A highway project is expected to cost $1,700,000 initially. The annual operating and maintenance cost after the first year is $5,000 and will increase by $500 each year for a project lifespan of 20 years. At the end of the tenth year, the project must be resurfaced at a cost of $300,000. (a) Calculate the present worth of costs for this project over a 20-year period if the annual interest rate is 5%. (b) Convert the value obtained in (a) to equivalent uniform annual costs.
What will be an ideal response?
(a) Calculate the present worth using Equation 13.4:
PW = 1,700,000 + 4,762 + 4,989 + 5,183 + 5,348 + 5,485 + 5,597 + 5,685 +
5,753 + 5,801 + 5,832 + 5,847 + 5,847 + 5,834 + 5,808 + 5,772 + 5,726 +
5,672 + 5,610 + 5,540 + 5,465 + 5,384 + 184,173 = 1,995,729
Therefore, the present worth (cost) for this project is $1,995,729.
(b) Convert the above present worth cost to EUAC using Equation 13.6.
Since the project is analyzed for 20 years, n = 20.
EUAC = PW(A/P, 5%, 20)
EUAC = (1995729) [0.05 (1 + 0.05)20] / [(1 + 0.05)20 – 1]
EUAC = (1995729) (0.080243)
EUAC = 160142
Therefore, the EUAC for this project will be $160,142.
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