Capitalized Cost
In computing the present worth of the costs associated with a proposed scheme, it is often
advantageous to select an analysis period of infinite duration. The present worth of the fu-
ture costs is then referred to as the capitalized cost of the scheme.
Since each expenditure recurs indefinitely during the analysis period, the various costs
constitute a group of perpetuities. Thus, the capitalized cost C 0 is Cc = (P - L)^ 1 +
L + CIi 1 , or C 0 = (P - L)U 1 + P + CIi 1.
If an asset is considered to have an infinite life span, these equations reduce to C 0 = P
- CIi 1. In these equations, i = il9n= N.
DETERMINATION OF CAPITALIZED COST
Two methods of conveying water for an industrial plant are being analyzed. Method A
uses a tunnel, and method B a ditch and flume. The costs are as follows:
Method A Method B
Tunnel Ditch Flume
First cost, $ 180,000 50,000 40,000
Salvage value, $ ... ... 5,000
Life, years Infinite 50 15
Operating cost, $/year 2,300 2,000 3,600Evaluate these two alternatives on the basis of capitalized cost, using a 5 percent interest
rate.
Calculation Procedure:
- Compute the capitalized cost of the first alternative
Since the tunnel has an infinite life, C 0 = P + CIi 1 = $180,000 + $2300/0.05 = $226,000. - Compute the capitalized cost of the second alternative
Using the capital-recovery factor for n = 50 years, i = 5 percent, we find for the ditch C 0 =
($50,000/0.05)(0.05478) + $2000/0.05 = $94,780.
Using a similar procedure for the flume, which has a 15-year life, gives C 0 =
($35,000/0.05)(0.09634) + $5000 + $3600/0.05 = $144,440. The total capitalized cost for
method B = the sum of the flume and ditch costs, or $239,220. Since method A costs less,
it is more economical.
CAPITALIZED COST OFASSET WITH
UNIFORM INTERMITTENT PAYMENTS
What is the capitalized cost of a bridge costing $85,000 and having-a 25-year life, a
$10,000 salvage value, $400 annual maintenance cost, and repairs at 5-year intervals of
$2000, if the interest rate is 5 percent?