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

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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... + (8,000/1.15)
= $173.91

NPV(y2) = -12,000 + (6,000/1.15) +
[5,500/(1.15 x 1.15)] + [4,000/(1.15 x 1.15)]
= $400.76

NPV(y3) = -12,000 + (6,000/1.15) +
[5,500/(1.15 x 1.15)] + [4,750/(1.15 x 1.15 x 1.15)] + 0
= $499.38

Step 2: Calculate the optimal replacement cycle

NPV (1) = 173.91 x [1.15/(1.15-1)]
= $1,333.31

NPV ...