Please help me with this One year ago, your company purchased a machine used in

Question

Please help me with this

One year ago, your company purchased a machine used in manufacturing for
$110,000. You have learned that a new machine is available that offers many
advantages; you can purchase it for $155,000 today. It will be depreciated on a
straight-line basis over ten years and has no salvage value. You expect that the new
machine will produce a gross margin (revenues minus operating expenses other
than depreciation) of $55,000 per year for the next ten years. The current machine
is expected to produce a gross margin of $24,000 per year. The current machine is
being depreciated on a straight-line basis over a useful life of 11 years, and has no
salvage value, so depreciation expense for the current machine is $10,000 per year.
The market value today of the current machine is $60,000. Your company%u2019s tax rate
is 42%, and the opportunity cost of capital for this type of equipment is 10%. Should
your company replace its year-old machine?

Explanation / Answer

Hi,

Please find the answer as follows;

Incremental revenues: 0

Incremental costs: -155000

Depreciation: 10000 per year

Capital Gain on Salvage: 60000

Cash Flow from Salvage Value: 60000 - (60000)(0.42) = 34800

Replacing the Machine will increae EBITDA = 55000 - 24000 = 31000

Increase in Depreciation Expense = 15500 - 10000 = 5500

Free Cash Flow = 31000*(1-.42) + 5500*.42 = 20290 (Year 1 to Year 10)

Year 0 Free Cash Flow = -155000 + 60000 + 40000*.42 = -78200

NPV of Replacement = -78200 + 20290/(1+.10)^1 + 20290/(1+.10)^2 + 20290/(1+.10)^3 + 20290/(1+.10)^4 + 20290/(1+.10)^5+ 20290/(1+.10)^6 + 20290/(1+.10)^7 + 20290/(1+.10)^8 + 20290/(1+.10)^9 + 20290/(1+.10)^10 = 46473.27

Yes, the machine should be replaced.

Thanks.

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