Engineers at the West Virginia DOT have identified 3 viable sites for a new brid

Question

Engineers at the West Virginia DOT have identified 3 viable sites for a new bridge across the Ohio River. The 3 sites are all within 15 miles of each other, but the land and construction costs vary. The bridge that would directly link the cities on opposite sides of the river would have the lowest travel costs (shortest distance), but it would also have the highest construction cost because of property values. The bridge location just north of the two cities would involve less travel time than the one to the south. The costs associated with each bridge are shown in the table below. Using the Benefits cost ratio method and an interest rate of 6% per year, determine which location is preferred, assuming that whichever bridge is built will be permanent.

Explanation / Answer

If a particular cost or benefit is expected to occur permanently, then it shall be termed as perpetuity.
Thus, the P.V. of the perpetuity is: [Expected Cost or Benefit] / [Interest Rate]

LOCATION-S
The annual maintenance cost is $150,000
Thus, the P.V. of annual maintenance cost = 150,000 / 6% = $2.5M
Initial Investment = $50M
Total P.V. of costs = $2.5M + $50M = $52.5M

The savings in user cost is $7.6M.
Thus, the P.V. of savings in user cost = 7.6M / 6% = $126.7M

Thus, Benefit-Cost ratio = P.V. of Benefits / P.V. of Costs
= 126.7M / 52.5M
= 2.4127

LOCATION-D
The annual maintenance cost is $130,000
Thus, the P.V. of annual maintenance cost = 130,000 / 6% = $2.17M
Initial Investment = $75M
Total P.V. of costs = $2.17M + $75M = $77.17M

The savings in user cost is $4.1M.
Thus, the P.V. of savings in user cost = 4.1M / 6% = $68.3M

Thus, Benefit-Cost ratio = P.V. of Benefits / P.V. of Costs
= 68.36M / 77.17M
= 0.8855

LOCATION-N
The annual maintenance cost is $140,000
Thus, the P.V. of annual maintenance cost = 140,000 / 6% = $2.33M
Initial Investment = $60M
Total P.V. of costs = $2.33M + $60M = $62.33M

The savings in user cost is $5.9M.
Thus, the P.V. of savings in user cost = 5.9M / 6% = $98.33M

Thus, Benefit-Cost ratio = P.V. of Benefits / P.V. of Costs
= 98.33M / 62.33M
= 1.5775

THUS, AS PER BENEFIT-COST RATIO LOCATION-S SHOULD BE CHOSEN.

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