Chapter 8, Problem 25P

Harper Engine Company needs $\text{\$631,000}$ to take a cash discount of 2.5/20, net 75. A banker will lend the money for 55 days at an interest cost of $\text{\$13,300}$ .

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

b. How much would it cost (in percentage terms) if Harper did not take the

cash discount but paid the bill in 75 days instead of 20 days?

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

d. If another banker requires a 10 percent compensating balance, how much must Harper borrow to end up with $\text{\$631,000}$ ?

e. What would be the effective interest rate in part d if the interest charge for 55 days were $\text{\$10,100}$ ? Should Harper borrow with the 10 percent compensating balance? (There are no funds to count against the compensating balance requirement.)

Summary Introduction

To calculate: The effective rate of interest for Harper Engine Company.

Introduction:

Effective rate:

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

Answer to Problem 25P

The effective rate of interest on the loan for Harper Engine Company is 13.82%.

Explanation of Solution

Calculation of the effective rate of interest:

$\begin{array}{c}\text{Effective Rate of Interest = }\frac{\text{Interest}}{\text{Principal}}\text{×}\frac{\text{Days in the year (360)}}{\text{Days Loan is Outstanding}}\\ =\frac{\$13,300}{\$631,000}\times \frac{360}{55}\\ =2.11\%\times 6.55\\ =13.82\%\end{array}$

$$ $$

Summary Introduction

To calculate: The cost of the discount lost for Harper Engine Company.

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 25P

The cost of lost discount for Harper Engine Company is 16.77%.

Explanation of Solution

Calculation of the cost of not availing a cash discount:

$\begin{array}{c}\text{Cost of lost Discount}=\frac{\text{Discount\%}}{\text{100\% }-\text{ Discount\%}}\times \frac{360}{\text{Final Due Date }-\text{ Discount Period}}\\ =\frac{2.50\%}{100\%-2.50\%}\times \frac{360}{\left(75-20\right)}\\ =2.56\%\times 6.55\\ =16.77\%\end{array}$

Summary Introduction

To calculate: Whether Harper Engine Company should borrow funds on the basis of the terms of the cash discount.

Introduction:

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 to be charged on an investment and a loan over a specific period of time.

Answer to Problem 25P

Yes, the funds should be borrowed and the cash discount shall be availed by Harper Engine Company as the cost of taking the loan, that is, 13.82%, is lower than the cost of not taking the discount, that is, 16.77%.

Explanation of Solution

Calculation of the effective rate of interest:

$\begin{array}{c}\text{Effective Rate of Interest = }\frac{\text{Interest}}{\text{Principal}}\text{×}\frac{\text{Days in the year}}{\text{Days Loan is Outstanding}}\\ =\frac{\$13,300}{\$631,000}\times \frac{360}{55}\\ =2.11\%\times 6.55\\ =13.82\%\end{array}$

Calculation of the cost of not availing a cash discount:

$\begin{array}{c}\text{Cost of lost Discount}=\frac{\text{Discount\%}}{\text{100\%}-\text{Discount\%}}\times \frac{360}{\text{Final Due Date}-\text{Discount Period}}\\ =\frac{2.50\%}{100\%-2.50\%}\times \frac{360}{\left(75-20\right)}\\ =2.56\%\times 6.55\\ =16.77\%\end{array}$

Summary Introduction

To calculate: The amount that Harper Engine Company should borrow to have $631,000.

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 25P

The amount to be borrowed by Harper Engine Company is $701,111.

Explanation of Solution

Calculation of the amount to be borrowed:

$\begin{array}{c}\text{Amount to be Borrowed }=\frac{\text{Amount needed}}{\left(1-C\right)}\\ =\frac{\$631,000}{\left(1-0.10\right)}\\ =\frac{\$631,000}{0.90}\\ =\$701,111\end{array}$

Summary Introduction

To calculate: The effective rate of interest, and determine whether Harper Engine Company should borrow with a compensating balance of 10%.

Introduction:

Effective rate:

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

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 25P

The effective rate of interest is 10.48%.

Yes, the funds should be borrowed and the cash discount should be availed by Harper Engine Company as the cost of taking the loan, that is, 10.48%, is lower than the cost of not availing the discount, that is, 16.77%.

Explanation of Solution

Calculation of the effective rate of interest:

$\begin{array}{c}\text{Effective Rate of Interest = }\frac{\text{Interest}}{\text{Principal}-\text{Compensating Balance}}\text{×}\frac{\text{Days in the year}}{\text{Days Loan is Outstanding}}\\ =\frac{\$10,100}{\$631,000}\times \frac{360}{55}\\ =1.60\%\times 6.55\\ =10.48\%\end{array}$