Question

1) A highway construction company is under contract to build a new roadway through a scenic area and two rural towns in Colorado. The road is expected to cost $18,000,000, with annual upkeep estimated at S150,000 per year. Additional income from tourist (Benefits) of $900,000 per year is estimated. The road is expected to have a useful commercial life of 20 years. Determine if the highway should be constructed at a discount rate of 6% per year, applying the Conventional B/C method. Remember to state your decision (Build or don't build). (50

Answer 1

Solution:

For this question, we shall use the conventional B/C (benefit-cost) method with Annual worth (AW)

B/C = AW(benefit from project)/AW(cost of proposed project)

Now, we are given that annual benefit from project (due to tourism) = $900,000 and annual cost (of maintenance) from project = $150,000. Further, initial cost (IC) = $18,000,000

Since, nothing is mentioned about the salvage value (post useful life is over), assuming it to be 0.

Annual worth of initial cost: (A/P, i, n) = [i(1+i)ⁿ/((1+i)ⁿ - 1)] where i is the interest or discount rate per year and n is the number of years of useful life. So, for this question, i = 6% and n = 20 years

AW of initial cost = IC*(A/P, 6%, 20)

So, (A/P, 0.06, 20) = [0.06(1+0.06)²⁰/((1+0.06)²⁰ - 1)] = 0.192/2.207 = 0.087 (approx)

So, AW of IC = 18000000*0.087 = $1,565,926.6

Thus, B/C = (900000/(1565926.6 + 150000)) = 900000/1715926.6 = 0.52

Since, B/C < 1, implying that the estimated annual benefits are lower than the cost, the project proposal should not be accepted. In other words, the highway should not be build.