The cash flows associated with each expansion site are summarized below. The expansion is planned for 5 years, and the interest rate is 12% per year. Use the B/C method to determine which site, if any, is the most acceptable. The monetary unit is $ million. Site A B C
Initial cost, $ 55 70 200
M&O Cost, $/year 3 4 6
Benefits, $/year 20 29 55
Disbenefits, $/year 0.5 2 2.1
A. Site A
B. Site C
C. Site B
D. None

C. Site B

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.

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