Question

A bank offers your firm a revolving credit arrangement for up to $68 million at an interest rate of 1.70 percent per quarter. The bank also requires you to maintain a compensating balance of 4 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 1.05 percent per quarter, and assumes that the bank uses compound interest on its revolving credit loans. (Do not round intermediate calculations. Round the final answers to 2 decimal places.)
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?

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

Effective annual interest rate %
c. What is your effective annual interest rate if you borrow $68 million immediately and repay it in one year?

Answer 1

Answer:

a) 4.27 %

b) 7.14%

c)  6.97%

Explanation:

a)

The effective annual interest rate (EAR) of your investment account is:

EAR = 1.0105⁴ – 1

EAR = 0.0427

EAR = 4.27 %

b)

The effective annual interest rate on the lending arrangement can be determined by the division of the interest on the loan by the amount of the loan.

Now to determine the interest cost on the loan ; we need to first find the opportunity cost of the compensation balace.

So;

opportunity cost of the compensation balace is as follows:

=  0.04 ($68,000,000 – $ 35,00,000) (1.0105)⁴ – 0.04 ($68,00,000 – $35,000,000)

=  0.04 (33,000,000) × 1.04267 – 0.04 (33,000,000)

= 1,376,324.4 – 1,320,000

= $56,324.4

Interest Cost = 35,000,000 (1.0170)⁴ – 35,000,000

=35,000,000 × 1.069753735521– 35,000,000

=$2,441,380.74

Finally ; since we know the interest cost ; the EAR of the loan in the amount of $35,000,000 is :

EAR =  (56324.4 + 2441380.74 ) / 35,000,000

=0.0714

=  7.14%

c)

The compensating balance is only applied to the unused portion of the credit line, so the EAR of a loan on the full credit line is:

EAR = 1.0170⁴ – 1

=0.06975

= 6.97%