The value of good wine increases with age. Thus if you are a wine dealer, you have the problem of deciding whether to sell you wine now, at a price of $P a bottle, or sell it later at a higher price. Suppose you know that the amount a wine-drinker is willing to pay for a bottle of wine t years from now is $P(1+20(sqr(t))). Assuming continuous compounding and a prevailing interest rate of 5% per year, when is the best time to sell your wine?
The goal is to maximize the net present value of the sale of the wine.
Revenue is given in the question
Revenue = P * (1 + 20 sqrt(t))
Revenue must be discounted by the time value of money, in this case 5% compounded continuously. This discount factor is ...
The solution provides a detailed look at optimizing the Net Present Value of an appreciating asset. The solution uses continuous compounding to discount the future cash flow. Basic concepts of differential calculus as used as well as solving quadratic equations.