## What is payback period?

**Payback period** (**PB**) is a financial metric for cash flow analysis that addresses questions like these:

How long does it take for investments, acquisitions, or actions to pay for themselves?

How long does it take for incoming returns to cover costs?

Or, put still another way: How long does it take to break even?

Like other financial metrics for cash flow analysis such as internal rate of return IRR and return on investment ROI, the payback period metric takes essentially an "Investment view" of an action or investment and its expected cash flow stream. Each of these metrics compares expected costs to expected returns in one way or another. Payback period for an action or investment is the time required for cumulative returns to equal cumulative costs.

Payback period is usually given in decimal years presented like this:

Payback period = 2.5 years.

## Contents

**Why is a shorter payback period better than a longer payback?**

Other things being equal, the investment that is repaid in the shorter time period is considered the better choice. The shorter time period is preferred because:

- Investment or action costs are recovered sooner and are available again for further use.
- A shorter payback period is viewed as less risky.

It is usually assumed that the longer the time required for covering funds, the more uncertain are the positive returns. For this reason, Payback period is often viewed as a measure of risk, or a risk-related criterion that must be met before funds are spent. A company might decide, for instance, to undertake no major expenditures that do not pay for themselves in, say, 3 years.

## How is payback period explained and calculated?

As an example, consider a five year investment whose cash flow consequences are summarized in the table below. The primary data for calculating payback period are the expected cash inflows and outflows from the action:

- Cash Inflows: $300 cash inflows are expected each year for years 1 through 5.
- Cash outflows: The initial cost is a cash outflow of $800 in year 1, followed by a cost (outflow) of $150 in year 2. There are no expected costs in years 3 through 5.

From these figures, the analyst creates two sets of cash flow numbers to use for the calculation (the bottom two rows of the table):

- Net cash flow. The net of cash inflows and outflows for each year.
- Cumulative cash flow. The sum of all cash inflows and outflows for all preceding years and the current year.

Expected Cash Flow | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
---|---|---|---|---|---|

Cash Inflows | 300 | 300 | 300 | 300 | 300 |

Cash Outflows | –800 | –150 | 0 | 0 | 0 |

Net Cash Flow | –500 | 150 | 300 | 300 | 300 |

Cumulative CF | –500 | –350 | –50 | 250 | 550 |

At what point in time does the investment break even? Look first to cumulative cash flow at the bottom, and it is clear that payback occurs sometime in Year 4. We know it occurs in Year 4 because cumulative cash flow is negative at Year 3 end and positive at Year 4 end. But where, precisely, is the break even event in Year 4? The answer can be seen roughly on a graph, showing PB as the point in time when cumulative cash flow crosses from negative to positive:

In reality, break even may occur any time in year 4 at the moment when the cumulative cash flow becomes 0. However, if the analyst has only annual cash flow data to work with (as in this example) and no further information about when cash flow appears within year 4, the analyst must assume the year's cash flows are spread evenly through the year.

In this case, payback period must be estimated by interpolation as illustrated here and in the next section. The assumption that cash flow is spread evenly through the years is represented by the straight lines between year end data points above.

Using the tabled data above, where cumulative cash flow clearly reaches 0 in Year 4, PB can be calculated (estimated) as follows;

Payback period = Y + ( A / B ) where

Y = The number of years *before* the payback year. In the example, Y = 3.0 years.

A = Total remaining to be paid back at the start of the break even year, to bring cumulative cash flow to 0. In the example, A = $50.

B = Total (net) paid back in the entire payback year. In the example B = 300.

For the example,

Payback period = 3+ (50) / (300)

= 3 + 1/6

= 3.17 Years

PB calculated this way is an estimate based on interpolation between two period end points (between the end of Year 3 and the end of Year 4). Interpolation was necessary because we have only annual cash flow data to work with.

## How is payback period explained in mathematical terms?

The payback period "formula" in the previous section is easy to understand because it describes in simple verbal terms the amounts to be added or divided. However, when the analyst tries to implement these instructions in a spreadsheet formula, the implementation becomes somewhat cumbersome. In any case, the spreadsheet programmer needs at least a simple understanding of the quantities that must be identified and used in calculating payback period.

Consider again the cumulative cash flow curve (such as that shown above for the tabled example), but now focused on the break even year (here, Year 4) and the year before that (Year 3).

The blue line rising from lower left to upper right is cumulative cash flow, graphed in straight line segments between year end points.

With simple principles of plane geometry, it is possible to show that two ratios in the above figure are equivalent:

| A | / | B | = C / 1.0

This fraction, C, plus the number of whole years before the payback year (Y), is PB:

Payback Period = Y + C.

To implement the PB metric in a spreadsheet, the sheet must have access to individual annual figures for both net cash flow and cumulative cash flow (the last two rows of the table above). The programmer builds logical tests ( "IF" expressions in Microsoft Excel) to find the first year of positive cumulative cash flow. Then, with the payback year known, the calculations use annual and cumulative cash flows from the break even year and the year before that, to calculate the lengths of line segments A and B from the diagram above. (See Financial Metrics Pro for working examples.)

## What are important considerations in using the payback metric?

Payback period is an appealing metric because its meaning is easily understood. Nevertheless, here are some points to keep in mind when using payback period:

- PB cannot be calculated if the positive cash inflows do not eventually outweigh the cash outflows. That is why this metric is of little use when used with a pure "costs only" business case or cost of ownership analysis.
- There can be more than one payback period for a given cash flow stream. PB examples such as the one above typically show cumulative cash flow increasing continuously. In real world cash flow results, however, cumulative cash flow can decrease as well as increase from period to period. When cumulative cash flow is positive in one period, but negative again in the next, there can be more than one break even point in time.
- The PB metric by itself says nothing about cash flows coming after cumulative cash flow first reaches 0. One investment may have a shorter PB than another, but the latter may go on to greater cumulative cash flow over time.
- The payback calculation ordinarily does not recognize the time value of money (in a discounting sense).