Payback

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Payback time is widely 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 + ... + F_np         (1)

or

F₀ - (F₁ + F₂ + ... + F_np) = 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 + ... + F_np / (1 + i)^np        (2)

or

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

where

i = interest rate

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