Two options for a new bridge are being considered. The first bridge costs $2,000
ID: 2614674 • Letter: T
Question
Two options for a new bridge are being considered. The first bridge costs $2,000,000 to build and lasts for 40 years. The bridge costs $200,000 a year to maintain in year 1, and this cost increases by 05% each year. The second bridge costs $1,5000,000 to build and lasts for 30 years. The maintenance cost of the 2nd bridge is $195,000 a year, increasing by $1,110 per year. The annual interest rate is 5%. If a bridge is going to be needed for the indefinite future, perform a Present Worth Analysis to determine whether the 1st or 2nd bridge should be built.Explanation / Answer
Option 1 bridge 1 Cost= 20,00,000.00 Life= 40Years year Cash flow pv @ 5% pv of cash flow 0 20,00,000.00 1 2000000 1 2,00,000.00 0.952380952 190476.1905 2 2,01,000.00 0.907029478 182312.9252 3 2,02,005.00 0.863837599 174499.5141 4 2,03,015.03 0.822702475 167020.9635 5 2,04,030.10 0.783526166 159862.9222 6 2,05,050.25 0.746215397 153011.6541 7 2,06,075.50 0.71068133 146454.0118 8 2,07,105.88 0.676839362 140177.4113 9 2,08,141.41 0.644608916 134169.8079 10 2,09,182.12 0.613913254 128419.6733 11 2,10,228.03 0.584679289 122915.973 12 2,11,279.17 0.556837418 117648.1456 13 2,12,335.56 0.530321351 112606.0822 14 2,13,397.24 0.505067953 107780.1073 15 2,14,464.23 0.481017098 103160.9598 16 2,15,536.55 0.458111522 98739.77583 17 2,16,614.23 0.436296688 94508.07115 18 2,17,697.30 0.415520655 90457.72524 19 2,18,785.79 0.395733957 86580.96559 20 2,19,879.72 0.376889483 82870.35278 21 2,20,979.12 0.358942365 79318.76623 22 2,22,084.01 0.341849871 75919.39054 23 2,23,194.43 0.325571306 72665.70237 24 2,24,310.40 0.31006791 69551.45798 25 2,25,431.96 0.295302772 66570.68121 26 2,26,559.12 0.281240735 63717.65202 27 2,27,691.91 0.267848319 60986.8955 28 2,28,830.37 0.255093637 58373.17141 29 2,29,974.52 0.242946321 55871.46406 30 2,31,124.39 0.231377449 53476.97275 31 2,32,280.02 0.220359475 51185.10249 32 2,33,441.42 0.209866167 48991.45524 33 2,34,608.62 0.19987254 46891.82144 34 2,35,781.67 0.1903548 44882.17195 35 2,36,960.58 0.181290285 42958.6503 36 2,38,145.38 0.172657415 41117.56528 37 2,39,336.10 0.164435633 39355.38391 38 2,40,532.79 0.156605365 37668.7246 39 2,41,735.45 0.149147966 36054.35069 40 2,42,944.13 0.142045682 34509.16423 Total 18.16 56,73,739.78 Equated annual cost= pv of cash flow/(pvaf I,n)= 3,12,446.32 Option 2 Bridge 2 cost= 1,50,00,000.00 life= 30year year Cash flow pv @ 5% pv of cash flow 0 1,50,00,000.00 1 15000000 1 195000 0.952380952 185714.2857 2 196110 0.907029478 177877.551 3 197220 0.863837599 170366.0512 4 198330 0.822702475 163166.5818 5 199440 0.783526166 156266.4586 6 200550 0.746215397 149653.4978 7 201660 0.71068133 143315.997 8 202770 0.676839362 137242.7174 9 203880 0.644608916 131422.8658 10 204990 0.613913254 125846.0778 11 206100 0.584679289 120502.4015 12 207210 0.556837418 115382.2814 13 208320 0.530321351 110476.5438 14 209430 0.505067953 105776.3814 15 210540 0.481017098 101273.3398 16 211650 0.458111522 96959.30363 17 212760 0.436296688 92826.48326 18 213870 0.415520655 88867.40246 19 214980 0.395733957 85074.88608 20 216090 0.376889483 81442.04835 21 217200 0.358942365 77962.2816 22 218310 0.341849871 74629.24536 23 219420 0.325571306 71436.85592 24 220530 0.31006791 68379.27625 25 221640 0.295302772 65450.90632 26 222750 0.281240735 62646.37371 27 223860 0.267848319 59960.52469 28 224970 0.255093637 57388.41555 29 226080 0.242946321 54925.30427 30 227190 0.231377449 52566.64256 Total 16.37245103 18184798.98 Equated annual cost= pv of cash flow/(pvaf I,n)= 11,10,694.97 answer option 1= equated annual cost= 3,12,446.32 Option 2 equated annual cost= 11,10,694.97 Since the cost of option 1 is least. It is preferable to built bridge 1.
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