100 VALUATION, DEPRECIATION AND THE RATE-BASE
By the compound interest annuity method of computation,
in the selected illustration at 6 per cent interest, the allowance
for replacement would be 0.646 per cent of the cost of the sys-
tem, which is only one-third of the actual requirement, and this
allowance, as already explained, would only then be justified if
amortization had covered the entire period in the life of each
part of the pipe during which there was no expenditure for re-
placements, so that the inadequate annual allowance could be
supplemented by the earnings of an accumulated replacement
fund.
In a plant which is made up of a multiplicity of parts of
various periods of usefulness, those which have the same expect-
ancy should, as before stated, be grouped together. For each
group, the replacement requirement can then be estimated
separately, and from the several amounts thus ascertained the
total requirement is determined.
The rule previously laid down for a hypothetical case is not
strictly applicable under the conditions as they actually present
themselves. There can be no absolute conformity between the
assumed period of usefulness of the various parts of a plant and
the time during which they actually prove useful.
The probable useful life or expectancy is merely the average
life, which is often not reached and is just as often exceeded.
Thus, again referring to the pipe line, it is to be assumed that
while some of it may serve beyond the average period of useful-
ness of such pipe, other parts thereof, from one cause or another,
will require replacement early in its life. Consequently, any
rule such as that previously laid down, which indicates a uni-
form replacement requirement in successive periods, with a
sudden rise in the requirement at the beginning of each new
period, if the plant be one that is steadily growing, will require
some modification.
The simplest modification of the foregoing rule is to assume
gradual changes in the annual replacement requirement as the
age of the plant increases, instead of the sudden changes, and
then to call this requirement at all times inversely proportional
