Question

In exchange for a $400 million fixed commitment line of credit, your firm has agreed to do the following:

1. Pay 1.97 percent per quarter on any funds actually borrowed.
2. Maintain a 1 percent compensating balance on any funds actually borrowed.
3. Pay an up-front commitment fee of 0.23 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 $227 million of the line and pays it off in one year. What is the effective annual interest rate on this $227 million loan? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
  
Effective annual rate             %

Answer 1

a). Effective Annual Interest Rate = [(1 + Interest per period)^(Number of compounding periods in a year)] -1

= [1.0197]⁴ - 1 = 1.0812 - 1 = 0.0812, or 8.12%

b). 5% Compensating Balance = $227 x 0.05 = $11.35 million

Upfront Commitment Fee = 0.23% x 227 = $522,100

Amount Availed = Loan Amount - Compensating Balance - Upfront Commitment Fee

= $227,000,000 - $11,350,000 - $522,100 = $215,127,900

Interest Cost = $227,000,000 * 8.12% = $18,423,154.77

EAR = $18,423,154.77 / $215,127,900 = 0.0856, or 8.56%