Question

Three designs have been proposed to improve traffic flow at a major intersection in a heavily traveled suburban area. For the present condition the annual maintenance cost is $100,000. The first alternative is to improve traffic signals. The second alternative includes traffic signal improvements and intersection widening. The third alternative involves extensive work including grade separation. Using Benefit Cost Ratio, determine the most suitable alternative if the analysis period is 20 years and the annual interest is 10%. Additional information between options are provided below (20): Alternative Capital Cost, $ Annual Annual Savings Maintenance, $ (accidents), $ Do-nothing 100,000 500,000 15,000 7,000 600,000 10,000 7,000 800.000 5.000 9.000

Answer 1

Given, Annual maintenance cost = 100,000

Doing nothing - For 20 yrs total cost for doing nothing= 100,000*20=2,000,000

BCR=0/2000000= 0

1st alternative-

capital cost =600,000  

maintenance cost= 15,000*20= 300,000

savings = 7000/ yr

total savings for 20 years = 422,323

( since annual interest is of 10% compounded annually on savings, first yrs saving compounded annually for 20 yrs, second years for 19 years, third yrs saving compounded for 18 yrs.. and so on..)

Benefit = 422,323, cost = 600000+300000= 900,000,

therefore BCR = 422,323/900000=0.469

Alternative Cost maintenance savings savings for 20 yrs BCR

2nd 600,000 10000*20 7,000 422,323 0.528

3rd 800,000 5000*20 9,000 542,990 0.6033

Thus, constructing a Grade separator will cost initially highest amount but considering the low maintenance cost and savings by safety by accident prevention will yield highest benefit to cost ratio therefore being a better option for 20 years.