A bank offers your firm a revolving credit arrangement for up to $70 million at

Question

A bank offers your firm a revolving credit arrangement for up to $70 million at an interest rate of 1.75 percent per quarter. The bank also requires you to maintain a compensating balance of 5 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 1.10 percent per quarter, and assume that the bank uses compound interest on its revolving credit loans.

A bank offers your firm a revolving credit arrangement for up to $70 million at an interest rate of 1.75 percent per quarter. The bank also requires you to maintain a compensating balance of 5 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 1.10 percent per quarter, and assume that the bank uses compound interest on its revolving credit loans. 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? b. What is your effective annual interest rate on the lending arrangement if you borrow $36 million immediately and repay it in one year? c. What is your effective annual interest rate if you borrow $70 million immediately and repay it in one year?

Explanation / Answer

a. Effective Annual Interest Rate (the Opportunity Cost) on the revolving Credit Arrangement:

Quarterly Interest on Bank Investment Account: 1.10% Per Quarter

EAR = (1 + i / n)n -1

i = 1.10 x 4 = 4.40%, n = 4

EAR = (1 + 4.40 / 4)4 - 1

EAR = 4.47%

b. Amount Borrowed = $36 million

Compensating Balance required in Non - Bearing Interest Account: Unused Amount = 70-36 = 34 million

34,000,000 x 5% = $1,700,000

EAR on $36 million = (1 + 0.0175)4 - 1

EAR = 7.19%

EAR on Opportunity Cost of 1,700,000 = 4.47%

Proportion of Amount deposited in Non interest Bearing Account = 1.7 / 36 = 4.722222%

Opportunity Cost on Non Interest Bearing Account = 4.722222 x 0.0447 = 0.21108332

Total EAR = 7.19 + 0.21108332 = 7.40%

c. EAR on borrowing of $70 million = 7.19%

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