Engineering Economy - please solve it in detials!! A governmental agency is cons
ID: 2428749 • Letter: E
Question
Engineering Economy - please solve it in detials!!
A governmental agency is considering four independent projects, each having 30- year projected useful lives. The current budget for this agency allows notmore than $35,000,000 to be spent, in terms of initial investments, and the nominal interest rate is 10% per year. Using the B C-ratio method, which of the projects shown below should be selected? Use PW & Conventional B/C method. ProjectInitial InvestmentAnnual CostsAnnual Benefits $12,000,000 20,000,000 10,000,000 14,000,000 $1,250,000 4,500,000 750,000 1,850,000 $3,250,000 8,000,000 1,250,000 4,050,000Explanation / Answer
Time = 30 years
R = 10%
For project A:
Uniform annual investment = 12000000/((1-1/1.1^30)/.1) = $1272950.98
B-C ratio = 3250000/(1250000 + 1272950.98)
B-C ratio = 1.29
NPW of the project A = (3250000 - 1250000)*(1-1/1.1^30)/.1 - 12000000 = $6853828.93
For project B:
Uniform annual investment = 20000000/((1-1/1.1^30)/.1) = $2121584.97
B-C ratio = 8000000/(4500000 + 2121584.97)
B-C ratio = 1.21
NPW of the project B = (8000000-4500000)*(1-1/1.1^30)/.1 – 20000000 = $12994200.63
For project C:
Uniform annual investment = 10000000/((1-1/1.1^30)/.1) = $1060792.48
B-C ratio = 1250000/(750000 +1060792.48)
B-C ratio = .69
NPW of the project C = (1250000-750000)*(1-1/1.1^30)/.1 – 10000000 = -$5286542.77
For project D:
Uniform annual investment = 14000000/((1-1/1.1^30)/.1) = $1485109.48
B-C ratio = 4050000/(1850000 + 1485109.48)
B-C ratio = 1.21
NPW of the project D = (4050000-1850000)*(1-1/1.1^30)/.1 – 14000000 = $6739211.82
Since project C has B-C ratio of .69 that is less than 1 and NPW that is negative, so it cannot be accepted.
Since project A, has highest B-C ratio, then it will be selected. Afterwards, the project B and project D both have B-C ratio of 1.21, but project B has relatively bigger NPW than that of D, so project B will also be selected.
So, project selected are project A and B.
It will utilize the total budget of (12000000+32000000) = $32000000.
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