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The break-Even point in business means the point at which your business is neither making a profit or a loss (The money you are spending is equal to the money you are making). In the long-term it can be the point the point at which the money you invested into the business (capital) is recovered. In the short-term it can be the point at which the money spent on stock (inventory) is recovered.
Payback period is the time it will take for the business to reach the break-even point. Take note that payback periods can be very long especially for businesses where a lot of money has been invested.