midland chemcial is negotating a loan from manhattan bank and trust. the small chemical company needs to borrow 500,000. the bank offers a rate of 81/4 percent with a 20 percent compensating balance requirement, or as an alternative, 93/4 percent with additional fees of 5,500 to cover services the bank is providing. In either case the rate on the loan is floating and the loan would be for one year. a. Which loan carries a lower effective rate? Consider fees to be the equivalent of other interest. b. if the loan with a 20 percent compensating balance requirement were to be paid off in 12 monthly payment, what would the effective rate be? (principal equals amount borrowed minus the compensating balance.) c. asume the proceeds from the loan with the compensating balance requirement will be used to take cash discounts. Disregard part b about installment payments and use the loan cost from part a. If the terms of the cash discount are 1.5/10, net 50, whould the firm borrow the funds to take the discount? d. assume the firm actually takes 80 days to pay its bills and would continue to do so in the future if it did not take the cash discount. Should it take the cash discount? e. because the interest rate on the loans is floating, it can go up as interest rates go up. Assume that the prime rate goes up 2 percent and the quoted rate on the loan goes up the same amount. What would then be the effective rate on the loan with compensating balances? Convert the interest to dollars as the first step in your calculation. f. in order to hedge against the possible rate increase described in part e, Midland decides to hedge its position in the futures market. Assume it sells 500,000 worth of 12-month futures contracts on Treasury bonds. One year later, interest rates go up 2 percent across the board and the Treasury bond futures have gone down to $488,000. Has the firm efectively hedged the 2 percent increase in interest rates on the bank loan as described in part e? Determine the answer in dollar amounts.
To answer these questions, let's break them down one by one.
a. To determine which loan carries a lower effective rate, we need to calculate the effective rate for each option. The effective rate takes into account both the interest rate and any additional fees as the equivalent of interest.
For the first option with a compensating balance requirement, the formula for calculating the effective rate is:
Effective rate = (Interest paid + Fees) / (Loan amount - Compensating balance)
Calculating for the first option:
Interest paid = (81/4)% * $500,000 = $10,250
Fees = 0 (since there are no additional fees)
Loan amount - Compensating balance = $500,000 - (20/100 * $500,000) = $400,000
Effective rate = ($10,250 + $0) / $400,000 = 0.025625 = 2.56%
For the second option with additional fees:
Interest paid = (93/4)% * $500,000 = $12,250
Fees = $5,500
Loan amount - Compensating balance = $500,000
Effective rate = ($12,250 + $5,500) / $500,000 = 0.0355 = 3.55%
Therefore, the first loan with a compensating balance requirement carries a lower effective rate (2.56%) compared to the second option (3.55%).
b. If the loan with a 20% compensating balance requirement were to be paid off in 12 monthly installments, we need to calculate the effective rate based on the principal amount.
Principal = Loan amount - Compensating balance = $500,000 - (20/100 * $500,000) = $400,000
We can use a loan amortization formula to calculate the monthly payment:
Monthly payment = Principal / (1 - (1 + Interest rate per period)^(-Number of periods))
Number of periods = 12 (since it's a one-year loan with monthly payments)
Interest rate per period = (81/4)% / 12 = 0.00677
Using this information, calculate the monthly payment and the effective rate.
c. This question requires considering the loan cost from part a and comparing it with the cash discount terms.
d. To evaluate whether the firm should take the cash discount, we need to compare the discount to the cost of borrowing funds for 80 days (the time it takes to pay bills).
e. This question requires recalculating the effective rate on the loan with compensating balances after the prime rate and the quoted rate on the loan increase by 2 percent. Convert the interest to dollars as the first step.
f. Lastly, to determine if the firm effectively hedged against the 2 percent increase in interest rates, we need to calculate the difference in the cost of borrowing funds with and without the hedge, given the change in interest rates and the Treasury bond futures.