Chapter 8, Problem 26P

Summit Record Company is negotiating with two banks for a $\text{\$151,000}$ loan. Fidelity Bank requires a 28 percent compensating balance, discounts the loan, and wants to be paid back in four quarterly payments. Southwest Bank requires a 14 percent compensating balance, does not discount the loan, but wants to be paid back in 12 monthly installments. The stated rate for both banks is 10 percent. Compensating balances will be subtracted from the $\text{\$151,000}$ in determining the available funds in part a.

a. Calculate the effective interest rate for Fidelity Bank and Southwest Bank. Which loan should Summit accept?

b. Recompute the effective cost of interest, assuming that Summit ordinarily maintains $\text{\$42,280}$ at each bank in deposits that will serve as compensating balances.

c. Does your choice of banks change if the assumption in part b is correct?

Summary Introduction

To calculate: The effective rate of interest for Summit Record Company, and determine whether Fidelity Bank or Southwest Bank should be chosen by the company.

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.

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 26P

The effective rate of interest for Fidelity Bank is 25.81% and that for Southwest Bank is 21.47%.

Thus, Southwest Bank should be chosen by the company as it has the lowest effective rate of interest.

Explanation of Solution

Calculation of the effective rate of interest for Fidelity Bank:

$\begin{array}{c}\text{Effective Interest Rate}=\frac{2\times \text{Annual No}\text{.Payments}\times \text{Interest}}{\begin{array}{l}\left(\text{Total no}\text{. of payments}+1\right)\\ \times \left(\begin{array}{l}\text{Principal}-\text{Compensating Balance}\\ -\text{Stated Compensating balance}\end{array}\right)\end{array}}\\ =\frac{2\times 4\times \$15,100}{\left(4+1\right)\times \left(\$151,000-\$42,280-\$15,100\right)}\\ =\frac{\$120,800}{\$468,100}\\ =25.81\%\end{array}$

Calculation of the effective rate of interest for Southwest Bank:

$\begin{array}{c}\text{Effective Intetrest Rate}=\frac{2\times \text{Annual No}\text{.Payments}\times \text{Interest}}{\left(\text{Total no}\text{. of payments}+1\right)\times \left(\text{Principal}-\text{ Compensating Balance}\right)}\\ =\frac{2\times 12\times \$15,100}{\left(12+1\right)\times \left(\$151,000-\$21,140\right)}\\ =\frac{\$362,400}{\$1,688,180}\\ =21.47\%\end{array}$

Working Note:

Calculation of the interest for Fidelity Bank:

$\begin{array}{c}\text{Interest}=\text{Borrowings}\times \text{Interest Rate}\\ =\$151,000\times 10\%\\ =\$15,100\end{array}$

Calculation of the compensating balance for Fidelity Bank:

$\begin{array}{c}\text{Compensating Balance}=\text{Borrowings}\times \text{Interest Rate}\\ =\$151,000\times 28\%\\ =\$42,280\end{array}$

Calculation of the stated compensation balance for Fidelity Bank:

$\begin{array}{c}\text{Stated Compensating Balance}=\text{Borrowings}\times \text{Interest Rate}\\ =\$151,000\times 10\%\\ =\$15,100\end{array}$

Calculation of the interest for Southwest Bank:

$\begin{array}{c}\text{Interest}=\text{Borrowings}\times \text{Interest Rate}\\ =\$151,000\times 10\%\\ =\$15,100\end{array}$

Calculation of the compensating balance for Southwest Bank:

$\begin{array}{c}\text{Compensating Balance}=\text{Borrowings}\times \text{Interest Rate}\\ =\$151,000\times 14\%\\ =\$21,140\end{array}$

Summary Introduction

To calculate: The effective cost of interest for Summit Record Company.

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.

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 26P

The effective rate of interest for Fidelity Bank is 17.78% and that for Southwest Bank is 18.46%.

Explanation of Solution

Calculation of the effective rate of interest for Fidelity Bank:

$\begin{array}{c}\text{Effective Interest Rate}=\frac{2\times \text{Annual No}\text{.Payments}\times \text{Interest}}{\begin{array}{l}\left(\text{Total no}\text{. of payments}+1\right)\times \\ \left(\text{Principal}-\text{Stated Compensating Balance}\right)\end{array}}\\ =\frac{2\times 4\times \$15,100}{\left(4+1\right)\times \left(\$151,000-\$15,100\right)}\\ =\frac{\$120,800}{\$679,500}\\ =17.78\%\end{array}$

Calculation of the effective rate of interest for Southwest Bank:

$\begin{array}{c}\text{Effective Interest Rate}=\frac{2\times \text{Annual No}\text{.Payments}\times \text{Interest}}{\left(\text{Total no}\text{. of payments}+1\right)\times \left(\text{Principal}\right)}\\ =\frac{2\times 12\times \$15,100}{\left(12+1\right)\times \$151,000}\\ =\frac{\$362,400}{\$1,963,000}\\ =18.46\%\end{array}$

Summary Introduction

To determine: Whether the choice of banks remains the same if the assumption taken in part (b) is correct.

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.

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 26P

Yes, the choice of bank would remain the same if the assumptions in part (b) are taken to be correct.

Explanation of Solution

Since the effective rate of Fidelity Bank is lower than that of Southwest Bank, Fidelity Bank should be chosen over Southwest Bank if compensating balance is to be maintained by both banks. The effective cost of the loan by Fidelity Bank would be lesser.