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

Question

Bentley Leach · 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 $P×1.05t.  If the dealer instead waited t years to sell then he would get, R2=$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=109.6yrs  From the graph you can see that, for the first 109 yrs 8 months, 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 8 months, 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 whetherto sell your wine now, at a price of

Answered question

Answer & Explanation

New Questions in Other