Question

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:

-       A.       B.       C.       D.       E.       F.       G.       H.       I.       J.       K.    What is the total annual cost of Alternative X?       -       A.       B.       C.       D.       E.       F.       G.       H.       I.       J.       K.    What is the total annual cost of Alternative Y?       -       A.       B.       C.       D.       E.       F.       G.       H.       I.       J.       K.    What is the B/C ratio of Alternative X?       -       A.       B.       C.       D.       E.       F.       G.       H.       I.       J.       K.    What is the B/ C ratio of Alternative Y?       -       A.       B.       C.       D.       E.       F.       G.       H.       I.       J.       K.    What is the incremental B/C (ΔB/C) ratio between the two alternatives, X and Y?       -       A.       B.       C.       D.       E.       F.       G.       H.       I.       J.       K.    Which alternative, if any, should be chosen?

A. [AED 43,742] B. [Alternative Y] C. [DO NOTHING (DN)] D. [-0.59] E. [1.49] F. [3.2] G. [AED 60,552] H. [AED 23,742] I. [AED 10,552] J. [-2.97] K. [Alternative X]

Answer 1

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