In: Economics
The two ME alternatives shown are under consideration for
facility improvements in a company in Abu Dhabi. Determine which
one should be selected based on a B/C analysis. Assume an interest
rate of 10% per year and a 5-year study period.
Alternative X | Alternative Y | |
First costs, AED | 40,000 | 90,000 |
Annual M&O costs, AED per year | 50,000 | 20,000 |
Benefits, AED per year | 120,000 | 150,000 |
Disbenefits, AED per year | 30,000 | 10,000 |
Match the closest correct answers for the below questions:
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Answer a)
Initial Cost of Alternate X AED 40,000
Annual cost is given by, PV= P * (1- (1+r)^-n) / r , P= to be calculated, r = 10%, n= 5 years, PV = AED 40000
Hence 40000 = P * (1-(1+10%)^-5 /10%
40000 = P * (1-(1.1)^-5 /0.1
40000 = P * (1-0.6209) /0.1
40000 = P * 0.3791/0.1
P= 40000 *0.1 / 0.3791
P =AED 10551.31
Hence annual cost is AED 10551.31, in addition AED 50000 is spent on annual O&M. Hence total annual cost is 10551.31+50000 = AED 60551.31
Hence option G is correct
Answer b
Initial Cost of Alternate Y AED 90,000
Annual cost is given by, PV= P * (1- (1+r)^-n) / r , P= to be calculated, r = 10%, n= 5 years, PV = AED 90000
Hence 000000 = P * (1-(1+10%)^-5 /10%
90000 = P * (1-(1.1)^-5 /0.1
90000 = P * (1-0.6209) /0.1
90000 = P * 0.3791/0.1
P= 90000 *0.1 / 0.3791
P =AED 23740.44
Hence annual cost is AED 123740.44, in addition AED 20000 is spent on annual O&M. Hence total annual cost is 23740.44+20000 = AED 43740.44
Hence option A is correct
Answer c)
Total Benefit from Alternate X = AED 120,000
Net Benefit = Benefit - Disbenefit = 120000-30000 = AED 90000
Total Cost of Alternate X = AED 60551.31
Benefit/ Cost Ratio = 90000/60551.31 = 1.486
Hence option E is correct
Answer d)
Total Benefit from Alternate Y = AED 150,000
Net Benefit = Benefit - Disbenefit = 150000-10000 = AED 140000
Total Cost of Alternate Y = AED 43740.44
Benefit/ Cost Ratio = 140000/43740.44 = 3.2
Hence option F is correct
Answer e)
Incremental Benefit from X to Y = Benefit Y - Benefit X = 140000 - 90000 = 50000
Incremental Cost from X to Y = Cost Y - Cost X = 43740.44 - 60551.31 = -16810.87
Incremental Benefit/ Cost = 50000/ (-16810.87) = -2.97
Hence option J is correct
Answer f)
Since Alternate Y has higher Benefit Cost ratio Alternate Y should be chosen
Hence option B is correct