Chapter 8, Problem 24P

Neveready Flashlights Inc. needs $\text{\$340,000}$ to take a cash discount of 3/17, net 72. A banker will lend the money for 55 days at an interest cost of $\text{\$10,400}$ .

a. What is the effective rate on the bank loan?

b. How much would it cost (in percentage terms) if the firm did not take the cash discount, but paid the bill in 72 days instead of 17 days?

c. Should the firm borrow the money to take the discount?

d. If the banker requires a 20 percent compensating balance, how much must the firm borrow to end up with the $\text{\$340,000}$ ?

e. What would be the effective interest rate in part d if the interest charge for 55 days were $\text{\$13,000}$ ? Should the firm borrow with the 20 percent compensating balance? (The firm has no funds to count against the compensating balance requirement.)

Summary Introduction

To calculate: The effective rate of interest for Neveready Flashlights Inc.

Introduction:

Effective interest rate

Also termed as annual equivalent rate, it is the rate actually charged on an investment or a loan over a specific time period.

Answer to Problem 24P

The effective rate of interest on the loan is 20.04% for Neveready Flashlights Inc.

Explanation of Solution

Calculation of the effective rate of interest:

$\begin{array}{c}\text{Effective Rate of Interest = }\frac{\text{Interest}}{\text{Principal}}\text{×}\frac{\text{Days in the year (360)}}{\text{Days Loan is Outstanding}}\\ =\frac{\$10,400}{\$340,000}\times \frac{360}{55}\\ =3.06\%\times 6.55\\ =20.04\%\end{array}$

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Summary Introduction

To calculate: The cost of the discount lost for Neveready Flashlights Inc.

Introduction:

Cash Discount:

Also known as early payment discount, it is given by the seller to procure early cash payments from customers.

Answer to Problem 24P

The cost of the discount lost is 20.24% for Neveready Flashlights Inc.

Explanation of Solution

The calculation of the cost of not availing a cash discount:

$\begin{array}{c}\text{Cost of lost Discount}=\frac{\text{Discount\%}}{\text{100\% }-\text{ Discount\%}}\times \frac{360}{\text{Final Due Date }-\text{ Discount Period}}\\ =\frac{3\%}{100\%-3\%}\times \frac{360}{72-17}\\ =\frac{3\%}{97\%}\times \frac{360}{55}\\ =3.09\%\times 6.55\\ =20.24\%\end{array}$

Summary Introduction

To determine: Whether Neveready Flashlights Inc. should borrow funds on the basis of the terms of the cash discount.

Cash Discount:

Also known as early payment discount, it is given by the seller to procure early cash payments from customers.

Effective interest rate:

Also termed as annual equivalent rate, it is the rate actually charged on an investment or a loan over a specific time period.

Answer to Problem 24P

Yes, the funds should be borrowed and the cash discount should be availed by Neveready Flashlights Inc. as the cost of taking the loan, that is, 20.04%, is lower than the cost of not availing the discount, that is, 20.24%.

Explanation of Solution

Calculation of the effective rate of interest:

$\begin{array}{c}\text{Effective Rate of Interest = }\frac{\text{Interest}}{\text{Principal}}\text{×}\frac{\text{Days in the year (360)}}{\text{Days Loan is Outstanding}}\\ =\frac{\$10,400}{\$340,000}\times \frac{360}{55}\\ =3.06\%\times 6.55\\ =20.04\%\end{array}$

Calculation of the cost of not availing a cash discount:

$\begin{array}{c}\text{Cost of lost Discount}=\frac{\text{Discount\%}}{\text{100\% }-\text{ Discount\%}}\times \frac{360}{\text{Final Due Date }-\text{ Discount Period}}\\ =\frac{3\%}{100\%-3\%}\times \frac{360}{72-17}\\ =\frac{3\%}{97\%}\times \frac{360}{55}\\ =3.09\%\times 6.55\\ =20.24\%\end{array}$

Summary Introduction

To calculate: The amount that Neveready Flashlights Inc. should borrow to have $ 340,000.

Introduction:

Compensating Balance:

Also known as offsetting balance, it is the minimum balance that the borrowing company needs to maintain in its bank account. This benefits the lender by lowering their cost of lending.

Answer to Problem 24P

The amount to be borrowed by Neveready Flashlights Inc. is $425,000

Explanation of Solution

Calculation of the amount to be borrowed:

$\begin{array}{c}\text{Amount to be Borrowed }=\frac{\text{Amount needed}}{\left(1-C\right)}\\ =\frac{\$340,000}{\left(1-.20\right)}\\ =\frac{\$340,000}{.80}\\ =\$425,000\end{array}$

Summary Introduction

To calculate: The effective rate of interest, and whether Neveready Flashlights Inc. should borrow with a 20% compensating balance.

Introduction:

Compensating Balance:

Also known as offsetting balance, it is the minimum balance that the borrowing company needs to maintain in its bank account. This benefits the lender by lowering their cost of lending.

Effective interest rate:

Also termed as annual equivalent rate, it is the rate actually charged on an investment or a loan over a specific time period.

Answer to Problem 24P

The effective rate of interest for Neveready Flashlights Inc. with a 20% compensating balance is 25.02% if an interest of $13,000 is charged for 55 days.

No, the funds should not be borrowed by Neveready Flashlights Inc. as the effective rate, that is, 25.02%, is greater than cash discount.

Explanation of Solution

Calculation of the effective rate of interest:

$\begin{array}{c}\text{Effective Rate of Interest = }\frac{\text{Interest}}{\text{Principal}-\text{Compensating Balance}}\text{ ×}\frac{\text{Days in the year }}{\text{Days Loan is Outstanding}}\\ =\frac{\$13,000}{\$425,000-\$85,000}\times \frac{360}{55}\\ =3.82\%\times 6.55\\ =25.02\%\end{array}$

Working Note:

Calculation of the compensating balance:

$\begin{array}{c}\text{Compensating Balance}=\text{Borrowings }\times 20\%\\ =\$425,000\times 20\%\\ =\$85,000\end{array}$

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