A project is being planned to provide energy and recreational benefits. The esti
ID: 1111947 • Letter: A
Question
A project is being planned to provide energy and recreational benefits. The estimated benefits and costs expected to be derived from the three alternatives under consideration are listed as follows 3) Decision Alternatives $6,000,000 $10,000,000 $22,000,000 Initial Cost Annual Benefits $1,000,000 $1,200,000 $1,800,000 Energy sales Pollution control $250,000 $350,000 Community Benefits $350,000 $450,000 Recreational Benefits | $100,000 $200,000 $500,000 $600,000 $350,000 O&M; Costs $200,000 $250,000 $350,000 The interest rate is 10% and the life of each project is estimated to be 50 years Find the benefit-cost ratio for each alternative. Select the best alternative, according to Bc(O a. b.Explanation / Answer
a) To calculate Benefit cost ratio we divide the sum of present value of all benefits with sum of present value of all costs
Present value = benefit or cost/(1+r)n, where r is interest rate and n is number of years
r = 10%
For project A, annual benefit = energy sales + pollution control + community benefits + recreational benefits
Annual benefit = 1000000+250000+350000+100000 = $1,700,000
Initial cost = $6,000,000
Annual costs would be O&M costs = $200,000
Present value of benefits = 1700000/(1.1)1 + 1700000/(1.1)2 + ............................... + 1700000/(1.1)49 + 1700000/(1.1)50 = 16855184.63
Present value of cost = 6000000 + 200000/(1.1)1 + 200000/(1.1)2 + .................. + 200000/(1.1)49 + 200000/(1.1)50 = 7982962.90
Benefit cost ratio = 16855184.63/7982962.90 = 2.11
For project B, annual benefit = energy sales + pollution control + community benefits + recreational benefits
Annual benefit = 1200000+350000+450000+200000 = $2,200,000
Initial cost = $10,000,000
Annual costs would be O&M costs = $250,000
Present value of benefits = 2200000/(1.1)1 + 2200000/(1.1)2 + ............................... + 2200000/(1.1)49 + 2200000/(1.1)50 = 21812591.87
Present value of cost = 10000000 + 250000/(1.1)1 + 250000/(1.1)2 + .................. + 250000/(1.1)49 + 250000/(1.1)50 = 12478703.62
Benefit cost ratio = 21812591.87/12478703.62 = 1.75
For project C, annual benefit = energy sales + pollution control + community benefits + recreational benefits
Annual benefit = 1800000+500000+600000+350000 = $3,250,000
Initial cost = $22,000,000
Annual costs would be O&M costs = $350,000
Present value of benefits = 3250000/(1.1)1 + 3250000/(1.1)2 + ............................... + 3250000/(1.1)49 + 3250000/(1.1)50 = 32223147.08
Present value of cost = 22000000 + 350000/(1.1)1 + 350000/(1.1)2 + .................. + 350000/(1.1)49 + 350000/(1.1)50 = 25470185.1
Benefit cost ratio = 32223147.08/25470185.1 = 1.27
b) We will choose the alternative with highest value of Benefit cost ratio
Highest value value of benefit cost ratio is for project A so we will choose project A
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