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IEMS 326 Notes06Replacement

# IEMS 326 Notes06Replacement - Repeated Investment and...

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Repeated Investment and Replacement IEMS 326 Lecture 6

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Unequal Study Periods What if # years is unequal for 2 alternatives? a machine that lasts 6 years vs. a machine that lasts 8 years a project that ends in 2 years vs. a project that ends in 3 years What happens next? It’s over. We must invest again. Continue until time horizon T.
One-Time Project Mutually exclusive alternatives So what? Pick larger NPV. Yearly cashflows C0, C1, C2 yield NPV2 = C0 + C1/(1+r) + C2/(1+r) 2 . Yearly cashflows D0, D1, D2, D3 yield NPV3 = D0 + D1/(1+r) + D2/(1+r) 2 + D3/(1+r) 3 .

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Infinitely Repeated Investment Pick larger equivalent annuity . NPV2 = A/(1+r) + A/(1+r) 2 . NPV3 = B/(1+r) + B/(1+r) 2 + B/(1+r) 3 . Solve NPV = (A/r)(1 – (1+r) -t ) for A: A = NPV * r / (1 – (1+r) -t ). t = lifespan Consider least common multiple of lifespans.
Fixed Time Horizon Last, partial cycle matters. Truncate last cycle and use salvage value. Or, possibly, mix different alternatives. Examples: AaAaAaA-x BbbBbbB-x AaAaBbb

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How Does Repetition Take Place? Is there a short time horizon over which
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IEMS 326 Notes06Replacement - Repeated Investment and...

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