ELEMENTS WHICH REDUCE VALUE
ceived as annuity will be 7a, and this will fall short of meeting
the actual expenditures by an amount expressed by (1 — na)
which, at 6 per cent per annum, is the interest on — bo)
2 (1 —
dollars; or, expressed in percentage of the cost, is Ice 2 7a)
per cent of the total investment in the plant.
For a plant not subject to further growth, with a uniform
useful life of all its parts, and constructed progressively, there
should be, at 6 per cent interest, an unexpended interest-bearing
balance in the replacement fund as follows:
When the useful life is five years:
2 (1 —
EG Sa 0) 37.7 per cent of the total investment.
When the useful life is ten years:
2 (1 —
ml ost) = 40.2 per cent of the total investment.
When the useful life is twenty years:
201 ioe
role opty) = 38.0 per cent of the total investment.
When the useful life is forty years:
2 (1 —
tect lr = 0.2585) = 30.9 per cent of the total investment.
If earnings have been adequate to provide an interest-bearing
replacement fund, then these percentages represent the probable
accumulation in such a fund.
Some amount such as shown by these figures, depending on
the expectancy, represents the accumulation of replacement
annuities during that period of the plant’s life during which
the actual replacement expenditures were less than the annuity.
If the annual allowance for maintenance in the past has been
based on the requirements of operation and repair without
surplus to meet future replacements and if there has been no spe-
cial allowance for amortization, the current allowance for amor-
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