Your firm is considering the following three alternative bank loans for $1,000,000:
a) 10 percent loan paid at year end with no compensating balance
b) 9 percent loan paid at year end with a 20 percent compensating balance
c) 6 percent loan that is discounted with a 20 percent compensating balance requirement
Assume that you would normally not carry any bank balance that would meet the 20 percent compensating balance requirement. What is the rate of annual interest on each loan?
a) 10%
b) 7.2%
c) 4.8%
To calculate the annual interest rate for each loan, we need to consider the effective cost of borrowing after taking into account any compensating balances.
a) Loan a: 10 percent loan, paid at year end with no compensating balance
The rate of interest on this loan is simply 10 percent.
b) Loan b: 9 percent loan, paid at year end with a 20 percent compensating balance
In this case, the effective cost of borrowing is higher due to the requirement of a 20 percent compensating balance. To calculate the effective interest rate, we need to divide the interest expense by the amount of the loan less the compensating balance:
Effective interest rate = (Interest expense / (Loan amount - Compensating balance)) x (1 / (1 - Compensating balance))
= (9% / (1 - 20%)) x (1 / (1 - 20%))
= (9% / 0.8) x (1 / 0.8)
= 11.25%
Therefore, the annual interest rate for loan b is 11.25%.
c) Loan c: 6 percent loan that is discounted with a 20 percent compensating balance requirement
In this case, the loan amount is discounted by 20 percent upfront. To calculate the effective interest rate, we need to divide the interest expense by the loan amount net of the discount:
Effective interest rate = (Interest expense / (Loan amount - Discounted amount)) x (1 / (1 - Discounted amount))
= (6% / (1 - 20%)) x (1 / (1 - 20%))
= (6% / 0.8) x (1 / 0.8)
= 7.5%
Therefore, the annual interest rate for loan c is 7.5%.
To calculate the rate of annual interest on each loan, we need to understand the concept of compensating balances and how they affect the effective interest rate.
A compensating balance is a portion of a loan that the borrower is required to hold as a deposit in a bank, set against the loan. It serves as collateral for the loan and is typically expressed as a percentage of the loan amount. For example, if the compensating balance requirement is 20 percent, the borrower must keep 20 percent of the loan amount as a minimum balance in the bank.
Now, let's calculate the rate of annual interest for each loan:
a) 10 percent loan paid at year end with no compensating balance:
In this case, there is no compensating balance requirement, so the entire loan amount of $1,000,000 can be used freely. Therefore, the interest rate remains at 10 percent.
b) 9 percent loan paid at year end with a 20 percent compensating balance:
For this loan, the compensating balance requirement is 20 percent. This means the borrower needs to keep 20 percent of the loan amount, i.e., $200,000, as a minimum balance in the bank. Therefore, the effective loan amount is $800,000 ($1,000,000 - $200,000). To calculate the effective interest rate, we divide the interest expense by the effective loan amount:
Interest Expense = $1,000,000 * 9% = $90,000
Effective Interest Rate = $90,000 / $800,000 = 0.1125 or 11.25%
c) 6 percent loan that is discounted with a 20 percent compensating balance requirement:
In this case, the loan amount is discounted by the compensating balance requirement. This means that the lender will only provide the borrower with 80 percent of the loan amount. Therefore, the effective loan amount is $800,000 ($1,000,000 * 80%). To calculate the effective interest rate, we divide the interest expense by the effective loan amount:
Interest Expense = $1,000,000 * 6% = $60,000
Effective Interest Rate = $60,000 / $800,000 = 0.075 or 7.5%
So, the rate of annual interest for each loan is:
a) 10 percent
b) 11.25 percent
c) 7.5 percent