Two mutually exclusive alternatives are being considered for pollution control e
ID: 2729658 • Letter: T
Question
Two mutually exclusive alternatives are being considered for pollution control equipment. The economic data is given below:
A B
Initial cost $20,000 $38,000
Annual expenses $5,500 $5,000
Useful life 5 years 9 years
Salvage value at the end $1,000 $3,000
Of useful life
The study period is 9 years. If alternative A is selected, a portable system would be leased for the last 4 years at a cost of $10,000 per year including all expenses. If the MARR is 15% per year, which alternative should be selected?
Explanation / Answer
For Alternative A,
Present value of annuity factor PVAF(r,n) = {1-(1+r)-n}/r
PVAF (15%,5) = (1-1.15-5)/0.15 = 3.3522
PVAF(15%,4) = (1-1.15-4)/0.15 = 2.8550
Present value of annual expenses = $5,500 * 3.3522 = $18,437.10
Present value of lease expenses at the end of Year 5 = $10,000*2.8550 = $28,550
Present value of lease expenses as on today = $28,550/1.155 = $14,194.40
Present value of salvage value = $1,000/1.155 = $497.18
Total present worth = Initial cost + Preent value of annual expenses + present value of lease expenses – Present value of salvage value
Total present worth = $20,000 + $18,437.10 + $14,194.40 - $497.18 = $52,134.32
For Alternative B,
Present value of annuity factor PVAF(r,n) = {1-(1+r)-n}/r
PVAF (15%,9) = (1-1.15-9)/0.15 = 4.7716
Present value of annual expenses = $5,000 * 4.7716 = $23,858
Present value of salvage value = $3,000/1.159 = $852.78
Total present worth = Initial cost + Present value of annual expenses – Present value of salvage value
Total present worth = $38,000 + $23,858, - $852.78 = $61,005.32
Hence Alternative A should be selected
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