Three transportation projects have been proposed to increase the safety in and around a residential neighborhood. Each project consists of upgrading existing street signing to highly retroreflective sheeting to increase visibility. The following table shows the initial construction costs, annual operating costs, useful life of the sheeting, and the salvage values for each alternative. Assume that the discount rate is 10%. Calculate the present worth for each alternative and determine the preferred project based on the economic criteria.

Question

What will be an ideal response?

Answer 1

Use Equation 13.4.
Calculate the present worth for Alternative I.
PWI = 19,000 + 2,500(P/A, 10%, 10) – 3,000(P/F, 10%, 10)
PWI = 19,000 + 2,500(6.145) – 3000(0.3855)
PWI = 33,206
Therefore, the present worth of Alternative I is $33,206.
Calculate the present worth of Alternative II. In order to compare this alternative
to the others, Alternative II must be analyzed using the prevailing useful life
values in the other alternatives (10 years).
PWII = 8000 + 4000(P/A, 10%, 10) + (8000 – 900)(P/F, 10%, 5) – 900(P/F, 10%,
10)
PWII = 8000 + 4000(6.145) + 7100(0.6209) – 900(0.3855)
PWII = 36641
Therefore, the present worth of Alternative II is $36,641.
Calculate the present worth for Alternative III.
PWIII = 20,000 + 2,500(P/A, 10%, 10) – 4,600(P/F, 10%, 10)
PWIII = 20,000 + 2,500(6.145) – 4,600(0.3855)
PWIII = 33,589.2
Therefore, the present worth of Alternative III is $33,589.
Since Alternative I has the lowest net present worth of costs, it is the best
alternative to choose based on the economic criteria provided.