Question

In exchange for a $580 million fixed commitment line of credit, your firm has agreed to do the following:

1.	Pay 2 percent per quarter on any funds actually borrowed.
2.	Maintain a 3 percent compensating balance on any funds actually borrowed.
3.	Pay an up-front commitment fee of .17 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. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Effective annual interest rate

%

b.	Suppose your firm immediately uses $250 million of the line and pays it off in one year. What is the effective annual interest rate on this $250 million loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Effective annual interest rate

%

Answer 1

Answers:

a) 8.45%

b) 8.62%

Explanation:

a.

For every dollar borrowed, you pay interest of:

Interest = $1[(1 + .020)⁴− 1]

Interest = $.082

You also must maintain a compensating balance of 4 percent of the funds borrowed, so for each dollar borrowed, you will only receive:

Amount received = $1(1 − .03)

Amount received = $.97

We can adjust the EAR equation we have been using to account for the compensating balance by dividing the EAR by one minus the compensating balance, so:

EAR = [(1.010)4− 1]/(1 − .04)

EAR = .082 / .97

AR = .0845, or 8.45%

.

b.

The EAR is the amount of interest paid on the loan divided by the amount received when the loan is originated. The amount of interest you will pay on the loan is the amount of the loan times the effective annual interest rate, so:

Interest = $250,000,000[(1.020)⁴− 1]

Interest = $20,608,040

For whatever loan amount you take, you will only receive 97 percent of that amount since you must maintain a 3 percent compensating balance on the portion of the credit line used. The credit line also has a fee of .170 percent, so you will only get to use:

Amount received = .97($250,000,000) − .0017($580,000,000)

Amount received = $239,014,000

So, the EAR of the loan is:

EAR = $20,608,040/$239,014,000

EAR = .0862, or 8.62%