calculate the upfront fee:
- Upfront fee: 0.25%
- Amount of upfront fee = Loan commitment x Upfront fee = $100 x 0.25% = $0.25

4. Calculate the back-end fee:
- Back-end fee: 0.5%
- Amount of back-end fee = unused proportion of the loan x Back-end fee = (1-0.8) x $100 x 0.5% = $0.50

5. Calculate the reserve requirement:
- Reserve requirement: 10%
- Amount of reserve required = Loan commitment x Reserve requirement = $100 x 10% = $10

6. Calculate the total cost of the loan:
- Total cost of the loan = upfront fee + back-end fee + amount of compensating balance + amount of reserve required = $10.75

7. Calculate the net amount received by the borrower:
- Net amount received by the borrower = Loan commitment - total cost of the loan = $100 - $10.75 = $89.25

8. Calculate the promised return on the loan commitment:
- Promised return on the loan commitment = (Interest earned - Interest paid) / Amount received by the borrower
- Interest earned = Loan commitment x Effective interest rate x Average draw-down = $100 x 12% x 80% = $9.60
- Interest paid = $0.25 (upfront fee) + $0.50 (back-end fee) = $0.75
- Promised return on the loan commitment = ($9.60 - $0.75) / $89.25 = 0.1067 or 10.67% (rounded to two decimals)

However, we need to add the risk premium to this promised return to get the final answer:
Promised return on the loan commitment + Risk premium = 10.67% + 2% = 12.67% (rounded to two decimals)

The only answer choice that comes close to this result is D) 13.67%. We can see that this answer choice is incorrect, as it is higher than the effective interest rate. Therefore, the best choice is:

Answer: D
 The promised return on the loan commitment is 10.67% (rounded to two decimals). None of the answer choices is correct.

Assume a Bank Grants a Loan Commitment at an Interest