The Value of Capital and the Interest on Capital (continued). VI-- Capitalization Interest is always an aliquot part of capital value, and capital value is always a multiple of interest. Where interest is 5%, for example, the interest is 1/20 of the capital value, and the capital value is equal to 20 times the interest. It is this fact which renders it possible to determine the value of capital, not by deducting interest from gross return, but by another method which leads to precisely the same result -- namely, by means of a corresponding multiplication of interest, or, to use the ordinary term, by capitalisation. Whether discounting or capitalisation is preferred will depend upon circumstances. With circulating capital discounting is the usual method, as the gross return in this case forms the nearest and clearest basis. With fixed capital, if the wearing out is comparatively rapid, and the gross returns are few in number, discounting will be the preferable method in this case also; but if a long series of gross returns is to be taken into account, capitalisation will be preferred.
Capitalisation is easiest where the gross return contains no quota for wear and tear, and is therefore entirely net return.
This would be the case with a capital which never wore out, which promised rent to all eternity, and a rent, moreover, absolutely secure. To carry through the process of discounting here would be laborious in the highest degree; the rent of each separate year would have to be separately calculated, until that rent was reached whose present value was zero; and not till then could the calculation be finished. How much simpler in such a case to multiply the year's rent in accordance with the rate of interest!
The result obtained in this fashion agrees with that given by the former and more laborious method, not merely approximately, but with mathematical exactitude, as any text-book of mathematics will confirm. The mathematical formula for the discounting of an eternal rent is simply the formula of capitalisation.
The calculation is a little more complicated when the gross returns contain quotas for wear and tear, and when repairs and the like must be covered and insurance premiums or premiums against risk retained out of these gross returns. In such cases all necessary deductions must first be made from the gross return before we get the net return which is to be capitalised, and this is very often exceedingly difficult in the individual case. The premiums just mentioned are frequently not deducted, but the amount of risk finds instead its expression simply in the rate of interest. The return, for example, of a business regarded as of doubtful solidity will be capitalised at a higher rate of interest, i.e. as a smaller multiple.(1*)NOTES:
1. All the separate principles here deduced for the calculating of capital value and interest are followed in practical life and are practically familiar to us. The theory of them, too, is often given. But they are always followed and taught under the assumption that the fact of interest and a fixed ratio of interest are given. Nothing is simpler, under such an assumption, than to capitalise a rent, or to show the method of capitalisation. But the duty of the theorist is to discover these laws, and, at the same time, to explain why such assumptions may be made. Whence comes interest? whence the rate of interest?
These are our fundamental questions. All the single laws which we have laid down are confirmed theoretically only if we have succeeded in explaining also the assumption on which they are based, i.e. the existence of interest and the rate of interest.
The analysis of the value of land which follows will once more give the reader occasion to notice how difficult it is with the matter in hand to escape arguing in a circle, and to prevent the entrance of any assumption which is itself in need of explanation.
