166 VALUATION, DEPRECIATION AND THE RATE-BASE 
article. The annual amortization installment is estimated from 
the original cost of an article less residual value and its probable 
life, by dividing the cost less residual value by the number of 
years of probable life. This method, like any other amortiza- 
tion method, is justified on the theory of the immediate applica- 
tion of the annual depreciation installment to the retirement of 
capital. In this respect both this method and the Equal Annual 
Payment Method differ essentially from the Sinking Fund Method 
and from the Unlimited Life Method, under neither of which 
any retirement of invested capital is taken into consideration. 
Unlimited Life Method. — The “ Unlimited Life Method ” of 
procedure, when rates are to be fixed, is justified by the fact 
that public utilities may generally be regarded as having per- 
petual life and that, ordinarily, capital need not be retired un- 
less the property is to be purchased. A public service property 
taken in its entirety may be treated, therefore, as though it had 
unlimited life. The property is kept in good condition by the 
repair of its parts and by replacements, as these parts become 
useless and have to be discarded. No part of the investment, 
if there be unlimited life, need be returned to the owner, but as 
the plant grows old and one part after another has to be replaced, 
he must be allowed to recover in the earnings the cost of each 
article as replaced. It is on this principle that many complex 
and, particularly, publicly owned properties are operated. In the 
early years of the life of a property made up of many parts, 
such as rails and ties, the replacement requirements will be 
small. As the property acquires age, the replacements — pro- 
vided that extensions are relatively unimportant and negligible 
in comparison with the extent of the property under considera- 
tion — will gradually increase to nearly the amount indicated 
by the Straight Line Method. The departure from this amount 
will be dependent upon the annual extensions of the system in 
relation to the entire investment. There will be ultimate agree- 
ment between the replacement requirement and the amount 
estimated by the Straight Line Method if the plant is one that 
has ceased to grow. The valuation for rate-fixing purposes