Ashley is thinking of buying a truckload of wine for investment

| January 30, 2017

Question
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 drinkWine 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? (Hint: When will Wine B be drunk?)

(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?

(Hint: When does the rate of return on holding wine get to 10%?)

(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? (Hint: 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

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