Question

You are trying to pick the least-expensive machine for your company. You have two choices: machine A, which will cost $100,000 to purchase and which will have operating cash flows of −$7,000 annually throughout the machine's expected life of three years; and machine B, which will cost $125,000 to purchase and which will have operating cash flows of −$2,600 annually throughout that machine's four-year life. Both machines will be worthless at the end of their life. If you intend to replace whichever type of machine you choose with the same thing when its life runs out, again and again out into the foreseeable future, and if your business has a cost of capital of 15 percent, answer the following 3 questions (for any question requiring an answer in dollars, show your answer in the rounded to the nearest dollar amount i.e. $123,456):

What is the EAC for machine A? ________

What is the EAC for machine B? _________

Which machine (A or B) should be chosen strictly based on this analysis? ________

Answer 1

(a)-Equivalent Annual Cost (EAC) for MACHINE-A

Period	Annual Cash Flow ($)	Present Value factor at 15.00%	Present Value of Cash Flow ($)
1	-7,000	0.869565	-6,086.96
2	-7,000	0.756144	-5,293.01
3	-7,000	0.657516	-4,602.61
TOTAL		2.283225	-15,982.58

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= -$15,982.58 - $100,000

= -$115,982.58 (Negative)

Equivalent Annual Cost (EAC) for Machine-A = Net Present Value / [PVIFA 15.00%, 3 Years]

= -$115,982.58 / 2.283225

= -$50,797.70 (Negative)

(b)-Equivalent Annual Cost (EAC) for MACHINE-B

Period	Annual Cash Flow ($)	Present Value factor at 15.00%	Present Value of Cash Flow ($)
1	-2,600	0.869565	-2,260.87
2	-2,600	0.756144	-1,965.97
3	-2,600	0.657516	-1,709.54
4	-2,600	0.571753	-1,486.56
TOTAL		2.854978	-7,422.94

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= -$7,422.94 - $125,000

= -$132,422.94 (Negative)

Equivalent Annual Cost (EAC) for Machine-A = Net Present Value / [PVIFA 15.00%, 4 Years]

= -$132,422.94 / 2.854978

= -$46,383.17 (Negative)

(c)-DECISION

Here, the MACHINE-B should be selected, since it has the lower Equivalent Annual Cost (EAC) of $46,383.17 as compared to the EAC of Machine-A.

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.