In discussing a possible loan with the firm’s banker, Smith found that the bank is willing to lend Dellvoe up to $800,000 for one year at a 9% simple, or quoted, rate. However, he forgot to ask what the specific terms would be.
1. Assume the firm will borrow $800,000. What would be the effective interest rate if the loan were based on simple interest? If the loan had been an 8% simple interest loan for six months rather than for a year, would that have affected the EAR?
2. What would be the EAR if the loan were a discount interest loan? What would be the face amount of a loan large enough to net the firm $800,000 of usable funds?
3. Assume now that the terms call for an installment (or add-on) loan with equal monthly payments. The add-on loan is for a period of one year. What would be Dellvoe’s monthly payment? What would be the approximate cost of the loan? What would be the EAR?
4. Now assume that the bank charges simple interest, but it requires the firm to maintain a 20% compensating balance. How much must Dellvoe borrow to obtain its needed $800,000 and to meet the compensating balance requirement? What is the EAR on the loan?
5. Now assume that the bank charges discount interest of 9% and also requires a compensating balance of 20%. How much must Dellvoe borrow, and what is the EAR under these terms?
6. Now assume all the conditions in part 4—that is, a 20% compensating balance and a 9% simple interest loan—but assume also that Dellvoe has $100,000 of cash balances that it normally holds for transactions purposes, which can be used as part of the required compensating balance. How does this affect (i) the size of the required loan and (ii) the EAR of the loan?