In exchange for a $400 million fixed commitment line of credit, your firm has ag
ID: 2736944 • Letter: I
Question
In exchange for a $400 million fixed commitment line of credit, your firm has agreed to do the following:
Ignoring the commitment fee, the effective annual interest rate on this line of credit is 7.83%
Suppose your firm immediately uses $211 million of the line and pays it off in one year. What is the effective annual interest rate on this $211 million loan?
In exchange for a $400 million fixed commitment line of credit, your firm has agreed to do the following:
1. Pay 1.81 percent per quarter on any funds actually borrowed. 2. Maintain a 5 percent compensating balance on any funds actually borrowed. 3. Pay an up-front commitment fee of 0.26 percent of the amount of the line.Ignoring the commitment fee, the effective annual interest rate on this line of credit is 7.83%
Suppose your firm immediately uses $211 million of the line and pays it off in one year. What is the effective annual interest rate on this $211 million loan?
Explanation / Answer
Interest = $1(0.0181) = 0.0181
We also must maintain a compensating balance of 5% of the funds borrowed, so for each dollar borrowed, we will only receive:
Amount received = $1(1-0.05) = $0.95
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 = [(1.0181)^4-1]/(1-0.05)
[1.0744-1]/0.95
0.0783 or 7.83%
b) effective interest rate is computed:
(Interest cost + Commitment fee)/(Amount drawn down - Commitment fee) = Effective interest rate
Interest cost = 1.81% quarterly on 211 million = 3.85 million
Commitment fees = 0.26% of balance = 0.26% of (400-211) = 0.49
($3.85 + $0.49)/($211 - $0.49) = 4.34/ 210.51 = 2.06%