Atoll bridge across the Mississippi River is being considered as a replacement for the current l-40 bridge linking Tennessee to Arkansas. Because this bridge, if approved, will become a part of the U.S. Interstate Highway system, the B-C ratio method must be applied in the evaluation. Assume that the initial surfacing of the bridge is included in the initial investment costs of the structure. a. What is the capitalized worth of the bridge (for the new design)? b. Determine the B-C ratio of the bridge over an infinite time horizon (for the new design) c. Should the initial design or the new design be selected? Click the icon to view the additional information about the initial and new designs. Click the icon to view the interest and annuity table for discrete compounding when the MARR is 9% per year. a. Calculate the CW value of the bridge for the new design. CW(9%) = $ million (Round to three decimal places.) i More Info - Initial design Investment costs of the structure are estimated to be $17,700,000, and $337,000 per year in operating and maintenance costs are anticipated. In addition, the bridge must be resurfaced every fourth year of its 20-year projected life at a cost of $1,270,000 per occurrence (no resurfacing cost in year 20). Revenues generated from the toll are anticipated to be $2,900,000 in its first year of operation, with a projected annual rate of increase of 2.25% per year due to the anticipated annual increase in traffic across the bridge. Assume that market (salvage) value for the bridge at the end of 20 years is zero and a MARR is 9% per year. New design Suppose that the toll bridge can be redesigned such that it will have a (virtually) infinite life. Revised costs and revenues (benefits) are given as follows: Capital investment: $21,700,000 Annual operating and maintenance costs: $256,000 Resurface cost every eighth year: $1,090,000 Structural repair cost, every 17th year: $1,710,000 Revenues (treated as constant, no rate of increase): $3,180,000 MARR remains at 9% per year. Print Done i More Info N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 35 40 45 50 Discrete Compounding; i = 9% Single Payment Uniform Series Compound Compound Capital Amount Present Amount Present Sinking Fund Recovery Factor Worth Factor Factor Worth Factor Factor Factor To Find F To Find P To Find F To Find P To Find A To Find A Given P Given F Given A Given A Given F Given P FIP P/F FIA P/A A/F A/P 1.0900 0.9174 1.0000 0.9174 1.0000 1.0900 1.1881 0.8417 2.0900 1.7591 0.4785 0.5685 1.2950 0.7722 3.2781 2.5313 0.3051 0.3951 1.4116 0.7084 4.5731 3.2397 0.2187 0.3087 1.5386 0.6499 5.9847 3.8897 0.1671 0.2571 1.6771 0.5963 7.5233 4.4859 0.1329 0.2229 1.8280 0.5470 9.2004 5.0330 0.1087 0.1987 1.9926 0.5019 11.0285 5.5348 0.0907 0.1807 2.1719 0.4604 13.0210 5.9952 0.0768 0.1668 2.3674 0.4224 15.1929 6.4177 0.0658 0.1558 2.5804 0.3875 17.5603 6.8052 0.0569 0.1469 2.8127 0.3555 20.1407 7.1607 0.0497 0.1397 3.0658 0.3262 22.9534 7.4869 0.0436 0.1336 3.3417 0.2992 26.0192 7.7862 0.0384 0.1284 3.6425 0.2745 29.3609 8.0607 0.0341 0.1241 3.9703 0.2519 33.0034 8.3126 0.0303 0.1203 4.3276 0.2311 36.9737 8.5436 0.0270 0.1170 4.7171 0.2120 41.3013 8.7556 0.0242 0.1142 5.1417 0.1945 46.0185 8.9501 0.0217 0.1117 5.6044 0.1784 51.1601 9.1285 0.0195 0.1095 6.1088 0.1637 56.7645 9.2922 0.0176 0.1076 6.6586 0.1502 62.8733 9.4424 0.0159 0.1059 7.2579 0.1378 69.5319 9.5802 0.0144 0.1044 7.9111 0.1264 76.7898 9.7066 0.0130 0.1030 8.6231 0.1160 84.7009 9.8226 0.0118 0.1018 13.2677 0.0754 136.3075 10.2737 0.0073 0.0973 20.4140 0.0490 215.7108 10.5668 0.0046 0.0946 31.4094 0.0318 337.8824 10.7574 0.0030 0.0930 48.3273 0.0207 525.8587 10.8812 0.0019 0.0919 74.3575 0.0134 815.0836 10.9617 0.0012 0.0912 Print Done Atoll bridge across the Mississippi River is being considered as a replacement for the current l-40 bridge linking Tennessee to Arkansas. Because this bridge, if approved, will become a part of the U.S. Interstate Highway system, the B-C ratio method must be applied in the evaluation. Assume that the initial surfacing of the bridge is included in the initial investment costs of the structure. a. What is the capitalized worth of the bridge (for the new design)? b. Determine the B-C ratio of the bridge over an infinite time horizon (for the new design) c. Should the initial design or the new design be selected? Click the icon to view the additional information about the initial and new designs. Click the icon to view the interest and annuity table for discrete compounding when the MARR is 9% per year. a. Calculate the CW value of the bridge for the new design. CW(9%) = $ million (Round to three decimal places.) i More Info - Initial design Investment costs of the structure are estimated to be $17,700,000, and $337,000 per year in operating and maintenance costs are anticipated. In addition, the bridge must be resurfaced every fourth year of its 20-year projected life at a cost of $1,270,000 per occurrence (no resurfacing cost in year 20). Revenues generated from the toll are anticipated to be $2,900,000 in its first year of operation, with a projected annual rate of increase of 2.25% per year due to the anticipated annual increase in traffic across the bridge. Assume that market (salvage) value for the bridge at the end of 20 years is zero and a MARR is 9% per year. New design Suppose that the toll bridge can be redesigned such that it will have a (virtually) infinite life. Revised costs and revenues (benefits) are given as follows: Capital investment: $21,700,000 Annual operating and maintenance costs: $256,000 Resurface cost every eighth year: $1,090,000 Structural repair cost, every 17th year: $1,710,000 Revenues (treated as constant, no rate of increase): $3,180,000 MARR remains at 9% per year. Print Done i More Info N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 35 40 45 50 Discrete Compounding; i = 9% Single Payment Uniform Series Compound Compound Capital Amount Present Amount Present Sinking Fund Recovery Factor Worth Factor Factor Worth Factor Factor Factor To Find F To Find P To Find F To Find P To Find A To Find A Given P Given F Given A Given A Given F Given P FIP P/F FIA P/A A/F A/P 1.0900 0.9174 1.0000 0.9174 1.0000 1.0900 1.1881 0.8417 2.0900 1.7591 0.4785 0.5685 1.2950 0.7722 3.2781 2.5313 0.3051 0.3951 1.4116 0.7084 4.5731 3.2397 0.2187 0.3087 1.5386 0.6499 5.9847 3.8897 0.1671 0.2571 1.6771 0.5963 7.5233 4.4859 0.1329 0.2229 1.8280 0.5470 9.2004 5.0330 0.1087 0.1987 1.9926 0.5019 11.0285 5.5348 0.0907 0.1807 2.1719 0.4604 13.0210 5.9952 0.0768 0.1668 2.3674 0.4224 15.1929 6.4177 0.0658 0.1558 2.5804 0.3875 17.5603 6.8052 0.0569 0.1469 2.8127 0.3555 20.1407 7.1607 0.0497 0.1397 3.0658 0.3262 22.9534 7.4869 0.0436 0.1336 3.3417 0.2992 26.0192 7.7862 0.0384 0.1284 3.6425 0.2745 29.3609 8.0607 0.0341 0.1241 3.9703 0.2519 33.0034 8.3126 0.0303 0.1203 4.3276 0.2311 36.9737 8.5436 0.0270 0.1170 4.7171 0.2120 41.3013 8.7556 0.0242 0.1142 5.1417 0.1945 46.0185 8.9501 0.0217 0.1117 5.6044 0.1784 51.1601 9.1285 0.0195 0.1095 6.1088 0.1637 56.7645 9.2922 0.0176 0.1076 6.6586 0.1502 62.8733 9.4424 0.0159 0.1059 7.2579 0.1378 69.5319 9.5802 0.0144 0.1044 7.9111 0.1264 76.7898 9.7066 0.0130 0.1030 8.6231 0.1160 84.7009 9.8226 0.0118 0.1018 13.2677 0.0754 136.3075 10.2737 0.0073 0.0973 20.4140 0.0490 215.7108 10.5668 0.0046 0.0946 31.4094 0.0318 337.8824 10.7574 0.0030 0.0930 48.3273 0.0207 525.8587 10.8812 0.0019 0.0919 74.3575 0.0134 815.0836 10.9617 0.0012 0.0912 Print Done
