Optimal Timing

Exponential functions arc used to express the value of goods that appreciate or depreciate over lime. Such goods include* wine, cheese, and land. Since a dollar in the future is worth less than a dollar today, its future salue must be discounted to a present value. Investors and speculators seek to maximize the present value of their avsetv as is illustrated in Example 10 and Problems 9.31 to 9.34.

EXAMPLE 10. The salue of cheese thai improves with age t* given by V - 1400« 125)" If the cost of capital under continuous compounding is 9 percent a year and there is no storage cost lor aging the cheese in company caves, how long should the company »tore the cheese?

The company wants to maximize the present value of the chccsc: P Ve m. .Substituting the given values of V and r. P * 1400(125 )v'r Taking the natural log.

In/* In 1400+ f"> la 125-00* Then taking the derivative and setting it equal to zero to maximi/c P.

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