184 VALUATION, DEPRECIATION AND THE RATE-BASE
The Sinking Fund Method, if correctly applied, involves, as
already stated, only a one time calculation of the annual depreciation
 or replacement increment and its result agrees with that
of the Equal Annual Payment Method.
The Unlimited Life Method is the most flexible. It may be
so applied as to give identical results with the Equal Annual
Payment and the Sinking Fund Method, or it may be applied
to vary somewhat therefrom so as to make the earnings requirements
 least in the early years.
Under the Sinking Fund Method, on the above assumption
with reference to absolute agreement of actual with probable life,
the annual requirement for $1oo of cost would be interest of
$6 and the amortization or depreciation increment of $7.59 for
each of the to years of life making a total of $13.59 for each
year.
Under the Unlimited Life Method, the replacement increment
 may be estimated as in the case of the Sinking Fund
Method, in which event the required annual earnings would be
$13.59 or they may be graded from a smaller amount in the
earlier years to a larger amount in the later years, in which
event the required annual earnings would appear on an increasing
 scale.
The extreme case has been assumed for the illustration of the
Unlimited Life Method in Table 13, that no provision whatever
is made for replacement until the article to be replaced fails.
This will account for the sudden increase noted for the eleventh
and twenty-first years, in each of which the replacement requirement
 is increased by $100. The first of the original articles fails
in the tenth year (actual life being assumed the same as the
probable life), and thereafter $100 of the original investment goes
out of use and has to be replaced annually until and after the
twenty-first year when the annual replacement requirement is
$200.