The federal government is planning a hydroelectric project for a river basin. Th
ID: 1091069 • Letter: T
Question
The federal government is planning a hydroelectric project for a river basin. The project will provide electrical energy to the local area and to the grid. With some enhancements to the basic plan, this project can also provide flood control, irrigation, and recreation benefits. Three enhancement alternatives, in addition to doing nothing, are considered. Each will have more or less cost and impact as follows: The interest rate is 5 percent, and the life of each of the enhancement alternatives is estimated to be 50 years. Calculate both the benefit/cost ratio and the value of B - C for each alternative. Is the best alternative the one with the maximum benefit/cost ratio? If the interest rate is 8 percent, which alternative will be preferred? Perform an incremental B/C analysis to confirm your answer to Pail b.Explanation / Answer
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17.8) The federal government is planning a hydroelectric project for a river basin. In addition to the production of electric power, this project will provide flood control, irrigation, and recreation benefits. The estimated benefits and costs expected to be derived from the three alternatives under consideration are listed below. Decision Alternatives A B C Initial Cost $8,000,000 $10,000,000 $15,000,000 Annual benefits or cost Power Sales $1,000,000 $ 1,200,000 $ 1,800,000 Flood Control Savings $ 250,000 $ 350,000 $ 500,000 Irrigation Benefits $ 350,000 $ 450,000 $ 600,000 Recreation Benefits $ 100,000 $ 200,000 $ 350,000 O&M Costs $ 200,000 $ 250,000 $ 350,000 The interest rate is 10%, and the life of each of the projects is estimated to be 50 years. a) Find the Benefit-Cost ratio for each alternative. Year A-in A-out A-Benefit A-Cost Year B-in B-out B-Benefit B-Cost Year C-in C-out C-Benefit C-Cost 0 $ 8,000,000 $8,000,000 0 $10,000,000 $10,000,000 0 $15,000,000 $15,000,000 1 $1,700,000 $ 200,000 $ 1,545,455 $ 181,818 1 $ 2,200,000 $ 250,000 $ 2,000,000 $ 227,273 1 $ 3,250,000 $ 350,000 $ 2,954,545 $ 318,182 2 $1,700,000 $ 200,000 $ 1,404,959 $ 165,289 2 $ 2,200,000 $ 250,000 $ 1,818,182 $ 206,612 2 $ 3,250,000 $ 350,000 $ 2,685,950 $ 289,256 3 $1,700,000 $ 200,000 $ 1,277,235 $ 150,263 3 $ 2,200,000 $ 250,000 $ 1,652,893 $ 187,829 3 $ 3,250,000 $ 350,000 $ 2,441,773 $ 262,960 4 $1,700,000 $ 200,000 $ 1,161,123 $ 136,603 4 $ 2,200,000 $ 250,000 $ 1,502,630 $ 170,753 4 $ 3,250,000 $ 350,000 $ 2,219,794 $ 239,055 5 $1,700,000 $ 200,000 $ 1,055,566 $ 124,184 5 $ 2,200,000 $ 250,000 $ 1,366,027 $ 155,230 5 $ 3,250,000 $ 350,000 $ 2,017,994 $ 217,322 6 $1,700,000 $ 200,000 $ 959,606 $ 112,895 6 $ 2,200,000 $ 250,000 $ 1,241,843 $ 141,118 6 $ 3,250,000 $ 350,000 $ 1,834,540 $ 197,566 7 $1,700,000 $ 200,000 $ 872,369 $ 102,632 7 $ 2,200,000 $ 250,000 $ 1,128,948 $ 128,290 7 $ 3,250,000 $ 350,000 $ 1,667,764 $ 179,605 8 $1,700,000 $ 200,000 $ 793,063 $ 93,301 8 $ 2,200,000 $ 250,000 $ 1,026,316 $ 116,627 8 $ 3,250,000 $ 350,000 $ 1,516,149 $ 163,278 9 $1,700,000 $ 200,000 $ 720,966 $ 84,820 9 $ 2,200,000 $ 250,000 $ 933,015 $ 106,024 9 $ 3,250,000 $ 350,000 $ 1,378,317 $ 148,434 10 $1,700,000 $ 200,000 $ 655,424 $ 77,109 10 $ 2,200,000 $ 250,000 $ 848,195 $ 96,386 10 $ 3,250,000 $ 350,000 $ 1,253,016 $ 134,940 11 $1,700,000 $ 200,000 $ 595,840 $ 70,099 11 $ 2,200,000 $ 250,000 $ 771,087 $ 87,623 11 $ 3,250,000 $ 350,000 $ 1,139,105 $ 122,673 12 $1,700,000 $ 200,000 $ 541,672 $ 63,726 12 $ 2,200,000 $ 250,000 $ 700,988 $ 79,658 12 $ 3,250,000 $ 350,000 $ 1,035,550 $ 111,521 13 $1,700,000 $ 200,000 $ 492,429 $ 57,933 13 $ 2,200,000 $ 250,000 $ 637,262 $ 72,416 13 $ 3,250,000 $ 350,000 $ 941,409 $ 101,383 14 $1,700,000 $ 200,000 $ 447,663 $ 52,666 14 $ 2,200,000 $ 250,000 $ 579,329 $ 65,833 14 $ 3,250,000 $ 350,000 $ 855,827 $ 92,166 15 $1,700,000 $ 200,000 $ 406,966 $ 47,878 15 $ 2,200,000 $ 250,000 $ 526,663 $ 59,848 15 $ 3,250,000 $ 350,000 $ 778,024 $ 83,787 16 $1,700,000 $ 200,000 $ 369,970 $ 43,526 16 $ 2,200,000 $ 250,000 $ 478,784 $ 54,407 16 $ 3,250,000 $ 350,000 $ 707,295 $ 76,170 17 $1,700,000 $ 200,000 $ 336,336 $ 39,569 17 $ 2,200,000 $ 250,000 $ 435,258 $ 49,461 17 $ 3,250,000 $ 350,000 $ 642,995 $ 69,246 18 $1,700,000 $ 200,000 $ 305,760 $ 35,972 18 $ 2,200,000 $ 250,000 $ 395,689 $ 44,965 18 $ 3,250,000 $ 350,000 $ 584,541 $ 62,951 19 $1,700,000 $ 200,000 $ 277,964 $ 32,702 19 $ 2,200,000 $ 250,000 $ 359,718 $ 40,877 19 $ 3,250,000 $ 350,000 $ 531,401 $ 57,228 20 $1,700,000 $ 200,000 $ 252,694 $ 29,729 20 $ 2,200,000 $ 250,000 $ 327,016 $ 37,161 20 $ 3,250,000 $ 350,000 $ 483,092 $ 52,025 21 $1,700,000 $ 200,000 $ 229,722 $ 27,026 21 $ 2,200,000 $ 250,000 $ 297,287 $ 33,783 21 $ 3,250,000 $ 350,000 $ 439,174 $ 47,296 22 $1,700,000 $ 200,000 $ 208,838 $ 24,569 22 $ 2,200,000 $ 250,000 $ 270,261 $ 30,711 22 $ 3,250,000 $ 350,000 $ 399,249 $ 42,996 23 $1,700,000 $ 200,000 $ 189,853 $ 22,336 23 $ 2,200,000 $ 250,000 $ 245,692 $ 27,920 23 $ 3,250,000 $ 350,000 $ 362,954 $ 39,087 24 $1,700,000 $ 200,000 $ 172,594 $ 20,305 24 $ 2,200,000 $ 250,000 $ 223,356 $ 25,381 24 $ 3,250,000 $ 350,000 $ 329,958 $ 35,534 25 $1,700,000 $ 200,000 $ 156,903 $ 18,459 25 $ 2,200,000 $ 250,000 $ 203,051 $ 23,074 25 $ 3,250,000 $ 350,000 $ 299,962 $ 32,304 26 $1,700,000 $ 200,000 $ 142,639 $ 16,781 26 $ 2,200,000 $ 250,000 $ 184,592 $ 20,976 26 $ 3,250,000 $ 350,000 $ 272,693 $ 29,367 27 $1,700,000 $ 200,000 $ 129,672 $ 15,256 27 $ 2,200,000 $ 250,000 $ 167,811 $ 19,069 27 $ 3,250,000 $ 350,000 $ 247,902 $ 26,697 28 $1,700,000 $ 200,000 $ 117,884 $ 13,869 28 $ 2,200,000 $ 250,000 $ 152,555 $ 17,336 28 $ 3,250,000 $ 350,000 $ 225,366 $ 24,270 29 $1,700,000 $ 200,000 $ 107,167 $ 12,608 29 $ 2,200,000 $ 250,000 $ 138,687 $ 15,760 29 $ 3,250,000 $ 350,000 $ 204,878 $ 22,064 30 $1,700,000 $ 200,000 $ 97,425 $ 11,462 30 $ 2,200,000 $ 250,000 $ 126,079 $ 14,327 30 $ 3,250,000 $ 350,000 $ 186,253 $ 20,058 31 $1,700,000 $ 200,000 $ 88,568 $ 10,420 31 $ 2,200,000 $ 250,000 $ 114,617 $ 13,025 31 $ 3,250,000 $ 350,000 $ 169,321 $ 18,235 32 $1,700,000 $ 200,000 $ 80,516 $ 9,472 32 $ 2,200,000 $ 250,000 $ 104,197 $ 11,841 32 $ 3,250,000 $ 350,000 $ 153,928 $ 16,577 33 $1,700,000 $ 200,000 $ 73,196 $ 8,611 33 $ 2,200,000 $ 250,000 $ 94,725 $ 10,764 33 $ 3,250,000 $ 350,000 $ 139,934 $ 15,070 34 $1,700,000 $ 200,000 $ 66,542 $ 7,829 34 $ 2,200,000 $ 250,000 $ 86,114 $ 9,786 34 $ 3,250,000 $ 350,000 $ 127,213 $ 13,700 35 $1,700,000 $ 200,000 $ 60,493 $ 7,117 35 $ 2,200,000 $ 250,000 $ 78,285 $ 8,896 35 $ 3,250,000 $ 350,000 $ 115,648 $ 12,454 36 $1,700,000 $ 200,000 $ 54,994 $ 6,470 36 $ 2,200,000 $ 250,000 $ 71,168 $ 8,087 36 $ 3,250,000 $ 350,000 $ 105,135 $ 11,322 37 $1,700,000 $ 200,000 $ 49,994 $ 5,882 37 $ 2,200,000 $ 250,000 $ 64,698 $ 7,352 37 $ 3,250,000 $ 350,000 $ 95,577 $ 10,293 38 $1,700,000 $ 200,000 $ 45,449 $ 5,347 38 $ 2,200,000 $ 250,000 $ 58,817 $ 6,684 38 $ 3,250,000 $ 350,000 $ 86,888 $ 9,357 39 $1,700,000 $ 200,000 $ 41,318 $ 4,861 39 $ 2,200,000 $ 250,000 $ 53,470 $ 6,076 39 $ 3,250,000 $ 350,000 $ 78,989 $ 8,507 40 $1,700,000 $ 200,000 $ 37,561 $ 4,419 40 $ 2,200,000 $ 250,000 $ 48,609 $ 5,524 40 $ 3,250,000 $ 350,000 $ 71,809 $ 7,733 41 $1,700,000 $ 200,000 $ 34,147 $ 4,017 41 $ 2,200,000 $ 250,000 $ 44,190 $ 5,022 41 $ 3,250,000 $ 350,000 $ 65,280 $ 7,030 42 $1,700,000 $ 200,000 $ 31,042 $ 3,652 42 $ 2,200,000 $ 250,000 $ 40,173 $ 4,565 42 $ 3,250,000 $ 350,000 $ 59,346 $ 6,391 43 $1,700,000 $ 200,000 $ 28,220 $ 3,320 43 $ 2,200,000 $ 250,000 $ 36,521 $ 4,150 43 $ 3,250,000 $ 350,000 $ 53,951 $ 5,810 44 $1,700,000 $ 200,000 $ 25,655 $ 3,018 44 $ 2,200,000 $ 250,000 $ 33,200 $ 3,773 44 $ 3,250,000 $ 350,000 $ 49,046 $ 5,282 45 $1,700,000 $ 200,000 $ 23,323 $ 2,744 45 $ 2,200,000 $ 250,000 $ 30,182 $ 3,430 45 $ 3,250,000 $ 350,000 $ 44,587 $ 4,802 46 $1,700,000 $ 200,000 $ 21,202 $ 2,494 46 $ 2,200,000 $ 250,000 $ 27,438 $ 3,118 46 $ 3,250,000 $ 350,000 $ 40,534 $ 4,365 47 $1,700,000 $ 200,000 $ 19,275 $ 2,268 47 $ 2,200,000 $ 250,000 $ 24,944 $ 2,835 47 $ 3,250,000 $ 350,000 $ 36,849 $ 3,968 48 $1,700,000 $ 200,000 $ 17,523 $ 2,061 48 $ 2,200,000 $ 250,000 $ 22,676 $ 2,577 48 $ 3,250,000 $ 350,000 $ 33,499 $ 3,608 49 $1,700,000 $ 200,000 $ 15,930 $ 1,874 49 $ 2,200,000 $ 250,000 $ 20,615 $ 2,343 49 $ 3,250,000 $ 350,000 $ 30,454 $ 3,280 50 $1,700,000 $ 200,000 $ 14,482 $ 1,704 50 $ 2,200,000 $ 250,000 $ 18,741 $ 2,130 50 $ 3,250,000 $ 350,000 $ 27,685 $ 2,981 $16,855,185 $9,982,963 $21,812,592 $12,478,704 $32,223,147 $18,470,185 A-I $8,000,000 B-I $10,000,000 C-I $15,000,000 C' $1,982,963 C' $ 2,478,704 C' $ 3,470,185 BC(10%) 1.69 BC(10%) 1.75 BC(10%) 1.74 b) Select the best alternative based on BC(I). The best alternative is Plan B since it has the highest BC value out of the set.Related Questions
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