Question

In: Economics

One year ago, a machine was purchased at a cost of $2,000, to be useful for...

One year ago, a machine was purchased at a cost of $2,000, to be useful for 6 years. However, the machine has failed to perform properly and has a cost of $500 per year per year for repairs, adjustments, and shutdowns. A new machine is available to accomplish the functions desired and has an initial cost of $3,500. Its maintenance costs are expected to be $50 per year during its service life of 5 years. The approximate market value of the present machine has been roughly $1,200. If the operating costs (other than maintenance) for both machines are equal, show whether it is economical to purchase the new machine. Perform a before-tax study using an interest rate of 12%, and assume that the salvage values will be negligible.

Expert Solution

Using PV = FV / (1 + r)ⁿ

r = rate of interest = 12%

n = period in year

Present Value of costs for current machine

PV_c0 = $1,200

PV_c1 = $500 / (1.12)¹ = $446.43

PV_c2 = $500 / (1.12)² = $398.6

PV_c3 = $500 / (1.12)³ = $355.89

PV_c4 = $500 / (1.12)⁴ = $317.76

PV_c5 = $500 / (1.12)⁵ = $283.71

PV of first cash flow

PV_current = PV_c0 + PV_c1 + PV_c2 + PV_c3 + PV_c4 + PV_c5

= $1,200 + $446.43 + $398.6 + $355.89 + $317.76 + $283.71

= $3,002.39

Present Value of costs for new machine

PV_n0 = $3,500

PV_n1 = $50 / (1.12)¹ = $44.64

PV_n2 = $50 / (1.12)² = $39.86

PV_n3 = $50 / (1.12)³ = $35.59

PV_n4 = $50 / (1.12)⁴ = $31.78.

PV_n5 = $50 / (1.12)⁵ = $28.37

PV of first cash flow

PV_new = PV_n0 + PV_n1 + PV_n2 + PV_n3 + PV_n4 + PV_n5

= $3,500 + $44.64 + $39.86 + $35.59 + $31.78 + $28.37

= $3,680.24

It is NOT economical to purchase the new machine.

Rahul Sunny answered 1 year ago

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