The cost of building Runyang Bridge in China, the world\'s third longest suspens
ID: 2653463 • Letter: T
Question
The cost of building Runyang Bridge in China, the world's third longest suspension bridge, was approximately $5 million. The indefinite upkeep costs are estimated to be $403,777 per year. Annual benefits of $340,000 and annual disbenefits of $41,000 have also been identified. Using an interest rate of 17% per year, determine the conventional B-C ratio.
Correct answer: 0.238
Please provide step by step solution to get to that correct answer.
The cost of building Runyang Bridge in China, the world's third longest suspension bridge, was approximately $5 million. The indefinite upkeep costs are estimated to be $403,777 per year. Annual benefits of $340,000 and annual disbenefits of $41,000 have also been identified. Using an interest rate of 17% per year, determine the conventional B-C ratio.
Correct answer: 0.238
Please provide step by step solution to get to that correct answer.
Explanation / Answer
We need to compute PV of both costs and benefits, Since both annual costs and benefits are for indefinite period, they form a perpetuity and PV of perpetuity can be calculated using the following formula:
PV = Annual cash flow/ Interest rate
Net Annual Benefits = 340,000-41,000
= 299,000
PV of annual benefits = 299,000/0.17
=$1,758,823.53
PV of annual up keeping cost = 403,777/0.17
= $2,375,158.82
PV of total cost = PV of annual up keeping cost + initial cost
= $2,375,158.82 +5,000,000
=$7,375,158.82
B-C ratio = PV of annual benefits/ PV of total cost
= $1,758,823.53/ 7,375,158.82
= 0.238
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