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.
B/C = AW of benefits / AW of costs
As equivalent AW values are already given,
B/C of A = 1800000 / 2000000 = 0.9
B/C of B = 5600000 / 4200000 = 1.33
B/C of C = 8400000 / 6800000 = 1.24
B/C of D = 2600000 / 2800000 = 0.93
B/C of E = 6600000 / 5400000 = 1.22
As only B/C ratio of B, C & E is more than 1, they would only be considered for incremental B/C analysis
Arranging alternative in increasing order of AW of cost
B < E < C
incremental B/C of (E - B) = (6600000 - 5600000) / (5400000 - 4200000) = 0.83
As incremental B/C is less than 1, Alt B is selected
incremental B/C of (C - B) = (8400000 - 5600000) / (6800000 - 4200000) = 1.08
As incremental B/C is more than 1, Alt C is selected
Alt C should be selected as per B/ C analysis
AW of C (best alternative) = 8400000 - 6800000 = 1600000
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