Question

Arabian Power Company has two ME alternatives available for producing power using Gas Turbines and providing energy at a remote wory with the cash low estimates associated with each alternative e given below. Use the conventional B/C ratio method to determine which alternative should be lected as an were ve of 10% per year over a 25-you study period One alternative must be selected Alternative X Alternative Y Fast costs, AED 1,000,000 900.000 Annual M&O costs, AED per year 380,000 359,500 Benefits, AED per year Salvage value, AED 500,000 30,000 459.00 10,000 7 Select the closest correct answers for the below questions from the answer's options provided What is the total annual cost of Alternative? A [630.190 AED) What is the total annual cost of Alternative? 8.01.31 What is the loc ratio of Alternative x? C146.566 AED) What is the B/C ratio of Alternative Y 0.11.871 What is the incremental B/C (A/C) ratio between the two alternatives. X and Y? E1490.168 AED Which alternative, if any, should be chosen? F. 1230.742 AED) G. [Alternative X

Answer 1

Total annual cost of Alternative X -

Total cost = annual interest on investment + annual operations and maintenance + annual depreciation cost

TAC = First cost x interest rate + M&O costs + {[(FC-SV) x i]/[(1+i)n-1]}

where FC= First cost and SV = Salvage value

TAC = 1,000,000(0.10) + 380,000 + {[(1,000,000-30,000) x 0.10]/[(1+0.10)25-1]} = 100,000 + 380,000 + [97,000/9.835] = 489,862.7351

Answer = E) 490,168 AED

Total annual cost of Alternative Y -

Total cost = annual interest on investment + annual operations and maintenance + annual depreciation cost

TAC = First cost x interest rate + M&O costs + {[(FC-SV) x i]/[(1+i)n-1]}

where FC= First cost and SV = Salvage value

TAC = 990,000(0.10) + 359,500 + {[(990,000-10,000) x 0.10]/[(1+0.10)25-1]} = 99,000 + 359,500 + [98,000/9.835] = 468,464.4128

Answer = C) 468,566 AED

B/C ratio of alternative X-

B/C = Present value of benefit/Present value of cost = B{[(1+i)n-1]/[i(1+i)n]} + SV(1+i)-n / FC + M&O cost(1+i)-n = {500,000{[1+0.1)25-1]/[0.1(1+0.1)25]} + 30,000(1+0.10)-25}/ 1,000,000 + 380,000{[1+0.1)25-1]/[0.1(1+0.1)25]} = (4538520.009 + 2768.88) / 3449275.207 = 1.316 Answer = B) 1.3

B/C ratio of alternative Y-

B/C = Present value of benefit/Present value of cost = B{[(1+i)n-1]/[i(1+i)n]} + SV(1+i)-n / FC + M&O cost(1+i)-n = {459,500{[1+0.1)25-1]/[0.1(1+0.1)25]} + 10,000(1+0.10)-25}/ 990,000 + 359,500{[1+0.1)25-1]/[0.1(1+0.1)25]} = (4170899.888 + 922.96) / 3263195.887 = 1.278 Answer = B) 1.3

Incremental B/C ratio between X and Y -

Incremental first cost = FCx-FCy = 1000000-990000 = 10,000

Incremental cost per year = Cx-Cy = 380,000 - 359,500 = 20,500

Incremental benefit per year = Bx-By = 500,000 - 459,500 = 40,500

Incremental Salvage value = SVx-SVy = 30,000-10,000 = 20,000

B/C = Present value of benefit/Present value of cost = B{[(1+i)n-1]/[i(1+i)n]} + SV(1+i)-n / FC + M&O cost(1+i)-n = {40,500{[1+0.1)25-1]/[0.1(1+0.1)25]} + 20,000(1+0.10)-25}/ 10,000 + 20,500{[1+0.1)25-1]/[0.1(1+0.1)25]} = (367620.1207 + 1845.92) / 196079.3204 = 1.88 Answer - D)1.87

Which alternative should be chosen?

On calculating the incremental B/C ratio, if B/C > 1 then we chose the higher cost alternative and if B/C < 1 then we chose the lower cost alternative. Hence in this case B/C = 1.87 >1. Thus we chose Alternative X which is the higher cost alternative. Answer - G) Alternative X