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Q12-5. A city government has to choose from among three types of town-dump sanit

ID: 2717912 • Letter: Q

Question

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