40 points An outer belt highway is being planned for a metro

(40 points) An outer belt highway is being planned for a metropolitan area in Tennessee. The initial cost is estimated to be $170,000,000. Benefits to the public are expected to be $15,000,000 per year. Maintenance costs are estimated at $1,200,000 per year. The beltway will have to be esurfaced every 10 years at a cost of $7,000,000. The road is to be maintained indefinitely. The ty\'s cost of funds is 6%. ed on maintaining the road in perpetuity, find the conventional benefit-cost ratio. lations in the space below. Show your

Solution

ANSWER:

Initial cost = $170,000,000

pw of initial cost will be $170,000,000

maintenance cost = $1,200,000 per year

pw of maintenance cost = maintenance cost(p/a,i,n)

i = 6% and n = infinity

pw of maintenance cost = 1,200,000(p/a,6%,infinity)

pw of maintenance cost = 1,200,000 * 16.667 = $20,004,000

resurfacing cost every 10 years = $7,000,000

pw of resurfacing cost = (resurfacing cost(p/f,i,n)) / i

pw of resurfacing cost = (7,000,000(p/f,6%,infinity)) / 6%

pw of resurfacing cost = (7,000,000 * 0.5584) / 6%

pw of resurfacing cost = $3,908,800 / 6% = $65,146,666.67

total costs = pw of resurfacing cost + pw of maintenance costs + pw of initial costs = 65,146,666.67 + 20,004,000 + 170,000,000 = $255,150,666.67

benefits = $15,000,000

pw of benefits = benefits(p/a,i,n) = 15,000,000(p/a,6%,infinity) = 15,000,000 * 16.667 = $250,005,000

benefit to cost ratio -= pw of benefits / pw of total costs = 250,005,000 / 255,150,666.67 = 0.9798

so the benefit to cost ratio is 0.9798