Math Problem Statement

A company is considering expanding their production capabilities with a new machine that costs $59,000 and has a projected lifespan of 6 years. They estimate the increased production will provide a constant $10,000 per year of additional income. Money can earn 1.5% per year, compounded continuously. Should the company buy the machine?

Solution

To determine whether the company should buy the machine, we can evaluate the Net Present Value (NPV) of the investment. The NPV takes into account the time value of money by discounting the future cash flows to their present value.

Steps to calculate the NPV:

  1. Initial Investment:
    The initial cost of the machine is $59,000.

  2. Annual Cash Inflows:
    The machine is expected to generate $10,000 per year for 6 years.

  3. Discount Rate:
    The discount rate given is 1.5% per year, compounded continuously. The formula for the present value of a continuous income stream

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Math Problem Analysis

Mathematical Concepts

Finance
Time Value of Money
Net Present Value (NPV)
Continuous Compounding

Formulas

NPV formula with continuous compounding

Theorems

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Suitable Grade Level

Business and Finance Professionals

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