Two designs have been proposed for a short span bridge in a rural area, as shown in the following table. The first proposal is to construct the bridge in two phases (Phase I now and Phase II in 25 years). The second alternative is to construct it in one phase. Assuming that the annual interest rate is 4%, determine which alternative is preferred using present worth analysis.

Question

What will be an ideal response?

Answer 1

Calculate the present worth of Alternative I. Note that the Phase II has an
additional annual maintenance cost to that of Phase I. This will require that the
annualized costs be "brought" back to the present condition at year 25, and then
this value needs to be brought back to year 0. Using Equation 13.4:
PWI = 14200000 + 75000(P/A, 4%, 50) + 12600000(P/F, 4%, 25) +
((25000(P/A, 4%, 25))(P/F, 4%, 25))
PWI = 14200000 + 75000(21.482) + 12600000(0.3751) +
25000(15.622)(0.3751)
PWI = 14200000 + 1611150 + 4726260 + 146495.31
PWI = 20683905.31
Therefore, the present worth of Alternative I is $20,683,905.
Next, calculate the present worth of Alternative II.
PWII = 22400000 + 100000(P/A, 4%, 50)
PWII = 22400000 + 100000(21.482)
PWII = 24548200
Therefore, the present worth of Alternative II is $24,548,200.
Based on the above economic analysis, Alternative I, consisting of a two-phase
construction process should be chosen. Alternative I has a lower net present worth
of costs than does Alternative II.