Run rate is a quick and dirty method to extend less than one year's worth of numbers to an entire year. It's an extrapolation of data from a period of time to a longer period. For example, if a company has sales of $100,000 a month, it could be extrapolated that is has a run rate of $1.2 million when it comes to sales.
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Calculating a run rate is a way of "annualizing" data that has been collected for a period that is less than one year. To do this, divide whatever number is being measured by the number of quarters that there is data, then multiply by four. For instance, if free cash flow over the first two quarters is $170 million, then the run rate would be $170 / 2 * 4 = $340 million.
When would you do this? Well, one time would be if the number being studied has recently turned positive, such as net income or cash flow. Or, if there is not sufficient data to estimate how the company has grown that amount in the past.
Be careful, however. Calculating a run rate assumes that conditions which existed during the time period measured will not change considerably over the rest of the year. This is not necessarily true. For instance, many retailers are very cyclical in their earnings, generating a large portion of their profits over the winter holiday season. If you use only the spring and summer to calculate a full-year run rate, then you will be underestimating the actual amount the company is likely to generate, sometimes by a lot. In other words, if you can, it is usually better to use an entire year's worth of data in generating your predictions.
Another caveat: Run rate does not take the company's ability to grow earnings over time (such as year over year) into account. If the company can grow earnings by 10%, then a run rate using only the first half of the year will likely underestimate the total amount of earnings the company can generate over the entire year.