payback period

Payback period The Meaning of Payback Period

Payback Period is a financial metric that answer the question: How long does it take for an investment to pay for itself? Or, how long does it take for incoming returns to cover costs? Or, put still another way: How long does it take for the investment to break even?

Like other financial metrics such as internal rate of return (IRR) and return on investment (ROI), payback period takes essentially an "Investment" view of the action, plan, or scenario and its estimated cash flow stream. Each of these metrics comparies investment costs to investment returns in one way or another. Payback period is the length of time required for cumulative incoming returns to equal the cumulative costs of an investment (e.g. purchase of computer software or hardware, training expenses, or new product development), usually measured in years.

Other things being equal, the investment with the shorter payback period is considered the better investment. The shorter payback period is preferred because:

The investment 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

payback period, the more uncertain are the positive returns. For this reason, payback period is often used 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 investments or expenditures that have a payback period over, say, 3 years.

• Payback Period Explained With an Example • Payback, Mathematically Speaking • Considerations for Using Payback Period

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Payback Period Explained 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 payback calculation are the expected cash inflows and outflows from the investment:

Cash Inflows: The investment will bring $300 cash inflow each year, for years 1 - 5. Cash outflows: The initial cost of the investment 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 - 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.

Investment Cash Flow

Year 1

Year 2

Year 3

Year 4

Year 5

Cash Inflows 300 300 300 300 300Cash Outflows – 800 –150 0 0 0Net Cash Flow – 500 150 300 300 300Cumulative Cash Flow

– 500 – 350 – 50 250 550

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

In reality, payback 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 has to be estimated by interpolation. That approach is 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 the payback year is clearly Year 4, payback period can be calculated (estimated) as follows;

Payback Period = Y + (A / B) where

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

A = Total remaining to be paid back at the start of the payback 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)

Payback Period = 3 + 1/6 = 3.17 Years

Payback period 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 includes simple verbal descriptions of the amounts to be added or divided. However, when the analyst attempts to implement the verbal instructions into a spreadsheet formula for payback, 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.

For this understanding, consider again the cumulative cash flow curve (such as that shown above for the tabled example), but now focused on the payback 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 as 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 payback period: Payback Period = Y + C.

To implement the payback period metric in a spreadsheet, the sheet must have access to the individual annual cash flow figures and the annual cumulative cash flow figures (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 payback year and the year preceding payback, to calculate the lengths of line segments A and B from the diagram above. (See Financial Metrics Pro for working examples).


Considerations for Using Payback Period

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

Payback cannot be calculated if the positive cash inflows do not eventually outweigh the cash outflows. That is why payback (like IRR) 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. Payback period 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 is more than one Payback Period point.

Payback period by itself says nothing about cash flows coming after the payback time. One investment may have a shorter payback period than another, but the latter may go on to greater cumulative cash flow over time.

Payback calculation ordinarily does not recognize the time value of money (in a discounting sense) nor does it reflect money coming in after payback (contrast with discounted cash flow and internal rate of return, above).

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