Question

A bank offers your firm a revolving credit arrangement for up to $78 million at an interest rate of 1.95 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 non-interest-bearing account. Assume you have a short-term investment account at the bank that pays 1.30 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 $44 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 $78 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

Solution:

a)Calculation of EAR(Effective annual Interest rate)

EAR=[1+Periodic rate of interest on short term investment account]^no.of period-1

=[1+0.013]^4-1

=0.0530 or 5.30%

b)In the given case,interest on loan shall includes the opportunity cost of the compensating balance.Opportunity cost is;

=[%compensating balance(Credit arrangement-Amount boorowed)*(1+0.013)^4]-[%compensating balance(Credit arrangement-Amount boorowed]

=[0.06*($78000,000-$44,000,000)*1.013^4]-[0.06($78000,000-$44000,000]

=$108,166.55

Interest on loan =[$44000,000*(1.0195)^4]-$44000,000

=$3533,697.38

EAR=Interest/Loan Amount

=($108,166.55+$3533,697.38)/$44000,000

=0.0828 or 8.28%

c)Calculation of EAR

EAR=[1+Periodic Interest rate for credit arrangement]^no. of a period-1

=[1+0.0195]^4-1

=0.0803 or 8.03%