Building the Business Case
Solution Matrix Ltd ®

Payback Period PB Explained
Definition, Meaning, and Example Calculations

Business Encyclopedia, ISBN 978-1-929500-10-9. Revised 2014-04-19.

The payback period metric measures the time required to break even.

Cash flow metrics like Payback Period measure characteristics of financial data that might not be apparent from a simple review of the data. Payback Period measures the time required for total cash outflows to equal total cash inflows, that is, the time required to break even.

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 the action or scenario and its estimated cash flow stream. Each of these metrics compares expected costs to expected returns in one way or another. Payback period is the time required for cumulative returns to equal cumulative costs (for example, the cumulative costs from the purchase of computer systems, training expenses, or new product development). PB period is usually given in decimal years presented like this:

Payback period = 2.5 years.

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. 

Contents

•  Payback period explained and calculated with an example
•  Payback period, mathematically speaking 
•  Considerations for using the payback metric

Payback period explained and calculated with an example

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:

When found graphically, payback period is the break even point in time.

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.

Payback period, mathematically speaking

The "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).

Mathematics for calculating payback period

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.)

Considerations for 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).

By Marty Schmidt. Copyright © 2004-

The Best Selling Authority

Business Case Essentials

The complete concise guide to what belongs in your case and why. The trusted authority on business case analysis provides clear, practical, step-by-step guidance with a special focus on:

  • Financial metrics, ROI
    NPV, IRR and TCO.
  • Non-financial benefits.
  • Measuring, minimizing risk.
  • Proof: "Making the case."
  • Industry, government, and nonprofit examples.

Essentials—the most frequently cited case-building guide in print.

Power Tools for
Business Professionals

Project
Progress Pro

Finish time-critical projects on time with the power of statistical process control tracking. The Excel-based system makes implementing project control charting easy to use—even for those without a statistical background.

Progress Pro—When projects simply have to finish on time.

Financial
Modeling Pro

A complete tutorial on building financial models for estimating costs, benefits, and business case results.

Modeling Pro—Live examples & templates for your own models.

Financial
Metrics Pro

Handbook, textbook, and live templates in one Excel tool. Comprehensive usage and implementation of ROI, IRR, Working capital, EPS, and 150+ more cash flow and financial statement metrics.

Metrics Pro features the Analyst Workbench & Chairman's View.

Business Case
Templates 2014

Integrated Word, Excel, and PowerPoint Template system designed to help you build a professional quality case quickly and easily.

Templates 2014—When you need a real business case.

The Premier Professional Training Seminars

Building the Business Case Seminar Participants

Learn how to make your case.

Train and practice with the leading authority on business case analysis. Join more than 16,000 professionals worldwide who have mastered the 6D Framework in Basic and Master Class seminars.

Earn professional education credit while you build your case!

Download case-building books and software when you register! Join the next class in...

   London
   New York City
   Kuala Lumpur

Twice Weekly Newsletter

Subscribe Free:
Business Case Newsletter