Question

Hi, I am not able to find the correct steps and answers to solve this problem. Please help. Thanks!

A bank offers your firm a revolving credit arrangement for up to $61 million at an interest rate of 1.48 percent per quarter. The bank also requires you to maintain a compensating balance of 2 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 .89 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? EAR: %

(b) What is your effective annual interest rate on the lending arrangement if you borrow $35 million immediately and repay it in one year? EAR: %

(c) What is your effective annual interest rate if you borrow $61 million immediately and repay it in one year? EAR: %

Answer 1

a). EAR = [1 + r]^m - 1 = [1.0089]⁴ - 1 = 1.0361 - 1 = 0.0361, or 3.61%

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 = [0.02($61,000,000 – $35,000,000)(1.0089)⁴] – [0.02($61,000,000 – $35,000,000)]

= $538,760.60 - $520,000 = $18,760.60

And the interest you will pay to the bank on the loan is:

Interest cost = $35,000,000(1.0148)⁴ – $35,000,000 = $37,118,453.93 – $35,000,000 = $2,118,453.93

So, the EAR of the loan in the amount of $35,000,000 is:

EAR = [$18,760.60 + $2,118,453.93] / $35,000,000 = $2,137,214.54 / $35,000,000 = 6.11%

c). EAR = 1.0148⁴ - 1 = 1.0605 - 1 = 0.0605, or 6.05%