Math Problem Statement

One year​ ago, your company purchased a machine used in manufacturing for $ 95 comma 000. You have learned that a new machine is available that offers many​ advantages; you can purchase it for $ 165 comma 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 comma 000 per year for the next ten years. The current machine is expected to produce a gross margin of $ 22 comma 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 $ 8 comma 636 per year. The market value today of the current machine is $ 65 comma 000. Your​ company's tax rate is 40 %​, and the opportunity cost of capital for this type of equipment is 12 %. Should your company replace its​ year-old machine? Question content area bottom Part 1 The NPV of replacing the​ year-old machine is ​$    enter your response here. ​(Round to the nearest​ dollar.)

Solution

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Math Problem Analysis

Mathematical Concepts

Net Present Value (NPV) Calculation
Depreciation
Cash Flow Analysis
Tax Shield Calculation

Formulas

Straight-line depreciation: Depreciation = (Cost - Salvage Value) / Useful Life
Tax Shield: Depreciation × Tax Rate
After-tax Cash Flow: (Gross Margin × (1 - Tax Rate)) + Tax Shield
NPV: ∑ (Cash Flows / (1 + Discount Rate)^t) - Initial Investment

Theorems

Time Value of Money
NPV Rule

Suitable Grade Level

Undergraduate Level (Finance/Accounting)