# Payback Time

## Investments and payback time

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

F_{0}= F_{1}+ F_{2}+ ... + F_{np}(1)

or

F_{0}- (F_{1}+ F_{2}+ ... + F_{np}) = 0

where

F_{0}= initial investment

F_{1}.. = cash flows in future periods

np = period where initial investment equals accumulated future cash flows

### Discounted Payback

Discounted payback can be expressed as

F_{0}= F_{1}/ (1 + i) + F_{2}/ (1 + i)^{2 }+ ... + F_{np}/ (1 + i)^{np}(2)

or

F_{0}- [F_{1}/ (1 + i) + F_{2}/ (1 + i)^{2 }+ ... + F_{np}/ (1 + i)^{np}] = 0

where

i = interest rate

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