Question

In exchange for a $500 million fixed commitment line of credit, your firm has agreed to do the following:

1. Pay 2.0% per quarter on any funds actually borrowed.

2. Maintain a 4% compensating balance on any funds actually borrowed.

3. Pay an up-front commitment fee of 0.200% 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. Round the final answer to 2 decimal places.)

Effective annual interest rate             %

b. Suppose your firm immediately uses $200 million of the line and pays it off in one year. What is the effective annual interest rate on this $200 million loan? (Do not round intermediate calculations. Round the final answer to 2 decimal places.)

Effective annual interest rate

Answer 1

Answer : (a.) Calculation of Effective Annual Interest rate

Effective Annual Interest Rate = [(1 + r)^n - 1 ] / [ 1 - Compensating Balance]

where

r is the rate of interest per period i.e 2.0% per quarter or 0.02

n is the number of periods in a year i.e 4 (as there are 4 quarters in a year)

Effective Annual Interest Rate = [(1 + 0.02)^4 - 1 ] / [ 1 - 0.04]

= [1.08243216 - 1] / 0.96

= 0.08243216 / 0.96

= 0.0858668333 or 8.59%

(b.) Calculation of Effective Annual Interest rate

Effective Annual Interest rate = Interest / Amount Received

Interest = 200million * [(1 + 0.02)^4 - 1 ]

= 16.486432 million

Amount Received = Amount after compensating balance and after paying up front commitment fee

= [(1 - 0.04) * 200 million] - Upfront fees

= 192 million - [0.002 * 500 million]

= 192 million - 1 million

= 191 million

Effective Annual Interest rate = 16.486432 million / 191 million

= 0.0863 or 8.63%