Question

New buses for a mass-transit agency cost $10 million and are expected to last for 10 years with a $1 million salvage value. The buses cost $500,000 to operate and maintain each year. If the system is used for 594,914 trips per year, with the average cost to the rider of $1.50, but providing $4.00 in benefits, and the interest rate is 4% per year, the benefit-cost ratio using PW for the investment will be

Correct answer is 0.90.

Please show all work by hand, and not excel! Thanks!

Answer 1

PW of annual benefits = 594,914 x $4 x P/A(4%, 10) = $2,379,656 x 8.1109 = $19,301,152

PW of salvage value = $1,000,000 x P/F(4%, 10) = $1,000,000 x 0.6756 = $675,600

PW of annual costs = [(594,914 x $1.5) + 500,000] x P/A(4%, 10) = ($892,371 + 500,000) x 8.1109

= $1,392,371 x 8.1109 = $11,293,382

Benefit cost ratio = PW of annual benefits / (First cost + PW of annual costs - PW of salvage value)

= $19,301,152 / $(10,000,000 + 11,293,382 - 675,600)

= $19,301,152 / $20,617,782

= 0.94