Refi Question

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I have a question that I believe can be answered more easily than the way I am going about it.

In the case where someone takes out a loan and then decides to refinance at a lower interest rate later, I am trying to figure the break point where it makes since to do so. For example, if some took out a loan at 8 percent for 15 years and then maybe a few years later can get that loan refinanced at 6 percent (which will extend the period of the loan, as it will start back to 15 years again) how does one determine where it is too late to feasibly make this transition considering that the one is getting a lower interest rate, but extending the period of the loan at the same time. Is there some formula or some guide to determine this?

Thank you,
Robert12