Question

Fernandez has applied for a revolving credit line of $ 9 million to assist in marketing a new product line. The terms of the loan will be as follows:

(a) All the loans will be discount loans.

(b) A fixed commitment fee of 0.2 percent will be charged.

(c) The compensatory balance requirements will be 3 percent on the total credit line and 2 percent on the outstanding loans.

(d) The bank will pay 1 percent interest on demand deposits.

(e) The rate of interest to be charged will be the prime rate plus 3 percent.

(f) The bank will use the "actual/360" accrual method to compute interest payments.

(g) The credit line will be extended for a period of three years.

The loan officer estimates that Mr. Fernandez will use about 53 percent of the credit line on average. If the prime rate is 10 percent and the required reserve rate on demand deposits is 17 percent.

What is the effective cost to Mr. Fernandez?

Enter your answer in decimals, keep 4 decimal places (e.g., enter 15.12% as .1512).

Answer 1

To start with a few basic definitions for terms used in the question:

1. Discount Loan - A short term loan where interest is charged upfront before loan amount is disbursed. Borrower is then supposed to pay the full principle disbursed.

2. Commitment Fee - Fee charged by lender for the commitment to lend money to the borrower. For a revolving line of credit, commitment fee is calculated as Average Unused Commitment * Commitment Fee

Commitment Fee Amount = % Commitment Fee * Unused Credit Line * Credit Line,

where, unused credit = 100% - Avg credit line used = 100% - 53% = 47%

so, Commitment Fee =0.2%*47%*9 = 0.01

3. Compensatory Balance Required - Its a safety balance required by lender that can be used to offset loan. Its kept as deposit by lender

Compensatory balance = 3% of Total Credit Line + 2% of outstanding loan = 3% * 9 + 2% * 53% * 9 = 0.3654

4. Interest earned on compensatory balance = Compensatory Balance * 1% = 0.003654

5. Interest rate as actual/360 method = 13% (prime rate + 3%)

So, effective annual interest rate = 13%*365/360 = 13.18%

So, Interest Expense = 13.18% * 53% * 9 = 0.628686

6. So the Total cost to Mr. Fernandez is

= Commitment Fee + Interest Expense - Interest Income

= 0.01 + 0.628686 - 0.003654

=0.635032

7. Principle amount used to Mr Fernandez

= Used Credit Line - Interest Expense - Compensatory Balance Required *(1- reserve rate of 17%)

= 53% * 9 - 0.628686 - 0.3654 * (1-0.17)

=3.838032

So effective interest rate = Total Cost of Credit / Available Credit

=0.635032/3.838032

=16.55% or 0.1655 (This is the answer to the problem)

Please note that this kind of problems are not really dependent on dollar value of credit line available

Quick Solution will be = Total Cost of Credit / Credit

Total Cost of Credit= (Interest Expense on used credit Line + Commitment Fee - Interest Income on compensatory balance)

Available Credit = Used Credit Line - Interest Expense - (1- reserve rate)*compensatory balance