The value of good wine increases with age. Thus, if you are a wine dealer, you have the problem of deciding whether to sell your wine now, at a price of $P a bottle, or to sell it later at a higher price. Suppose you know that the amount a wine-drinker is willing to pay for a bottle of this wine t years from now is $P(1+20?t). Assuming continuous compounding and a prevailing interest rate of 5% per year, when is the best time to sell your wine?

Question

SchulzD · Accepted Answer

If the dealer sold the bottle now for $P, and invested that $p at 5%, the return would be, R1=P(1.05)t, which means that after t years, the dealer would have $P*1.05^t. If the dealer instead waited t years to sell then he would get, R 2 = $P(1 + 20rt(t)). To find the value of t which would make both returns equal,set R1 = R2. P⋅1.05t=P(1+20rt(t)) 1.05t=1+20rt(t) 1+20rt(t)−1.05t=0 There are a few ways to solve this. Newton-Raphson method, on your calculator may be able to do it, or some equation-solving software (eg DeadLine) Anyway, the answer is: t=109.6 yrs  From the graph you can see that, for the first 109 yrs 8months, the dealer will get a greater return by waiting for the buyer to buy, rather than investing $P at 5% interest compounded annually. Since the dealer is unlikely to last for another 109 yrs and 8months, then he can sell at any time he wishes for a greater return.

The value of good wine increases with age. Thus, if you are a wine dealer, you have the problem of deciding whether to sell your wine now, at a price

Answered question

Answer & Explanation

New Questions in Other