A transit project is being evaluated. This project is expected to cost $10M to c

Question

A transit project is being evaluated. This project is expected to cost $10M to construct and have a life of 30 years. The benefits associated with the project is $1.2M per year; however the disbenefits associated with the project is $300,000 in year 1 and will decrease by 8% each year. Maintenance and operation costs are $50,000 in the first year and will increase by $5,000 each year thereafter. Given a return on investment of 5%, calculate the conventional and the modified B/C ratios. Should the transit agency invest?

HOW CAN I DO THIS BY HAND?

Explanation / Answer

Cost of the project = 10 million.

Life of the project=30 years.

Benefits=$1.2million.

Disbenefits =$300,000 in year 1 and there by decrease by 8% per year.

Maintenance and operation costs=$50,000 perr year and will increase by $5,000.

Present value of costs=$10,000,000+$3,875,661.93=$13,875,661.93.

Conventional B/C ratios=$18,446,941.23/$13,875,661.93

=1.3294.

Modified B/C ratios:

Modified B/C ratio = (Benefits-Disbenefits-Maintenance costs)/(Initial investments-Salvage value)

Substituting the values in the formula =$14,571,279.30/$10,000,000.

=1.4571.

Year Benefits (A) Disbenefits (B) Maintenance and operating costs (C ) Present value factor(D) Present value of Benefits(E )=(D)*(A) Present value of disbenefits (F)=(D)*(B+C) 1 $1,200,000.00 $300,000.00 $50,000.00 0.952380952 $1,142,857.14 $333,333.33 2 $1,200,000.00 $276,000.00 $55,000.00 0.907029478 $1,088,435.37 $300,226.76 3 $1,200,000.00 $253,920.00 $60,000.00 0.863837599 $1,036,605.12 $271,175.90 4 $1,200,000.00 $233,606.40 $65,000.00 0.822702475 $987,242.97 $245,664.22 5 $1,200,000.00 $214,917.89 $70,000.00 0.783526166 $940,231.40 $223,240.62 6 $1,200,000.00 $197,724.46 $75,000.00 0.746215397 $895,458.48 $203,511.19 7 $1,200,000.00 $181,906.50 $80,000.00 0.71068133 $852,817.60 $186,132.06 8 $1,200,000.00 $167,353.98 $85,000.00 0.676839362 $812,207.23 $170,803.11 9 $1,200,000.00 $153,965.66 $90,000.00 0.644608916 $773,530.70 $157,262.44 10 $1,200,000.00 $141,648.41 $95,000.00 0.613913254 $736,695.90 $145,281.59 11 $1,200,000.00 $130,316.54 $100,000.00 0.584679289 $701,615.15 $134,661.31 12 $1,200,000.00 $119,891.21 $105,000.00 0.556837418 $668,204.90 $125,227.84 13 $1,200,000.00 $110,299.92 $110,000.00 0.530321351 $636,385.62 $116,829.75 14 $1,200,000.00 $101,475.92 $115,000.00 0.505067953 $606,081.54 $109,335.05 15 $1,200,000.00 $93,357.85 $120,000.00 0.481017098 $577,220.52 $102,628.77 16 $1,200,000.00 $85,889.22 $125,000.00 0.458111522 $549,733.83 $96,610.78 17 $1,200,000.00 $79,018.08 $130,000.00 0.436296688 $523,556.03 $91,193.90 18 $1,200,000.00 $72,696.64 $135,000.00 0.415520655 $498,624.79 $86,302.24 19 $1,200,000.00 $66,880.91 $140,000.00 0.395733957 $474,880.75 $81,869.80 20 $1,200,000.00 $61,530.43 $145,000.00 0.376889483 $452,267.38 $77,839.15 21 $1,200,000.00 $56,608.00 $150,000.00 0.358942365 $430,730.84 $74,160.36 22 $1,200,000.00 $52,079.36 $155,000.00 0.341849871 $410,219.85 $70,790.05 23 $1,200,000.00 $47,913.01 $160,000.00 0.325571306 $390,685.57 $67,690.51 24 $1,200,000.00 $44,079.97 $165,000.00 0.31006791 $372,081.49 $64,828.99 25 $1,200,000.00 $40,553.57 $170,000.00 0.295302772 $354,363.33 $62,177.05 26 $1,200,000.00 $37,309.29 $175,000.00 0.281240735 $337,488.88 $59,710.02 27 $1,200,000.00 $34,324.54 $180,000.00 0.267848319 $321,417.98 $57,406.47 28 $1,200,000.00 $31,578.58 $185,000.00 0.255093637 $306,112.36 $55,247.82 29 $1,200,000.00 $29,052.29 $190,000.00 0.242946321 $291,535.59 $53,217.95 30 $1,200,000.00 $26,728.11 $195,000.00 0.231377449 $277,652.94 $51,302.88 Total $18,446,941.23 $3,875,661.93

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