Hi there,

The **payback period** refers to **the time needed to recover an investment**.

The **breakeven point **refers to the **situation where total revenues are equal to total costs**. The question is normally related to the quantity required to reach that point.

__PAYBACK PERIOD__

Let’s say that you have the following:

*I = Initial investment*

*CF = Yearly cash flow of the investment*

Assume for simplicity that the yearly cash flow is constant and there is no time value of money.

The payback period would be :

*Payback period = I / CF*

If the cash flow is not constant or there is time value of money, the formula becomes more complex, due to the fact the cash flow changes every year.

__BREAKEVEN POINT__

Let’s assume your goal is to find the quantity to reach breakeven.

You can just rearrange the breakeven formula, which is the following:

*R-VC-FC=0*

*⇔ p*q-c*q-FC=0*

Where

- R= Revenues
- VC= Variable Costs
- FC = Fixed Costs
- p = Price
- q = Quantity
- c = Variable Cost per Unit

To calculate the quantity, you can rearrange it as follows:

*p*q-c*q-FC=0*

*⇔ q=FC/(p-c)*

Hope this helps,

Francesco