In exchange for a $400 million fixed commitment line of credit, your firm has ag
ID: 2735182 • 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: Ignoring the commitment fee, what is the effective annual interest rate on this line of credit? Suppose your firm immediately uses $213 million of the line and pays it off in one year. What is the effective annual interest rate on this S213 million loan?Explanation / Answer
a)
EAR = [(1+APR÷n)^n-1]÷(1-Compensating balance)
APR is annual percentage rate
n is number of compounding per year
= [(1+1.83%)^4-1]÷(1-3%)
= 7.76%
b)
Total interest expense:
= $213,000,000×[(1+1.83%)^4-1]÷(1-3%)
= $16,520,448.23
Commitment fee:
= $400,000,000×0.28%
= $1,120,000
Total commitment fee and interest expense:
= $1,120,000+$16,520,448.23
= $17,640,448.23
Effective interest rate:
= $17,640,448.23÷($213,000,000×(1-3%)-$1,120,000)
= $17,640,448.23÷205,490,000
= 8.58%