Computation

In the linear Cost-Volume-Profit Analysis model,[2] the break-even point (in terms of Unit Sales (X)) can be directly computed in terms of Total Revenue (TR) and Total Costs (TC) as:

\begin{align} \text{TR} &=  \text{TC}\\ \text{P}\times \text{X} &= \text{TFC} + \text{V} \times \text{X}\\ \text{P}\times \text{X} - \text{V} \times \text{X} &= \text{TFC}\\ \left(\text{P} - \text{V}\right)\times \text{X} &= \text{TFC}\\ \text{X} &= \frac{\text{TFC}}{\text{P} - \text{V}} \end{align}

where:

  • TFC is Total Fixed Costs,
  • P is Unit Sale Price, and
  • V is Unit Variable Cost.

The Break-Even Point can alternatively be computed as the point where Contribution equals Fixed Costs.

The quantity \left(\text{P} - \text{V}\right) is of interest in its own right, and is called the Unit Contribution Margin (C): it is the marginal profit per unit, or alternatively the portion of each sale that contributes to Fixed Costs. Thus the break-even point can be more simply computed as the point where Total Contribution = Total Fixed Cost:

\begin{align} \text{Total Contribution} &=  \text{Total Fixed Costs}\\ \text{Unit Contribution}\times \text{Number of Units} &= \text{Total Fixed Costs}\\ \text{Number of Units} &= \frac{\text{Total Fixed Costs}}{\text{Unit Contribution}} \end{align}

In currency units (sales proceeds) to reach break-even, one can use the above calculation and multiply by Price, or equivalently use the Contribution Margin Ratio (Unit Contribution Margin over Price) to compute it as: \text{Break-even(in Sales)}  = \frac{\text{Fixed Costs}}{\text{C}/\text{P}}.

R=C Where R is revenue generated C is cost incurred i.e. Fixed costs + Variable Costs or Q X P(Price per unit)=FC + Q X VC(Price per unit) Q X P – Q X VC=FC Q (P-VC)=FC or Q=FC/P-VC=Break Even Point