Answer:
C. Site B
Step-by-step explanation:
A benefit-cost (B/C) method is a decision making techi=niques that uses benefit-cost ratio (BCR) to give a summary of overall relationship between the relative benefits and costs and a project being proposed.
To calculated the present values (PV) of Maintenance and Operations (M&O) Cost, Benefits and Disbenefits, we use cumulative discounting factor (CDF) for calculating the present value (PV) of an ordinary annuity as follows:
CDF = [{1 - [1 / (1 + r)]^n} / r] …………………………………. (1)
Where;
r = interest rate = 12%, or 0.12
n = number of years = 5
Substitute the values into equation (1), we have:
CDF = [{1 - [1 / (1 + 0.12)]^5} / 0.12] = 3.60
We can now calculate the B?C of each Site as follows as follows:
a. Calculation of B/C ratio of Site A
Initial cost = $55
PV of M&O Cost = M&O Cost per year * CDF = $3 * 3.60 = $10.80
PV of Benefits = Benefits per year * CDF =$20 * 3.60 = $72.00
PV of Disbenefits = Disbenefits per year * CDF = $0.5 * 3.60 = $1.80
PV of Total Cost = Initial cost + PV of M&O cost + PV of Disbenefits = $55 + $10.80 + $1.80 = $67.60
B/C ratio of Site A = PV of Benefits / PV of tota cost = $72.00 / $67.60 = 1.07
b. Calculation of B/C ratio of Site B
Initial cost = $70
PV of M&O Cost = M&O Cost per year * CDF = $4 * 3.60 = $14.40
PV of Benefits = Benefits per year * CDF =$29 * 3.60 = $104.40
PV of Disbenefits = Disbenefits per year * CDF = $2 * 3.60 = $7.20
PV of Total Cost = Initial cost + PV of M&O cost + PV of Disbenefits = $70 + $14.40 + $7.20 = $91.60
B/C ratio of Site A = PV of Benefits / PV of tota cost = $104.40 / $91.60 = 1.14
b. Calculation of B/C ratio of Site B
Initial cost = $200
PV of M&O Cost = M&O Cost per year * CDF = $6 * 3.60 = $21.60
PV of Benefits = Benefits per year * CDF =$55 * 3.60 = $198.00
PV of Disbenefits = Disbenefits per year * CDF = $2.1 * 3.60 = $7.56
PV of Total Cost = Initial cost + PV of M&O cost + PV of Disbenefits = $200 + $21.60 + $7.56 = $229.16
B/C ratio of Site A = PV of Benefits / PV of tota cost = $198.00 / $229.16 = 0.86
Conclusion
1. Since the B/C ratio of only Site A and Site B are greater than 1, both are acceptable.
2. But since Site B's B/C ratio of 1.14 is greater Site A's B/C ratio of 1.07, Site B is the most acceptable. Therefore, the correct option is C. Site B.