SECOND APPROXIMATION

This question is fundamental and typical in the secondapproximation.

The rate of interest is just as relevant to this initialchoice of uses for maximum present value as to the sub-sequent choice for shape alone, for it is used in findingthe present value; and when the rate changes, the relativepresent values of differently shaped streams may changeabout.

We shall suppose, as heretofore, that there is a uniformrate of interest in the community and that any individualis free either to borrow or to lend at that rate and up toany amount desired. Under this hypothesis the choiceamong the three available options will simply fall onthat one which yields the maximum present value,reckoned at the market rate of interest.

Let us assume a market rate of interest at five per cent.To reckon the three respective present values, supposethe use of the land for mining purposes will yield an in-come stream, let us say, as follows: $2000 the first year,$1800 the second, $1600 the third, and so on, diminishingannually by $200 to the point of the mine’s exhaustion.The present value of these ten sums, discounted at fiveper cent, is $9110. If the land is used for farming pur-poses and yields a net income of $450 a year perpetually,the present value at five per cent will be $9000. If, finally,the land is used for forestry purposes, we shall suppose ityields the following sums: zero for the first two years,$300 for the third, $400 for the fourth, $500 for the fifth,and $500 thereafter forever—then the value of the land,reckoning at 5 per cent, will be $8820.

Under these conditions the choice will evidently fallon the mining use, because, for mining purposes, the landis worth $9110, which is greater than $9000, its value

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