Question

Five mutually-exclusive projects consisting of reinforcing dams, levees, and embankments are available for funding by a certain public agency. The following tabulation shows the equivalent annual benefits and costs for each: Project Annual Benefits Annual Costs A $1,800,000 $2,000,000 B $5,600,000 $4.200,000 C $8,400,000 $6,800,000 D $2,600,000 $2,800,000 E $6,600,000 $5,400,000 Assume that the projects are of the type for which the benefits can be determined with considerable certainty and that the agency is willing to invest money in any project as long as the B-C ratio is at least one. Determine the annual worth (AW) of the best project that the public agency will select. The agency’s MARR is 10 % per year and the project lifetimes are each 15 years.

Answer 1

Project	Annual Benefits	Annual Costs
A	1,800,000	2,000,000
B	5,600,000	4,200,000
C	8,400,000	6,800,000
D	2,600,000	2,800,000
E	6,600,000	5,400,000

As equivalent annual benefits and annual cost of each project is provided. First, calculate B/C ratio to find the highest value for a project. Select the project on the basis of B/C ratio and then find the present worth of selected project on the basis of (P/A, 10%, 15 Year).

Calculate B-C ratio of project A -

Annual benefits = $1,800,000

Annual costs = $2,000,000

B-C ratio = Annual benefits/Annual costs = $1,800,000/$2,000,000 = 0.90

The B-C ratio of Project A is 0.90.

Calculate B-C ratio of project B -

Annual benefits = $5,600,000

Annual costs = $4,200,000

B-C ratio = Annual benefits/Annual costs = $5,600,000/$4,200,000 = 1.33

The B-C ratio of Project B is 1.33.

Calculate B-C ratio of project C -

Annual benefits = $8,400,000

Annual costs = $6,800,000

B-C ratio = Annual benefits/Annual costs = $8,400,000/$6,800,000 = 1.24

The B-C ratio of Project C is 1.24.

Calculate B-C ratio of project D -

Annual benefits = $2,600,000

Annual costs = $2,800,000

B-C ratio = Annual benefits/Annual costs = $2,600,000/$2,800,000 = 0.93

The B-C ratio of Project D is 0.93.

Calculate B-C ratio of project E -

Annual benefits = $6,600,000

Annual costs = $5,400,000

B-C ratio = Annual benefits/Annual costs = $6,600,000/$5,400,000 = 1.22

The B-C ratio of Project E is 1.22.

It has been stated that the agency is willing to invest money in any project as long as the B-C ratio is at least one. The B-C ratio of project A and D are less than 1. So, they will not be considered. Out of remaining three projects, B-C ratio is highest in the case of Project B.

Hence, Project B will be selected.

Annual worth of the project B = -(Annual cost)+annual benefit (P/A, 10%, 15 year)

Annual benefits = $5,600,000

Annual costs = $4,200,000

Annual worth=-(4, 200,000) + 5, 600,000(P/A, 10%, 15 year)

                     =4,200,000

So, Annual worth of the project in which company will invest is $4,200,000.