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?

$200.00

To calculate the annual interest rate on each loan, we need to take into account the effect of the compensating balance.

a) 10 percent loan paid at year end with no compensating balance:
This loan does not require a compensating balance. Therefore, the annual interest rate is simply 10 percent.

b) 9 percent loan paid at year end with a 20 percent compensating balance:
In this case, the bank requires a compensating balance equal to 20 percent of the loan amount ($1,000,000) or $200,000. This means that in order to borrow $1,000,000, you need to deposit $200,000 in a non-interest-bearing account for the duration of the loan. Hence, the effective loan amount is $800,000 ($1,000,000 - $200,000). To calculate the annual interest rate, we divide the interest paid by the effective loan amount: (Loan Interest / Effective Loan Amount) * 100. In this case, the interest paid is $72,000 ($800,000 * 9%) and the effective loan amount is $800,000. Therefore, the annual interest rate is (72,000 / 800,000) * 100 = 9%.

c) 6 percent loan that is discounted with a 20 percent compensating balance requirement:
This loan is discounted, which means that the bank deducts the compensating balance requirement upfront. In this case, the compensating balance is 20 percent of the loan amount ($1,000,000) or $200,000. The loan amount that you actually receive is the loan amount minus the compensating balance requirement, which is $800,000 ($1,000,000 - $200,000). The interest paid is $48,000 ($800,000 * 6%). To calculate the annual interest rate, we divide the interest paid by the effective loan amount: (Loan Interest / Effective Loan Amount) * 100. In this case, the interest paid is $48,000 and the effective loan amount is $800,000. Therefore, the annual interest rate is (48,000 / 800,000) * 100 = 6%.

So, the rates of annual interest on each loan are:
a) 10 percent
b) 9 percent
c) 6 percent