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iRobot Company 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 14 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 $487,000, annual operating costs of $29,000, and a 6-year life. Machine B costs $315,000, has annual operating costs of $51,200, and a 4-year life. The firm currently pays no taxes. Which machine should be purchased and why

Answer :

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Answer:

Machine A should be purchased because it has a lower equivalent annual cost . Hence, it is cheaper.

Explanation:

Equivalent Annual cost is the Present Value of the total cost over the investment period divided by the appropriate annuity factor.

Step 1 : Equivalent Annual cost of Machine A

PV of cash flows

PV of purchase cost = 487,000

PV of annual operating  cost of $29,000

= 29,000× (1-(1+0.14)^(-6))/0.14

= 112,771.35

Total PV = 487,000 + 112,771.35= 599,771.35

Equivalent annual cost = 599,771.35 /3.889

Equivalent annual cost =  154,235.70

Step 2: Equivalent Annual cost of Machine B

PV of purchase cost = 315,000

PV of annual operating  cost of $51,200

= 51,200× (1-(1+0.14)^(-4))/0.14

= 149,182.07

Total PV = 315,000+ 149,182.07

=  464,182.07  

Equivalent annual cost =  464,182.07/2.9137

Equivalent annual cost =   159,309.51

Step 3: Compare equivalent Annual cost

Comparing the two equivalent costs, we conclude that Machine A should be purchased because it has a lower equivalent annual cost and therefore it is cheaper.

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