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

Question:

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

1. Pay 1.82 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 0.27 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?

b) Suppose your firm immediately uses $212 million of the line and pays it off in one year. What is the effective annual interest rate on this $212 million loan?

Effective Annual Interest Rate:

The actual interest rate that an investment is earning is called effective annual interest rate. To calculate the effective rate, number of compounding during a one year is considered.

Answer and Explanation:

Given data:

Line of credit = $400,000,000

Interest rate = 1.82% per quarter

Commitment fee = 0.27%

Compensating balance = 1%

Loan amount = $212,000,000

Calculation:

a)

{eq}Effective \ annual \ interest \ rate \ = \ \dfrac{\left ( 1 \ + \ Interest \ rate \right )^4 \ - \ 1}{1 \ - \ Compensating \ balance} \\ Effective \ annual \ interest \ rate \ = \ \dfrac{\left ( 1 \ + \ 1.82\% \right )^4 \ - \ 1}{1 \ - \ 1\%} \\ Effective \ annual \ interest \ rate \ = \ \dfrac{\left ( 1 \ + \ 0.0182 \right )^4 \ - \ 1}{1 \ - \ 0.01} \\ Effective \ annual \ interest \ rate \ = \ \dfrac{\left ( 1.0182 \right )^4 \ - \ 1}{0.99} \\ Effective \ annual \ interest \ rate \ = \ \dfrac{1.07481 \ - \ 1}{0.99} \\ Effective \ annual \ interest \ rate \ = \ \dfrac{0.07481}{0.99} \\ Effective \ annual \ interest \ rate \ = \ 0.07556 \ or \ 7.556\% {/eq}


b)

{eq}Interest \ paid \ = \ \left ( Loan \ amount \ \times \ \left ( 1 \ + \ Interest \ rate \right )^4 \right ) \ - \ Loan \ amount \\ Interest \ paid \ = \ \left ( 212,000,000 \ \times \ \left ( 1 \ + \ 1.82\% \right )^4 \right ) \ - \ 212,000,000 \\ Interest \ paid \ = \ \left ( 212,000,000 \ \times \ \left ( 1 \ + \ 0.0182 \right )^4 \right ) \ - \ 212,000,000 \\ Interest \ paid \ = \ \left ( 212,000,000 \ \times \ 1.0182^4 \right ) \ - \ 212,000,000 \\ Interest \ paid \ = \ 227,860,072.76 \ - \ 212,000,000 \\ Interest \ paid \ = \ \$15,860,072.76 {/eq}


Amount received = ((1 - Compensating balance) * Loan amount) - (Commitment fee * Line of credit)

Amount received = ((1 - 1%) * 212,000,000) - (0.27% * 400,000,000)

Amount received = ((1 - 0.01) * 212,000,000) - (0.0027 * 400,000,000)

Amount received = (0.99 * 212,000,000) - 1,080,000

Amount received = 209,880,000 - 1,080,000

Amount received = $208,800,000


{eq}Effective \ annual \ interest \ rate \ = \ \dfrac{Interest \ paid}{Amount \ received} \ \times \ 100 \\ Effective \ annual \ interest \ rate \ = \ \dfrac{15,860,072.76}{208,800,000} \ \times \ 100 \\ Effective \ annual \ interest \ rate \ = \ 7.596\% {/eq}


Learn more about this topic:

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Real Interest Rate: Definition & Calculation

from Intro to Business: Help and Review

Chapter 25 / Lesson 5
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