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Payback Time

Investments and payback time

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Payback time is often used to determine the attractiveness of an investment. Payback time is

  • the number of periods required for cumulative benefits to equal cumulative costs

In general - the smaller the payback period, the better the investment.

Undiscounted Payback

Undiscounted payback can be expressed as

F0 = F1 + F2 + ... + Fnp                   (1)

or

F0 - (F1 + F2 + ... + Fnp) = 0

where

F0 = initial investment

F1 .. = cash flows in future periods

np = period where initial investment equals accumulated future cash flows

Discounted Payback

Discounted payback can be expressed as

F0 = F1 / (1 + i) + F2 / (1 + i)2 + ... + Fnp / (1 + i)np                   (2)

or

F0 - [F1 / (1 + i) + F2 / (1 + i)2 + ... + Fnp / (1 + i)np] = 0

where

i = interest rate

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  • en: payback investment time discounted undiscounted
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