Question

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 1

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

Step-by-step 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.