Question

Fancy Footwear has a line of credit with a local bank in the amount of $80,000. The loan agreement calls for interest of 7 percent with a compensating balance of 5 percent, which is based on the total amount borrowed. The compensating balance will be deposited into an interest-free account. What is the effective interest rate on the loan if the firm needs to borrow $75,000 for one year to cover operating expenses

Answer 1

Answer:

Ans. The effective interest rate on the loan if the firm needs to borrow $75,000 for one year  would be 7.37% effective annual.

Explanation:

Hi, well, first we need to establish the amount to be borrowed, taking into account that there is a compensating balance of 5%. This means that the 5% of the loan goes into an account that pays no interest, and that will happen for a year.

First we need to find the amount to be borrowed, that is:

$AmountBorrowed=\frac{AmountNeeded}{(1-CompensatingBalance)}$

$AmountBorrowed=\frac{75,000}{(1-0.05)} =78,947.37$

Ok, that means that we need to ask for $78,947.37, the compensating balance is $78,947.37*0.05=3,947.37, that means that Fancy Footwear will receive: $78,947.37 - 3,947.37 = 75,000.

Now, the amount to be paid at the end of the loan can be calculated with the following equation:

$FutureValue=PresentValue(1+r)^{n}$

Where:

Future Value= Is the money to be paid to the bank

Present Value= The money that Fancy Footwear has borrowed

r = The effective annual rate on the amount borrowed.

n= Periods (in years) to pay the loan

Everything looks like this.

$FutureValue=78,947.37(1+0.07)^{1} =84,473.68$

Therefore, we need to pay $84,473.37, but we can now get our compensating balance, so our real cash flow in year 1 (1 year after the credit) is $84,473.68 - $3,947.37 = $80,526.32

In order to find the effective interest rate of this loan, we can use MS Excel and use the function "IRR" or, solve the following equation for R.

$FutureValue=PresentValue(1+R)^{n}$

That is:

$80,526.32=75,000(1+R)^{1}$

$\frac{80,526.32}{75,000} =1-R$

$\frac{80,526.32}{75,000} -1=R=0.0737$

SO, the effective cost of the debt is 7.37% effective annually.

Best of luck