A bank offers your firm a revolving credit arrangement for up to $72 million at

Question

A bank offers your firm a revolving credit arrangement for up to $72 million at an interest rate of 1.80 percent per quarter. The bank also requires you to maintain a compensating balance of 6 percent against the unused portion of the credit line, to be deposited in a non-interest-bearing account. Assume you have a short-term investment account at the bank that pays 1.15 percent per quarter, and assume that the bank uses compound interest on its revolving credit loans.

What is your effective annual interest rate (an opportunity cost) on the revolving credit arrangement if your firm does not use it during the year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What is your effective annual interest rate on the lending arrangement if you borrow $38 million immediately and repay it in one year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What is your effective annual interest rate if you borrow $72 million immediately and repay it in one year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

A bank offers your firm a revolving credit arrangement for up to $72 million at an interest rate of 1.80 percent per quarter. The bank also requires you to maintain a compensating balance of 6 percent against the unused portion of the credit line, to be deposited in a non-interest-bearing account. Assume you have a short-term investment account at the bank that pays 1.15 percent per quarter, and assume that the bank uses compound interest on its revolving credit loans.

Explanation / Answer

a. What is your effective annual interest rate (an opportunity cost) on the revolving credit arrangement if your firm does not use it during the year?

Solution-

Effective annual interest rate = (1 + 0.0115)4 - 1

Effective annual interest rate = 0.04679 or 4.67%

b. What is your effective annual interest rate on the lending arrangement if you borrow $38 million immediately and repay it in one year?

Solution-

Opportunity cost = .06($72,000,000 – $38,000,000)(1.0115)4 – .06($72,000,000 – $38,000,000)

Opportunity cost = $95,471.18

Interest pay on the loan to the bank......

Interest cost = $38,000,000(1.018)4 – 38,000,000

Interest cost = $2,810,762.45

Effective annual interest rate of the loan in the amount of $38 million is:

Effective annual interest rate= ($2,810,762.45+ $95,471.18) / $38,000,000

Effective annual interest rate = .0765 or 7.65%

c. What is your effective annual interest rate if you borrow $72 million immediately and repay it in one year?

Solution-

Effective annual interest rate of a loan (full credit line)........

Effective annual interest rate = (1.018)4 -1

Effective annual interest rate = 0.0739 or 7.39%

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