Question

The answer is shown in the picture, i want to know how they got it, please show all your work and if you are using excel please show your formulas, Thank You and good luck.

Toll lanes on a section of the 1-40 freeway are being considered in order to reduce traffic congestion and travel times Since this is a government project, the B-C ratio method must be applied in the evaluation. Construction costs of the project are estimated to be $16,200,000, and $324,000 per year in operating and maintenance costs are anticipated. In addition, the lanes must be resurfaced every fourth year of their 20-year projected life at a cost of $1,240,000 per occurrence (no resurfacing cost in year 20). Savings in travel times and revenues generated from the tolls are anticipated to be $2,436,000 in the first year of operation, with a projected annual rate of increase of 2.5% per year due to the anticipated annual increase in traffic. In addition, environmental analysis estimates that the project will result in increased noise and air pollution that will cause an additional societal health cost of $336,000 the first year and the cost is also projected to increase at 2.5% per year Assuming zero market (salvage) value at the end of 20 years and a MARR of 8% per year, should the toll lanes be constructed? Also assume that the initial surfacing of the lanes is included in the initial construction costs Click the icon to view the interest and annuity table for discrete compounding when the MARR is 8% per year The conventional benefit-cost ratio of the project with PW is 1.13. (Round to two decimal places.) According to the B-C ratio method, the toll lanes should o A. not be constructed B. be constructed

Answer 1

The above table shows the whole calculation where 2nd column representing revenue shows the revenue generated every year in the 20-year life of the freeway,given the 2.5% rate of increase per year. formula is : R₁ + R₁(1.025) + R₁(1.025)² + .....+ R₁(1.025)¹⁹, where R₁ is the revenue in the first year.

Resurfacing cost Environmental cost Net Revenue MRR PV of Net Revenue Year Revenue Construction cost AMC 0 1,62,00,000 1,62,00,000 1.0000 3,36,000 17,76,000 0.9259 3,44,400 18,28,500 0.8573 18,82,313 0.7938 6,97,470 0.7350 3,70,881 19,94,007 0.6806 20,51,957 0.6302 3,89,65721,11,356 0.5835 9,32,240 0.5403 22,34,646 0.5002 22,98,612 0.4632 23,64,178 0.4289 11,91,382 0.3971 4,51,883 25,00,267 0.3677 25,70,873 0.3405 4,74,759 26,43,245 0.3152 14,77,426 0.2919 27,93,462 0.2703 5,11,264 28,71,398 0.2502 29,51,283 0.2317 5,37,146 30,33,165 0.2145 Benefit-cost Ratio 1.1816 1 24,36,000 2 24,96,900 3 25,59,323 426,23,306 5 26,88,888 27,56,110 7 28,25,013 8 28,95,638 9 29,68,029 10 30,42,230 11 31,18,286 12 31,96,243 13 32,76,149 14 33,58,053 15 34,42,004 16 35,28,054 17| 36,16,256 18 37,06,662 19 37,99,329 20 38,94,312 3,24,000 3,24,000 3,24,000 3,24,000 3,24,000 3,24,000 3,24,000 16,44,444 15,67,644 14,94,240 5,12,662 13,57,088 12,93,081 12,31,956 5,03,660 11,17,879 10,64,702 10,13,955 4,73,114 9,19,343 8,75,282 8,33,261 4,31,247 7,54,986 7,18,565 6,83,848 6,50,760 1,91,41,718 3,53,010 3,61,835 12,40,000 3,80,153 3,99,398 4,09,383 4,19,618 4,30,108 4,40,861 12,40,000 3,24,000 3,24,000 3,24,000 3,24,000 12,40,000 3,24,000 3,24,000 3,24,000 3,24,000 3,24,000 3,24,000 3,24,000 4,63,180 12,40,000 4,86,628 4,98,794 5,24,045

AMC(annual maintenance cost is fixed) and the initial construction cost is also fixed. Resurfacing cost occurs every 4th year.

environmental cost also increases by 2.5% every year. Therefore,applying the same formula as in revenue calculation.

Net Revenue is calculated as : Revenue - (AMC+resurfacing cost+ environmental cost)

Present value of net revenue is calculated by using MARR = 8% as the discount rate.

benefit:cost ratio is 19,171,418/16,200,000 = 1.18

Thus, the toll lanes must be constructed.