# 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 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.

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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 + ...

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