Question

There are two ways for finding the benefit to cost ratio (B/C Ratio)

B/C Ratio = [ Annual Benefits-Annual Disbenefits] / [Annual Cost of Implementing Project]

B/C Ratio = [NPV of Benefits-NPV of Disbenefits] / [NPV of Implementing Project]

• If the B/C Ratio is greater than one, we can infer that the project is worth undertaking.

Note that there can only be one B/C ratio for a project (unlike IRR which can at times have multiple values)

Problem: The City of Greenview is planning a new by-pass road with benefits, dis-benefits and costs listed in the table below:

Benefits
Additional business and commerce	$5,000,000	per year
Estimated future economic activity	$1,250,000	per year
Reduction in accidents	$500,000	per year
Dis-benefits
Destruction of vegetable gardens	$500,000	per year
Reduction in business on present road	$250,000	per year
Cost
Initial Cost	$39,000,000	over 30 years
Maintenance Cost	$256,000	per year

Note that Initial Cost is present value. You may convert into annual cost over 30 years at a specific rate. You may state your assumptions for any data that you think is missing.

1. (20 pts) Based on B/C Ratio analysis, should the city construct the by-pass? The rate that the city uses for its economic analysis is 5%.
2. (30 pts) Reconsider the problem, but this time assume that the additional business is estimated to go up by 1% every year, and the estimated future economic activity is expected to go up by 2% every year. For the dis-benefits, the vegetable gardens are estimated to bring in additional business to the tune of 7.5% per year, and the present business on the existing road is estimated to grow by 4.5% if it is left alone. On the cost side, the maintenance costs for the road are estimated to go up by 8% every year. With these estimated increases, we would now like to determine the B/C ratio for the project and whether is still worth undertaking. (the project life is 30 years)
3. (50 pts) Perform your own sensitivity analysis. One correct statement is enough to get full point.

Answer 1

Part (A)

By-pass should be constructed becuase benefit cost ratio is greater than 1

Part (B)

Project should be considered for investment as benefit cost ratio is greater than 1

Part (C)

	50% less	40% less	30% less	20% less	10% less	as given in question	10% more	20% more	30% more	40% more	50% more
Benefits (per year)
additional business & commerce	2,500,000	3,000,000	3,500,000	4,000,000	4,500,000	5,000,000	5,500,000	6,000,000	6,500,000	7,000,000	7,500,000
estimated future economic activity	625,000	750,000	875,000	1,000,000	1,125,000	1,250,000	1,375,000	1,500,000	1,625,000	1,750,000	1,875,000
reduction in accidents	250,000	300,000	350,000	400,000	450,000	500,000	550,000	600,000	650,000	700,000	750,000
Disbenefits (per year)
destruction of vegetable garden	250,000	300,000	350,000	400,000	450,000	500,000	550,000	600,000	650,000	700,000	750,000
reduction in business on existing road	125,000	150,000	175,000	200,000	225,000	250,000	275,000	300,000	325,000	350,000	375,000
Cost
initial cost	19,500,000	23,400,000	27,300,000	31,200,000	35,100,000	39,000,000	42,900,000	46,800,000	50,700,000	54,600,000	58,500,000
maintenance cost (per year)	128,000	153,600	179,200	204,800	230,400	256,000	281,600	307,200	332,800	358,400	384,000
benefit-cost ratio	2.147	2.147	2.147	2.147	2.147	2.147	2.147	2.147	2.147	2.147	2.147