Exam 10: Asset Markets

Suppose that the cost of personal computers falls by 20% per year. To make this problem relatively easy, we will assume that their quality does not change and that computers never wear out. You plan to get one sometime. What is the rational way to decide when to buy one?

Shiver's annual fuel bill for home heating is 900 dollars per year. He considers three alternative plans for insulating his house. Plan A would reduce his annual fuel bill by 15%, plan B would reduce it by 20%, and plan C would eliminate his need for heating fuel altogether. The plan A insulation job would cost Shivers 900 dollars, plan B would cost him 1,600 dollars, and plan C would cost him 9,900 dollars. If the interest rate is 10% and his house and the insulation job last forever, which plan is the best for Shivers?

Shivers's annual fuel bill for home heating is 800 dollars per year. He considers three alternative plans for insulating his house. Plan A would reduce his annual fuel bill by 15%, plan B would reduce it by 20%, and plan C would eliminate his need for heating fuel altogether. The plan A insulation job would cost Shivers 800 dollars, plan B would cost him 1,100, dollars, and plan C would cost him 8,800 dollars. If the interest rate is 10% and his house and the insulation job last forever, which plan is the best for Shivers?

A zero coupon bond is a bond that pays no return until it comes due and then pays the holder of the bond its face value. Suppose that a $2,000 zero coupon bond will come due on January 1, 2020. If the interest rate is 5% and will remain 5% forever, what will this bond be worth on January 1, 2005?

A certain wine costs $3 a bottle to produce. The amount that people are willing to pay to drink it t years after it has been bottled is $2 + 3t. Storage costs, not including interest, are $.50 per year. If the interest rate is 5%, how much would a rational investor be willing to pay for it at the time it is bottled? Explain how you got your answer. Feel free to write formulas for present value calculations without working out the numerical answer if it involves long calculations. (Hint: How long would the wine be kept before it is drunk? At what price would it sell?)

Bank 1 offers a deal on deposits of $1,000 or more. You must leave your money in the bank for three years, but bank 1 will pay you 4% interest for the first year, 4% interest for the second year, and 7% interest for the third year. In response, bank 2 offers a deal that it claims is even better. It also requires you to deposit at least $1,000 and to leave it in the bank for three years, but it will pay 7% interest in the first year and then 4% in the second and third years. After three years, you can take your money out of either bank and do what you want with it. Both banks compound interest annually.