There are a number of reasons for not paving a rural road, including low traffic volume, property owners who do not want it paved, speed control, and political issues. On the other hand, paved roads have lower road-user operating costs and are less costly to maintain. In Washington County, a report prepared by the county engineer showed that the construction cost for a stabilized gravel road that will last 3 years is $1,025,000, with a maintenance cost of $355,000 per year. A bitumi­nous road will cost $3,525,000, but it will last for 10 years. Use i = 8% per year. (a) At what main­tenance cost per year (for the bituminous road) will the equivalent annual costs of the two roads be the same? (b) If the road is not paved and the annual maintenance cost of the stabilized gravel surface is

Question

actually 30% per year higher than esti­mated, how many years must this surface last for the two to break even, assuming the paved road maintenance would be the breakeven value deter­mined above? Answer these questions using man­ual and spreadsheet solution, as your instructor requests.

What will be an ideal response?

Answer 1

By hand

(a) Set annual costs equal to each other and solve for A, annual maintenance cost



1,025,000(A/P,8%,3) + 355,000 = 3,525,000(A/P,8%,10) + A

1,025,000(0.38803) + 355,000 = 3,525,000(0.14903) + A

A = $227,400



(b) Annual gravel road maintenance = 355,000(1.30) = $461,500; find n for the gravel

road



1,025,000(A/P,8%,n) + 461,500 = 3,525,000(A/P,8%,10) + 227,400

(A/P,8%,n) = [3,525,000(0.14903) + 227,400

– 461,500]/1,025,000

= 0.28413



n is between 4 and 5 years. By interpolation, n = 4.3 years

By spreadsheet

See the spreadsheet for explanation to display answers: (a) $227,405 per year, and

(b) 4.3 years using the PMT function to find A and Goal Seek to find n