A relocation of a stretch of rural highway is to be made. Alternate new route lo
ID: 1198613 • Letter: A
Question
A relocation of a stretch of rural highway is to be made. Alternate new route locations are designated as M and N. The initial investment by government highways agencies will be $3,000,000 for M and $5,000,000 for N. Annual highway maintenance costs will be $120,000 for M and $90,000 for the shorter location N. Relevant annual road user costs are estimated as $880,000 for M and $660,000 for N. Determine which highway is acceptable using the B/C ratio. Use an I of 8%, a 20-year study period, and assume salvage values equal to 20% of first cost.
Explanation / Answer
Route M:
Initial Investment: P = $3,000,000
Annual Maintenance Cost: A = $120,000
Annual Benefit: $880,000
Salvage Value = $600,000 (20% of $3,000,000)
i = 8%
n = 20 years
Annual Equivalent of costs = 3,000,000(A/P , 8% , 20) + 120,000 - 600,000(A/F , 8% , 20)
= 3,000,000 x 0.1019 + 120,000 - 600,000 x 0.0219
= 305,700 + 120,000 - 13,140
= $412,560
Annual Equivalent of Benefits = $880,000
B/C Ratio = Annual Equivalent of Benefits / Annual Equivalent of costs
= $880,000 / $412,560
= 2.13
Route N:
Initial Investment: P = $5,000,000
Annual Maintenance Cost: A = $90,000
Annual Benefit: $660,000
Salvage Value = $1,000,000 (20% of $5,000,000)
i = 8%
n = 20 years
Annual Equivalent of costs = 5,000,000(A/P , 8% , 20) + 90,000 - 1,000,000(A/F , 8% , 20)
= 5,000,000 x 0.1019 + 90,000 - 1,000,000 x 0.0219
= 509,500 + 90,000 - 21,900
= $577,600
Annual Equivalent of Benefits = $660,000
B/C Ratio = Annual Equivalent of Benefits / Annual Equivalent of costs
= $660,000 / $577,600
= 1.14
Since the B/C ratio of highway M is higher, it is acceptable.
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