In exchange for a $400 million fixed commitment line of credit, your firm has ag
ID: 2737096 • Letter: I
Question
In exchange for a $400 million fixed commitment line of credit, your firm has agreed to do the following: Pay 1.83 percent per quarter on any funds actually borrowed. Maintain a 3 percent compensating balance on any funds actually borrowed. Pay an up-front commitment fee of 0.28 percent of the amount of the line. Required: 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. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Effective annual rate % (b) Suppose your firm immediately uses S213 million of the line and pays it off in one year. What is the effective annual interest rate on this $213 million loan? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Effective annual rate %Explanation / Answer
a.To answer this part, we first need to calculate the EAR without compensating balance.
Formula: EAR = (1+i/n)n-1
Where, i = annual interest rate and n = number of compounding every year
=> EAR = (1+0.183)4 – 1 = 0.075234 or 7.5234%
Compensating Balance is a percentage amount of the borrowed amount, which you can’t withdraw from the approved loan. So, let’s assume, we borrow entire approved amount that is $400 million
Payable interest = $400,000,000 x 7.5234% = $30,093,586.44
Actual amount received from loan = $400,000,000 – 3% of $400,000,000 = $388,000,000
Applicable EAR = $30,093,586.44 / $388,000,000 = 0.077561 or 7.7561%
b. Up front commitment fee paid = $213,000,000 x 0.28% = $596,400
Annual Interest paid = $213,000,000 x 7.5234% = $16,024,834.78
Total amount paid on borrow fund = $16,024,834.78 + $596,400 = $16,621,234.78
Actual amount received from loan = $213,000,000 – 3% of $213,000,000 = $206,610,000
Effective Annual Interest on this loan = $16,621,234.78 / $206,610,000 = 0.080447 or 8.0447%