Break-even (economics) - Computation

Computation

In the linear Cost-Volume-Profit Analysis model, 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 quantity 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:

R=C, Where R is revenue generated, C is cost incurred i.e. Fixed costs + Variable Costs or Q * P(Price per unit) = TFC + Q * VC(Price per unit), Q * P - Q * VC = TFC, Q * (P - VC) = TFC, or, Break Even Analysis Q = TFC/c/s ratio=Break Even ®®

Read more about this topic:  Break-even (economics)

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