Answer:
The conventional B/C ratio is 1.83.
Explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
Officials from the City of Galveston and State of Texas gathered to celebrate the start of a beach restoration project that involves dumping sand and adding antierosion structures. The first cost of the project is $30 million with annual maintenance estimated at $340,000. If the restored/expanded beaches attract visitors who will spend $6.2 million per year, what is the conventional B/C ratio at the social discount rate of 8% per year. Assume the State wants to recover the investment in 20 years.
Explanation of the answers is now given as follows:
From the question, we have:
First cost = $30 million, or $30,000,0000
Estimated annual maintenance cost = $340,000
Expected annual revenue = Amount to spend per year by the visitors = $6.2 million, or 6,200,000
r = social discount rate per year = 8%, or 0.08
n = number of recover the investment years = 20
Incorporating the formula for calculating the present value of an ordinary annuity, we have:
B = Present worth of annual revenue = Estimated annual revenue * ((1 - (1 / (1 + r))^n) / r) = $6,200,000 * ((1 - (1 / (1 + 0.08))^20) / 0.08) = $60,872,513.93
C = Present worth of cost = First cost + (Estimated annual maintenance cost * ((1 - (1 / (1 + r))^n) / r)) = $30,000,0000 + ($340,000 * ((1 - (1 / (1 + 0.08))^20) / 0.08)) = $33,338,170.12
B/C ratio = B / C = $60,872,513.93 / $33,338,170.12 = 1.83
Therefore, the conventional B/C ratio is 1.83.
