Economics

1. Your finance company makes installment loans to households and small businesses that want to buy appliances or equipment. You are currently considering a loan to a business that wants to borrow $80,000. You have quoted an interest rate of “just 5.40 percent” to the prospective borrower, but you do not want to lend to him unless the true yield on the loan is at least 8.10 percent (assuming full repayment). Otherwise, you will devote your funds to an alternative investment. Consider the following possibilities:

(a) a loan using the discount method with one installment to be paid after one year;
(b) a loan using the add-on approach with two installments, one payment to occur after 6 months, and the other payment to occur after 12 months;

Are either of these possibilities acceptable to you company? Using the add-on approach and a payback period of one year, what is the minimum number of installment payments that you could accept? How big would each installment payment be? Explain. Use the constant-ratio formula to arrive at your answers.


2. The San Jose office of your company wants to put $100,000 in a reserve fund at a local bank. One bank quotes an interest rate of 1.70 percent, compounded annually. A second bank quotes an interest rate of 1.50 percent, compounded monthly. A third bank quotes an interest rate of 1.30 percent, compounded daily. Which bank should be chosen? Explain.


3. (a) Use the yield approximation formula to estimate the yield to maturity for a $1000 par-value bond with a coupon rate of 8.00 percent. The bond's current price is $900, and it matures in 15 years.
(b) If you sold the bond at a price of $950 after 10 years, what would be your holding period yield? Explain. Use the yield approximation formula again.


4. A $1000 par-value bond pays semi-annual coupon payments of $40. The bond will mature in just 6 months and is currently priced at $996.00 including the broker's commission. If you buy the bond and hold it until maturity, what would be your (annualized) internal rate of return? (Give an exact percentage answer to two decimal places.)