Question

Boston Engineering is analyzing two machines to determine which one it should purchase. Whichever machine is purchased will be replaced at the end of its useful life. The company requires a 12 percent rate of return and uses straight-line depreciation to a zero book value over the life of the machine. Machine A has a cost of $495,000, annual operating costs of $28,000, and a 3-year life. Machine B costs $302,000, has annual operating costs of $45,000, and a 2-year life. The firm currently pays no taxes. Which machine should be purchased and why?

		Machine A; because it will save the company about $11,500 a year
		Machine A; because it will save the company about $14,280 a year
		Machine B; because it will save the company about $8,760 a year
		Machine B; because it will save the company about $9,768 a year
		Machine B; because it will save the company about $10,400 a year

Answer 1

Machine A:

	Y0	Y1	Y2	Y3
Cash Flow	495,000	28,000	28,000	28,000
Discount Factors @12%		0.89	0.80	0.71
NPV	562,251
Equivalent Annual Annuity	234,093

For Machines A, we first see that NPV = 562,251 ( = 495000 +28000/(1+12%)+28000 /(1+12%)^2 + 28000 /(1+12%)^3)

Now we find the Equivalent Annnual Annuity (EAA) which is given by formula = r*NPV/(1 - (1+r)^-n)

where r= rate of discount =12%

and n = no. of period = 3 years

this gives EAA = 234,093

EAA means that the annualized cost of Machine A ie Annual equivalnet cost = 234,093

Sismilarly for Machine B:

	Y0	Y1	Y2
Cash Flow	302,000	45,000	45,000
Discount Factors @12%		0.89	0.80
NPV	378,052
Equivalent Annual Annuity	223,693

Please note that since life is different, NPV can not be used for comparison directly and hence it needs to be annualized in form of EAA to compare. ALl projects where life is different can be compared through EAA

EAA for Machine B = 223,693. This means that Machine B annual cost is lower (Machine A EAA = 234,093). Hence Machine B shoul dbe selected becuase it saves (234,093-223693 = 10,400 a year)

Hence Last option is correct. ie Machine B; because it will save the company about $10,400 per year.