2. The Citiville Town Council is considering constructing a new waste management

Question

2. The Citiville Town Council is considering constructing a new waste management following data are associated with facility. The with the three top bids that have been received for consideration: Alternative Useful Life, Years 10 10 10 Initial Cost$725,000 $895,000 $640,000 Annual Benefit 150,000 185,000 100,000 Annual M&O; 30,000 40,000 20,000 Using benefit-cost ratio analysis, determine which alternative should be selected (if any). Assume an interest rate of 5% per year. As a municipality, Citiville pays no taxes.

Explanation / Answer

Benefit Cost Ratio = Present value of all benefits / Present value of all costs

For Project A

R = 5%

Useful life (n) = 10 years

Present value of benefits = 150000*(1-1/(1+R)^n)/R = 150000*(1-1/1.05^10)/.05 = $1158260.24

Present value of all costs = Initial cost + Present value of O&M cost = 725000 + 30000*(1-1/(1+R)^10)/R

Present value of all costs = 725000 + 30000*(1-1/1.05^10)/.05 =$956652.05

Benefit Cost Ratio for Project A =1158260.24 / 956652.05 = 1.210

For Project B

R = 5%

Useful life (n) = 10 years

Present value of benefits = 185000*(1-1/(1+R)^n)/R = 185000*(1-1/1.05^10)/.05 = $1428520.96

Present value of all costs = Initial cost + Present value of O&M cost = 895000 + 40000*(1-1/(1+R)^10)/R

Present value of all costs = 895000 + 40000*(1-1/1.05^10)/.05 =$1203869.4

Benefit Cost Ratio for Project B =1428520.96 / 1203869.4 = 1.186

For Project C

R = 5%

Useful life (n) = 10 years

Present value of benefits = 100000*(1-1/(1+R)^n)/R = 100000*(1-1/1.05^10)/.05 =$772173.49

Present value of all costs = Initial cost + Present value of O&M cost = 640000 + 20000*(1-1/(1+R)^10)/R

Present value of all costs = 640000 + 20000*(1-1/1.05^10)/.05 =$794434.70

Benefit Cost Ratio for Project C = 772173.49 / 794434.70 = .9719

Thus,

Benefit Cost Ratio for Project A =1.210

Benefit Cost Ratio for Project B =1.186

Benefit Cost Ratio for Project C =.9719

Since, Benefit cost ratio for project A is highest that is 1.210. Thus, Project A should be selected.

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