Q12-5. A city government has to choose from among three types of town-dump sanit
ID: 2717912 • Letter: Q
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Q12-5. A city government has to choose from among three types of town-dump sanitary systems. Revenues (fee collections) from the residents would be $100,000 per year over the 15 year time span of the proposal. The interest rate is 8%, and no salvage value is associated with either system. Benefits B are defined as revenues minus operating costs, and the Investment is the cost C.
Q12-5. A city government has to choose from among three types of town-dump sanitary systems. Revenues (fee collections) from the residents would be $100,000 per year over the 15 year time span of the proposal. The interest rate is 8%, and no salvage value is associated with either system. Benefits B are defined as revenues minus operating costs, and the Investment is the cost C.
Annual Revenue Annual O&M cost Investment Design A $100,000 $52,000 $400,000 Design B $100,000 $60,000 $290,000 Design C $100,000 $72,000 $190,000 a. Which system should be selected using a B-C approach? b. Which system should be selected using a B/C approach?Explanation / Answer
Actual results given to you may differ due to discount factor used. I have used 4 digit factor for better accuracy Projcet A Discount factor @8% Year Annual Revenue Annual O&M Cost Investment Total Cost Benefit-cost PV of Benefit -cost PV benefits PV of costs 1 Year 0 400,000 400,000 (400,000) (400,000) - 400,000 0.92593 Year 1 100,000 52,000 52,000 48,000 44,444 92,593 48,148 0.85734 Year 2 100,000 52,000 52,000 48,000 41,152 85,734 44,582 0.79383 Year 3 100,000 52,000 52,000 48,000 38,104 79,383 41,279 0.73503 Year 4 100,000 52,000 52,000 48,000 35,281 73,503 38,222 0.68058 Year 5 100,000 52,000 52,000 48,000 32,668 68,058 35,390 0.63017 Year 6 100,000 52,000 52,000 48,000 30,248 63,017 32,769 0.58349 Year 7 100,000 52,000 52,000 48,000 28,008 58,349 30,342 0.54027 Year 8 100,000 52,000 52,000 48,000 25,933 54,027 28,094 0.50025 Year 9 100,000 52,000 52,000 48,000 24,012 50,025 26,013 0.46319 Year 10 100,000 52,000 52,000 48,000 22,233 46,319 24,086 0.42888 Year 11 100,000 52,000 52,000 48,000 20,586 42,888 22,302 0.39711 Year 12 100,000 52,000 52,000 48,000 19,061 39,711 20,650 0.36770 Year 13 100,000 52,000 52,000 48,000 17,650 36,770 19,120 0.34046 Year 14 100,000 52,000 52,000 48,000 16,342 34,046 17,704 0.31524 Year 15 100,000 52,000 52,000 48,000 15,132 31,524 16,393 10,855 855,948 845,093 B-C = 10,855 B/C = 1.013 Projcet B Discount factor @8% Year Annual Revenue Annual O&M Cost Investment Total Cost Benefit-cost PV of Benefit -cost PV benefits PV of costs 1 Year 0 290,000 290,000 (290,000) (290,000) - 290,000 0.92593 Year 1 100,000 60,000 60,000 40,000 37,037 92,593 55,556 0.85734 Year 2 100,000 60,000 60,000 40,000 34,294 85,734 51,440 0.79383 Year 3 100,000 60,000 60,000 40,000 31,753 79,383 47,630 0.73503 Year 4 100,000 60,000 60,000 40,000 29,401 73,503 44,102 0.68058 Year 5 100,000 60,000 60,000 40,000 27,223 68,058 40,835 0.63017 Year 6 100,000 60,000 60,000 40,000 25,207 63,017 37,810 0.58349 Year 7 100,000 60,000 60,000 40,000 23,340 58,349 35,009 0.54027 Year 8 100,000 60,000 60,000 40,000 21,611 54,027 32,416 0.50025 Year 9 100,000 60,000 60,000 40,000 20,010 50,025 30,015 0.46319 Year 10 100,000 60,000 60,000 40,000 18,528 46,319 27,792 0.42888 Year 11 100,000 60,000 60,000 40,000 17,155 42,888 25,733 0.39711 Year 12 100,000 60,000 60,000 40,000 15,885 39,711 23,827 0.36770 Year 13 100,000 60,000 60,000 40,000 14,708 36,770 22,062 0.34046 Year 14 100,000 60,000 60,000 40,000 13,618 34,046 20,428 0.31524 Year 15 100,000 60,000 60,000 40,000 12,610 31,524 18,915 52,379 855,948 803,569 B-C = 52,379 B/C = 1.065 Projcet C Discount factor @8% Year Annual Revenue Annual O&M Cost Investment Total Cost Benefit-cost PV of Benefit -cost PV benefits PV of costs 1 Year 0 190,000 190,000 (190,000) (190,000) - 190,000 0.92593 Year 1 100,000 72,000 72,000 28,000 25,926 92,593 66,667 0.85734 Year 2 100,000 72,000 72,000 28,000 24,005 85,734 61,728 0.79383 Year 3 100,000 72,000 72,000 28,000 22,227 79,383 57,156 0.73503 Year 4 100,000 72,000 72,000 28,000 20,581 73,503 52,922 0.68058 Year 5 100,000 72,000 72,000 28,000 19,056 68,058 49,002 0.63017 Year 6 100,000 72,000 72,000 28,000 17,645 63,017 45,372 0.58349 Year 7 100,000 72,000 72,000 28,000 16,338 58,349 42,011 0.54027 Year 8 100,000 72,000 72,000 28,000 15,128 54,027 38,899 0.50025 Year 9 100,000 72,000 72,000 28,000 14,007 50,025 36,018 0.46319 Year 10 100,000 72,000 72,000 28,000 12,969 46,319 33,350 0.42888 Year 11 100,000 72,000 72,000 28,000 12,009 42,888 30,880 0.39711 Year 12 100,000 72,000 72,000 28,000 11,119 39,711 28,592 0.36770 Year 13 100,000 72,000 72,000 28,000 10,296 36,770 26,474 0.34046 Year 14 100,000 72,000 72,000 28,000 9,533 34,046 24,513 0.31524 Year 15 100,000 72,000 72,000 28,000 8,827 31,524 22,697 49,665 855,948 806,282 B-C = 49,665 B/C = 1.062 a. Project B will be chosen in B-C approach as having highest value of $52,379 b. Project B will be chosen in B/C approach as having highest ratio of 1.065
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