Question

In exchange for a $400 million fixed commitment line of credit, your firm has agreed to do the following: Pay 1.84 percent per quarter on any funds actually borrowed. Maintain a 2 percent compensating balance on any funds actually borrowed. Pay an up-front commitment fee of 0.29 percent of the amount of the line. Based on this information, answer the following: a. Ignoring the commitment fee, what is the effective annual interest rate on this line of credit? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Effective annual rate % b. Suppose your firm immediately uses $214 million of the line and pays it off in one year. What is the effective annual interest rate on this $214 million loan? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a. Loan Amount = $400

Interest (Quarterly) % = 1.84%

Compensating Balance = 2%

Ignoring the commitment fee, the effective annual interest rate would be:

(((1+interest rate) ^4)-1)/ (1-compensating balance %)

(((1+0.0184) ^4)-1)/ (/1-.02)=7.72%

b. Now if the firm uses $214million of the total of the line credit of $400million then effective annual interest rate would be:

Interest Paid Annually = $214*((1.0184)*4)-1) % = $16.19

Amount Received = (1- compensating % balance)* Amount borrowed – commitment fee * line of credit

Amount Received = $214*(0.98) - $400*0.29% = $208.56

Effective annual interest rate = ($16.19/$208.56)*100

Or, Effective annual interest rate = 7.76%