Present Worth of Future CostsA cost analysis of alternative schemes may be performed by computing the present worth
of all expenses incurred in each scheme during a stipulated period called the analysis pe-
riod. This period should encompass an integral number of lives of each asset required un-
der the alternative schemes.
PRESENT WORTH OF FUTURE COSTS OF
ANINSTALLATION
A city contemplates increasing the capacity of existing water-transmission lines. Two
plans are under consideration: Plan A requires construction of a parallel pipeline, flow be-
ing maintained by gravity. The initial cost is $800,000, and the life is 60 years with an an-
nual operating cost of $1000. Plan B requires construction of a booster pumping station
costing $210,000 with a life of 30 years. The pumping equipment costs an additional
$50,000; it has a life of 15 years and a salvage value of $10,000. The annual operating
cost is $35,000. Which is the more economical plan if the interest rate is 6 percent?
Calculation Procedure:
- Construct a money-time diagram of the situation
Figure 5 shows the money-time diagram. Note that this diagram uses 60 years as the
analysis period. Record on the money-time diagram the capital expenditures during this
60-year period. - Compute the total present worth of the payments
For plan A, using the USPW factor for n = 60 years, we get PW = $800,000 +
$1000(16.161) = $816,160. For plan B, by using the SPPW factor for the payments
shown in Fig. 5, and the uniform series present-worth factor for the operating cost, PW =
$260,000 + $40,000(SPPW) + $250,000(SPPW) + $40,000(SPPW) + $35,000(USPW) -
$10,000(SPP W) - $260,000 + $40,000(0.4173) + $250,000(0.1741) + $40,000(0.0727) +
$35,000(16.161) - $10,000(0.0303) - $888,460.
Since the present worth of plan A is less than that of plan B, the scheme for plan A
should be adopted because it is more economical.
*Income from disposal of equipment.
Al I sums in units of $ 1000FIGURE 5. Money-time diagram.Time in
yeorsPlan BPlan A