Calculation Procedure:- Convert the assumed repair costs to an equivalent
series of uniform annual payments
Assume that the repairs are made at the end of every 5-year interval, including the re-
placement date. Using the SFP factor, we see the equivalent series of uniform annual pay-
ments R 1 = $2000(SFP) for j = 5 percent, n = 5 years, OrU 1 = $2000(0.18097) = $362. - Convert the true repair costs to an equivalent series of
uniform annual payments
Repairs are omitted when the bridge is scrapped at the end of 25 years, thereby saving
$2000 in the final 5-year period. Convert this amount to an equivalent series of uniform
annual payments (i.e., savings) and subtract from the result in step 1. Or, R 2 =
$2000(SFP) for j = 5 percent, n = 25 years. Or, R 2 = $2000(0.02095) = $42. Thus the an-
nual cost of the repairs = $362 - $42 = $320. - Compute the capitalized cost
Using the capital-recovery factor for / = 5 percent, n = 25 years, we get Cc =
($75,000/0.05)(0.07095) + $10,000 + $400/0.05 + $320/0.05 = $130,830.
Related Calculations'. An alternative solution could be worked as follows: Since
the $2000 saving at the end of every 25-year interval coincides in timing with the income
of $10,000 from the sale of the old bridge as scrap, this saving can be combined with the
salvage value to obtain an effective value of $12,000 for salvage. The annual cost of re-
pairs is therefore taken as $362, the value OfU 1 , step 1. Applying the capital-recovery fac-
tor gives C 0 = ($85,000 - $12,000)/0.05 + $12,000 + $400/0.05 + $362/0.05 =
$130,830. This agrees with the previously determined value.
CAPITALIZED COST OF AN ASSET WITH
NONUNIFORM INTERMITTENT PAYMENTS
A bridge has the same cost data as in the previous calculation procedure except for the re-
pairs, which are as follows:
End of year Repair cost, $
10 2000
15 3500
20 1500What is the capitalized cost of the bridge if the interest rate is 5 percent?
Calculation Procedure:- Compute the present worth of the repairs for one life span
Use the single-payment present-worth factor for each of the repair periods. Or, PW =
$2000(0.6139) + $3500(0.4810) + $1500(0.3769) = $3477.