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- 
97