Question

Problem 07.007 - Conventional B/C ratio for road improvement project The cost of grading and spreading gravel on a curvy rural road is expected to be $300,000. The road will have to be maintained at a cost of $28,000 per year. Even though the new road is not very smooth, it allows access to an area that previously could only be reached with off-road vehicles. The improved accessibility has led to a 166% increase in the property values along the road. If the previous market value of the property was $900,000, calculate the conventional B/C ratio using an interest rate of 6% per year and a 20-year study period. The conventional B/C ratio is

Answer 1

Sol:

Grading and Spreading gravel Cost = $300,000

cost = $34,000 per year

Property value increase % = 144%

Previous market value of property = $900,000

Interst rate = 6% per year

Study period = 20 years

To compute conventional Benefit cost ratio (B/C ratio):

Benefit = (Previous market value of property * Property value increase %) - Previous market value of property

Benefit = (900,000 * 144%) - 900,000

Benefit = 1,296,000 - 900,000 = $396,000

Cost = Grading and Spreading gravel Cost + (Maintenance Cost per annum (PMT), Interest rate, period)

Cost = 300,000 + (34,000, 6%, 20)

Cost = 300,000 + $389,977.32

Cost = $689,977.32

Benefit cost ratio (B/C) = Benefit / Cost

Benefit cost ratio (B/C) = 396,000 / 689,977.32 = 0.57

The conventional B/C ratio is 0.57