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

PROJECTS	Present Value of Annual Benefit	Present Value of Annual Cost	B/C Ratio	AW
A	13,690,943	15,212,159	0.899	-200,000
B	42,594,045	31,945,534	1.333	1,400,000
C	63,891,068	51,721,340	1.235	1,600,000
D	19,775,806	21,297,023	0.928	-200,000
E	50,200,125	41,072,829	1.222	1,200,000

Since there is no intitial cost, Annual Worth = Annual Benefits - Annual Cost

Present Value = Annuity*[(1-(1+r%)^-n)/r%]

According to AW Project C should be choosen while according to BCR Project B should be choosen.