Question

Environmental Economics Question:

A city is thinking about building a new expressway that will go through downtown. Construction occurs in periods 0, 1 and 2. The costs for each of these periods is $100. The benefits accrue in periods 2, 3 and 4, and equal $150. The discount rate is equal to 50%.

Calculate the present value of net benefits. Should the city build the freeway? And recommend a policy given the numerical value.

Answer 1

ANSWER:

cash flow in year 0 = cost in year 0 = -100

cash flow in year 1 = cost in year 1 = -100

cash flow in year 2 = cost in year 2 + benefits in year 2 = -100 + 150 = 50

cash flow in year 3 = benefits in year 3 = 150

cash flow in year 4 = 150

i = 50%

present worth = cash flow in year 0 + cash flow in year 1(p/f,i,n) + cash flow in year 2(p/f,i,n) + cash flow in year 3(p/f,i,n) + cash flow in year 4(p/f,i,n)

pw = -100 - 100(p/f,50%,1) + 50(p/f,50%,2) + 150(p/f,50%,3) + 150(p/f,50%,4)

pw = -100 - 100 * 0.6667 + 50 * 0.4444 + 150 * 0.2963 + 150 * 0.1975

pw = -100 - 66.67 + 22.22 + 44.445 + 29.625

pw = -70.38

so the present worth is -$70.38

since the present worth is negative so the freeway shouldn't be build.

since the present worth is negative , therefore other sources of income should be planned viathis expressway like opening various food points such that more tax can be collected from these points and also the government should think of increasing toll tax of vehicles passing through these expressways.