456 VALUATION, DEPRECIATION AND THE RATE-BASE
maining value if the cost of replacement at the end of its period
of usefulness may be estimated at $2500?
On page 465 in the 20-year life 6%, section of Table 33 at 11 years
in the right-hand column there are found in the column with the
bottom heading “ Present Value” the figures 68.7614 which
represent percentage. The remaining value estimated from cost
would be 0.687614 X 3000 = $2062.84; consequently the accrued
depreciation, estimated from cost, would be 3oco — 2062.84
= $037.16. The remaining value estimated from the cost to
replace will be 0.687614 X 2500 = $1719.04.
The actual accrued depreciation, therefore, will be
3000 — 1719.04 = $1280.96.
Demonstration of Error in Formule as Ordinarily Used in
Estimating Current Depreciation
That the ordinary depreciation formule based on expectancy
or probable remaining life must be in error, even if it be supposed
that the expectancy has been correctly ascertained, and that they
should be regarded only as approximation formula, can be demonstrated
as follows:
Let it be assumed that the failures of a large number of articles,
each representing an original investment of $100, which are all in
the same life class and of the same age, can be grouped in couples
such that for each article failing or going out of use s years before
the end of the term of the originally predicted probable life, there
will be another that fails s years after the end of this term.
If the probable life as originally determined was # years, and
some years of this life have already elapsed, the remaining actual
years of service of the first of the two articles under consideration
would be e — s years and of the second e -} s years, where e represents
the expectancy of all articles still in service and s is the departure
in years from this expectancy by each of the two articles
separately considered.
If the actual failure of these two articles could be correctly
forecast the current depreciation thereof would be estimated
from the following formule based on equation (41).
