- Convert the result of step 1 to an equivalent series of uniform
annual payments
Using the capital-recovery factor, we find the annual cost of repairs = $3477(CR), where
i = 5 percent, n = 25 years. Or, ca = $3477(0.07095) = $247. - Compute the capitalized cost
Using the same method as in step 3 of the previous calculation procedure gives Cc =
$106,430 + $10,000 + $8000 + $247/0.05 = $129,370.
Related Calculations: An alternative way of solving this problem is to combine
the present worth of the payments for repairs ($3477) with the initial cost ($85,000) to ob-
tain an equivalent initial cost P'. Then, P' = $88,477, and P' -L = $88,477 - $10,000 =
$78,477. By applying the capital-recovery factor, Cc = $129,370 as before.
STEPPED-PROGRAM CAPITALIZED COST
A firm plans to build a new warehouse with provision for anticipated growth. Two alter-
native plans are available.
Plan A Plan B
First cost, $ 100,000 80,000
Salvage value, $ 10,000 15,000
Life, years 25 30
Annual maintenance, $ 1,400 1,200 first 10 years,
1,800 thereafter
Cost of enlarging structure
10 years hence, $ ... 40,000If money is worth 10 percent, which is the more economical plan?
Calculation Procedure:
- Compute the total present worth of the second plan costs
Let P' represent the total present worth of the costs associated with plan B for one life
span. Using the SPPW for / = 10 percent, n = 10 years, for the cost of enlarging the struc-
ture, and the USPW for the annual maintenance after expansion, and the difference be-
tween the annual maintenance costs of this structure and the original structure, we get
P' = $80,000 + $40,000(0.3855) + $1800(9.427) - $600(6.144) = $108,700. - Compute the capitalized cost of each alternative
Using the capital-recovery factor for plan A with i = 10 percent, n = 25 years yields C 0 =
($100,000 - $10,000)/0.10 + $10,000 + $1400/0.10 = $123,150.
For plan B, by using the present worth from step 1, Cc = ($108,700 -
$15,000)/0.10 + $15,000 = $114,400. Note that the capital-recovery factor for
plan B is for 30 years.
Since plan B has the lower capitalized cost, it is more economical.