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Three alternative machine models are being considered for an ongoing operation. The three alternatives will be...

Three alternative machine models are being considered for an ongoing operation. The three alternatives will be used in the production of the same product. Therefore, the selection among the three will be based on total costs. Model A costs $105,000 and will last 4 years. Its real operating cost is $10,200/year. Model B costs $110,000 and will last 5 years. Its real operating cost is $9,400/year. Model C costs $125,000 and will last 6 years, Its real operating cost is $9,600/year. It is determined that the real opportunity cost of capital is 7%. Rank the three models from the best choice to the least choice. a. Best A, B, C Least b. Best C, B, A Least c. Best B, A, C Least d. Best A, C, B Least e. Best C, A, B Least

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Answer #1

To calculate the total cost of the three alternatives , the annuity formula shall be used

Total cost of each alternative = Initial cost of machine + Present value of operating costs

Present value of operating cost will be calculated with the annuity formula

PV = , here r = 7% or 0.07 ( cost of capital)

1. Model A

Initial cost of machine = $105,000

Present Value (PV) of operating costs = 10,200 [ 1 - (1+0.07)^ (-4) / 0.07]

total cost = $105,000 + $34,549.55 = $139,549.55

1. Model b

Initial cost of machine = $110,000

Present Value (PV) of operating costs = 9400 [ 1 - (1+0.07)^ (-5) / 0.07]

total cost = $110,000 + $38,541.86 = $148,541.86

1. Model c

Initial cost of machine = $125,000

Present Value (PV) of operating costs = 9600 [ 1 - (1+0.07)^(-6) / 0.07]

total cost = $125,000 + $45,758.78 = $170,757.78

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