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    Finance: Optimal replacement cycle for machinery and when it should be replaced.

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    Gillian is deciding whether to replace an old machine, and has assembled some information (refer to attachment File #1). She believes that the second-hand market value of either machine will decline over time in line with the depreciation schedule (eg. the old machine should sell for $3,000 today). If there are no taxes, and Gillian's required rate of return is 15% p.a.:

    1) What is the optimal replacement cycle for the new machine?
    2) Should the old machine be replaced now or next year?

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    Solution Preview

    1) Optimal Replacement Cycle

    Step 1: Find the Net Present Value (NPV) of the new machine for each of the 3 years.

    NPV(n) = Current value + Cash Flow(1) +
    Cash Flow(2) + Cash Flow(3) + ... +
    Cash Flow(n) + Salvage Value(n)

    where: Cash Flow = Revenue - Expenses
    Salvage value = Current value - Depreciation

    NPV(y1) = -12,000 + ...

    Solution Summary

    Gillian is deciding whether to replace an old machine. Using NPV analysis, the solution calculates the optimal replacement cycle and projects when the machine should be replaced.