170 VALUATION, DEPRECIATION AND THE RATE-BASE 
replace ” by the Sinking Fund Method, for old plants, with 
interest at 6 per cent and the hypothesis that actual life will 
conform to probable life, the theoretical accrued obligation to 
replace or what is equivalent, the theoretical accumulation in 
the fund as shown in Table 2, page 94, will be: 
Per cent 
For articles having 5 year life, about 38 
6¢ [44 10 [44 4 40 
fC ¢ 20 < ¢¢ 38 
[14 6 30 (44 £¢ 34 
14 (4 40 ¢ i’ fx 
cc SL ED {¢ € . 3 
[49 ¢ 60 né © 5 
These percentages apply strictly, of course, only to cases in 
which the age of the plant is greater than the life of its parts. 
They indicate the extent, however, to which an accumulating 
replacement or depreciation fund may exceed the demands upon 
it. In some measure, approximating this unexpended surplus, 
such a fund is available for outside investments. Interest on 
the same, when it represents the obligation to replace, must be 
earned by the owner for the benefit of the plant, consequently, 
it makes no difference to what purpose he applies this surplus, 
provided only that ample assurance remains that replacements 
will actually be made when necessary. Interest is to be added 
to this fund even when the same is invested in the plant and by 
the amount of such interest, the earnings will not be available 
for distribution as profit. 
When the capital is being amortized, the accumulations in 
the amortization fund are the absolute property of the owner. 
They are not subject to control by the rate-payer, yet, here, 
too, proper assurance may be expected that replacements will 
be duly made and it would not be unreasonable to expect an 
adequate special fund to be maintained to meet emergencies. 
Soundness of 100 Per Cent Appraisal as Rate-base. — In 
order to show beyond all question that the method of valuing 
at the investment without deduction of the depreciation in fix-