You are considering upgrading some manufacturing facilities by purchasing one of

Question

You are considering upgrading some manufacturing facilities by purchasing one of three different machines, each with the same production capacity. Machine A costs $30,000, has a life of 40 years, annual maintenance costs of $1500, and a salvage value of $5000. Machine B costs $20,000, has a life of 20 years, annual maintenance of $2000, and salvage value of $3000. Machine C costs $10,000, has a life of 10 years, annual maintenance of $4000, and no salvage value. Determine the most economical choice based on minimizing the present value of total costs. Use an annual discount rate of 10%. Assume that initial costs, annual maintenance, and discount rates are constant throughout the analysis period.

Explanation / Answer

Since the duration for which the machine is required is not mentioned in the question let us consider the analysis period be 10 years So we have the formula to calculate the present worth as (Present worth) = (Initial cost) + (P/A, 10%, 10yrs) (Maintenance cost) – (P/F, 10%, 10yrs) (Salvage Value) From tables we have P/F, 10%, 10yrs = 0.3855 P/A, 10%, 10yrs = 6.1446 For Machine A Initial cost = $30,000 Maintenance cost = $1500 Salvage Value = $5000 Therefore (Present worth) = ($30,000) + (6.1446) ($1500) – (0.3855) ($5000) (Present worth) = $37289.4 For Machine B Initial cost = $20,000 Maintenance cost = $2000 Salvage Value = $3000 Therefore (Present worth) = ($20,000) + (6.1446) ($2000) – (0.3855) ($3000) (Present worth) = $31132.7 For Machine B Initial cost = $10,000 Maintenance cost = $4000 Salvage Value = $ 0 Therefore (Present worth) = ($10,000) + (6.1446) ($4000) – (0.3855) ($ 0) (Present worth) = $34578.4 Since present value of the machine is minimum for B , it is the best alternative for 10yrs.

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