Ashley is thinking of buying a truckload of wine for investment purposes. He can borrow and lend as much as he likes at an annual interest rate of 10%. He is looking at three kinds of wine. To keep our calculations simple, let us assume that handling and storage costs are negligible.
• Wine drinkers would pay exactly $175 a case to drink Wine A today. But if Wine A is allowed to mature for one year, it will improve. In fact wine drinkers will be willing to pay $220 a case to drink this wine one year from today. After that, the wine gradually deteriorates and becomes less valuable every year.
• From now until one year from now, Wine B is indistinguishable from Wine A. But instead of deteriorating after one year, Wine B will improve. In fact the amount that wine drinkers would be willing to pay to drink Wine B will be $220 a case in one year and will rise by $10 per case per year for the next 30 years.
• Wine drinkers would be willing to pay $100 per case to drink Wine C right now. But one year from now, they will be willing to pay $250 per case to drink it and the amount they will be willing to pay to drink it will rise by $50 per case per year for the next 20 years.
(a) What is the most Ashley would be willing to pay per case for Wine A?
(b) What is the most Ashley would be willing to pay per case for Wine B?
(c) How old will Wine C be when it first becomes worthwhile for investors to sell off their holdings and for drinkers to drink it?
(d) What will the price of Wine C be at the time it is first drunk?
(e) What is the most that Ashley would be willing to pay today for a case of Wine C? (What is the present value of his investment if he sells it to a drinker at the optimal time?) Express your answer in exponential notation without calculating it out.