It does not make sense to find the breakeven point using a company's payback period. A company's payback period is concerned with the number of periods needed to pay back an initial investment with positive net income, while a company's breakeven point is concerned with the specific period in which its revenue will equal total costs and its net income will be zero.
The Breakeven Point
The breakeven point of a company can be defined as the accounting period that generates enough revenue to cover all of a company's expenses for that accounting period.
If, for example, a company has total monthly expenses prior to any taxes of $100, that company's breakeven point would be the month when its total revenue equals exactly $100. By definition, the company would earn no net income and would literally break even for that accounting period.
The breakeven point of a company can be found by either the exact volume of units needed to be sold to generate enough revenue to cover its total expenses, or by dividing the company's total fixed expenses by its contribution margin ratio.
The Payback Period
A company's payback period, on the other hand, doesn't care about a specific accounting period and instead focuses on the number of accounting periods needed to repay an initial investment. This makes it hard to use a company's payback period to calculate or find its breakeven point.
If, for example, a startup company takes on $100 in investments, the payback period would be the number of accounting periods needed to repay that initial $100 with net income. So, if the same company makes $10 a year, it would take 10 years to repay the initial investment, assuming 100% of its net income went to repayment.
Therefore, it would not make sense to use payback period to find a company's breakeven point, since both measure separate things.