# Payback Period

Payback period is the time in which the initial cash outflow of an investment is expected to be recovered from the cash inflows generated by the investment. It is one of the simplest investment appraisal techniques.

## Formula

The formula to calculate payback period of a project depends on whether the cash flow per period from the project is even or uneven. In case they are even, the formula to calculate payback period is:

 Payback Period = Initial Investment Cash Inflow per Period

When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use the following formula for payback period:

 Payback Period = A + B C

In the above formula,
A is the last period with a negative cumulative cash flow;
B is the absolute value of cumulative cash flow at the end of the period A;
C is the total cash flow during the period after A

Both of the above situations are applied in the following examples.

## Decision Rule

Accept the project only if its payback period is LESS than the target payback period.

## Examples

Example 1: Even Cash Flows
Company C is planning to undertake a project requiring initial investment of $105 million. The project is expected to generate$25 million per year for 7 years. Calculate the payback period of the project.

Solution
Payback Period = Initial Investment ÷ Annual Cash Flow = $105M ÷$25M = 4.2 years

Example 2: Uneven Cash Flows
Company C is planning to undertake another project requiring initial investment of $50 million and is expected to generate$10 million in Year 1, $13 million in Year 2,$16 million in year 3, $19 million in Year 4 and$22 million in Year 5. Calculate the payback value of the project.

Solution

 (cash flows in millions) CumulativeCash Flow Year Cash Flow 0 (50) (50) 1 10 (40) 2 13 (27) 3 16 (11) 4 19 8 5 22 30

Payback Period
= 3 + (|-$11M| ÷$19M)
= 3 + ($11M ÷$19M)
≈ 3 + 0.58
≈ 3.58 years