ELEMENTS WHICH REDUCE VALUE
to the useful life of any group of parts. This is sometimes re-
ferred to as the “Straight Line Method.” It might with equal
propriety be called a direct percentage method, as the inverse
ratio is usually expressed in percentage.
Under this direct percentage method, there would be allowed
2.5 per cent per annum of the replacement cost of all parts of a
plant having a go-year life; 3.33 per cent per annum of the re-
placement cost of all parts having a 3o-year life; 35 per cent per
annum of the replacement cost of all parts having a 20-year
life, and so on.
This method, applied to the hypothetical case of a pipe line,
constructed and extended one mile per year, and each mile
thereof having a useful life of exactly forty years, would, at the
end of the fortieth year, make the replacement requirement 2.5
per cent per annum, or one mile of pipe. At the end of the
sixtieth year, the requirement thus determined would be 2.5
per cent of the 6o miles of pipe then in service, or r. 5 miles of
pipe. This would be 50 per cent in excess of the amount actu-
ally replaced, which at that time would be only one mile. This
would also apply for any time before the pipe first laid has reached
the limit of its usefulness, as at 20 years. In the assumed case
there is no replacement requirement at 20 years; yet the straight
percentage method indicates 2.5 per cent of 20 miles of pipe,
or o.5 mile of pipe. It follows from this illustration that
the Straight Line Method would give results somewhat too
high.
By further analysis of this problem, the following formulae
have resulted, which are free from this objection and fulfill
every ordinary requirement. In devising these formule, the
fact was taken into account that there may be some replace-
ment requirement in the early years of a plant’s life, and that
this requirement gradually increases. These formulae apply
only to plants which have been developed gradually and are
being extended at a uniform annual rate.
Using the notation already introduced, and designating with
C the total cost of replacing the group of items, the probable
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