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Math Help - All Present Values are Equal? How?

  1. #1
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    All Present Values are Equal? How?

    You own a forest. You can choose when to cut down the lumber and sell it. We are assuming a very simple example; no inflation or anything. Just interest rate and present value really. You choose one year, and thats the year you cut down and sell all of it.
    So
    Is there a cirumstance in which one would not care when they cut down and sell the lumber, let's say over the next 50 years? How?

    So you can make up the prices of lumber over the next 50 years and how it will change each year; you can make up the interest rate and how it will change each year. How can it be done? What even is the situation? Is it where the present value of year N's monetary opportunity, N years from now is equal for all N?
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  2. #2
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    Generally, waiting to 'harvest' will increase your PV as long as the forest's value is increasing at a greater rate that your PV discount rate. The 'optimal harvesting' moment is that point in time at which the forest's value increase rate has diminished such that it exactly equals your discount rate.

    As a mini-illustration, suppose that by allowing the forest to grow, the expected selling price of the cut timber grows by 20%, 15%, 10%, and 8%, in the first four years, respectively. Suppose further that your discount rate for NPV purposes is 9%. In this case your NPV is optimized by cutting at the end of the third year.
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