A bank offers your firm a revolving credit arrangement for up to $63 million at

Question

A bank offers your firm a revolving credit arrangement for up to $63 million at an interest rate of 1.46 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 noninterest-bearing account. Assume you have a short-term investment account at the bank that pays .87 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. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

What is your effective annual interest rate on the lending arrangement if you borrow $37 million immediately and repay it in one year? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

What is your effective annual interest rate if you borrow $63 million immediately and repay it in one year? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

A bank offers your firm a revolving credit arrangement for up to $63 million at an interest rate of 1.46 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 noninterest-bearing account. Assume you have a short-term investment account at the bank that pays .87 percent per quarter, and assume that the bank uses compound interest on its revolving credit loans.

Explanation / Answer

a. The EAR of your investment account is:
Effective Annual Rate = (1+ stated Interest rate)^ number of compounding period - 1
Effective Annual Rate = (1+ 0.87%)^4 -1 = 3.53%

b.

To calculate the EAR of the loan, we can divide the interest on the loan by the amount of the loan. The interest on the loan includes the opportunity cost of the compensating balance. The opportunity cost is the amount of the compensating balance times the potential interest rate you could have earned. The compensating balance is only on the unused portion of the credit line, so:

Opportunity cost = .06($63,000,000 – 37,000,000)(1+ 0.87%)^4 – .06($63,000,000 – 37,000,000)      Opportunity cost = $55,000.58
And the interest you will pay to the bank on the loan is:                 

Interest cost = $37,000,000(1+1.46%)^4 – 37,000,000

Interest cost = $2,208,583.80
EAR = ($55,000.58 + $2,208,583.80)/$37,000,000 = 6.12%   

c.
Effective Annual Rate = (1+ stated Interest rate)^ number of compounding period - 1
Effective Annual Rate = (1+ 1.46%)^4 -1 = 5.97%

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