Question

A bank offers your firm a revolving credit arrangement for up to $66 million at an interest rate of 1.65 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 non-interest-bearing account. Assume you have a short-term investment account at the bank that pays 1.00 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? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b.	What is your effective annual interest rate on the lending arrangement if you borrow $34 million immediately and repay it in one year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
c.	What is your effective annual interest rate if you borrow $66 million immediately and repay it in one year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

     

Answer 1

(a)The effective annual interest rate  is:

EAR =( 1.01)⁴– 1

EAR = 0.04060 or 4.06%

(b)

The effective annual interest rate of the loan is calculated by dividing the interest on the loan by the loan amount. But the interest on loan also includes the opportunity cost of the compensating balance and the opportunity cost of compensating balance is the amount of the compensating balance times the potential interest rate earned. The compensating balance is the balance which is not used from the available balance of the credit line, so:

Opportunity cost = 0.02($66,000,000 –$ 34,000,000)(1.01)⁴– 0.02 ($66,000,000 – $34,000,000)

Opportunity cost = $665,986.56 - $ 640,000 = $ 25,986.56

And the interest paid to the bank on the loan amount is:

Interest cost = $34,000,000(1.0165)⁴– $ 34,000,000

Interest cost = $ 36,300,152.45 = $ 34,000,000 = $2,300,152.45

So, the EAR of the loan in the amount of $34,000,000 is calculated as:

EAR = ($ 25,986.56 + $2,300,152.45)/$34,000,000

EAR = $ 2,326,139 / $ 34,000,000

EAR = 0.0684 or 6.84%

(c)

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

EAR = (1.0165 )⁴– 1

EAR = 0.06765 or 6.77%