THE THEORY OF INTEREST

cent, and this equalizing rate is the rate of return overcost.

But we may reduce the comparison to its simplest formif we change the figures in the example to the following:

Table 7

Farming and Forestry Use Compared in Terms oj Rate of Return

Over Cost

Net Value ofFanning Use

Net Value ofForestry Use

Net Differencein Favor ofForestry Use

1st year .

$100

$000

—$100

2nd year.

100

210

+110

3rd year .

100

100

000

4th year .

100

100

000

Each subsequent year.

100

100

000

In this case the equalizing rate, or the rate of returnover cost, is evidently 10 per cent. At the cost of $100there is a return of $110, or 10 per cent over the $100.At 10 per cent the present worth of the two will be equal ;for the present worth of the return $110 due next year is,reckoning at 10 per cent, exactly $100 and the presentvalue of the cost, $100, due immediately, is also $100.

The example just given, in which the cost ($100) isonly one item and the return ($110) is also only one itemreceived one year later, is the simplest possible example.But the same principle holds true however complicatedmay be the series of items constituting the costs andreturns.

Perhaps the next simplest example is that in which oneoption shows in the present year a cost (of, say, $100)compared with the other but shows a return (of, say, $8)for every future year in perpetuity. Under these circum-stances the equalizing rate (or the rate of return overcost) is 8 per cent.

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