Equations for elements of cost are as follows:

Sales = Variable costs + Fixed Expenses ± Profit /Loss

Or

Sales – Variable Cost = Fixed Expenses ± Profit /Loss

Or

Sales – Variable Cost = Contribution

It is necessary to understand the following four concepts, their calculations, and applications to know the mathematical relation between cost, volume, and profit:

● Contribution

● Profit Volume Ratio (P/V Ratio or Contribution/Sales (C/S))

● Break-Even Point

● Margin of Safety

### Contribution

Contribution = Sales – Marginal Cost

We have already discussed contribution in Marginal Costing topic above.

### Profit-Volume Ratio

Profit / Volume (P/V) ratio is calculated while studying the profitability of operations of a business and to establish a relation between Sales and Contribution. It is one of the most important ratios, calculated as under:

^{P}⁄_{V} Ratio =

ContributionSales

=

Fixed Expenses+ProfitSales

=

Sales−Variable CostSales

=

Change in profits of ContributionsChange in Sales

The P/V Ratio shares a direct relation with profits. Higher the P/V ratio, more the profit and vice-a-versa.

### Break-Even Point

When the total cost of executing business equals to the total sales, it is called break-even point. Contribution equals to the fixed cost at this point. Here is a formula to calculate break-even point:

B.E.P (in units) =

Total Fixed ExpensesSelling Price per Unit − Marginal Cost per Unit

=

Total Fixed ExpensesContribution per Unit

Break-even point based on total sales:

=

Fixed Cost^{P}⁄_{V} Ratio

Calculation of output or sales value at which a desired profit is earned:

=

Fixed Expenses + Desired ProfitSelling Price per Unit − Marginal Cost per Unit

=

Fixed Expenses + Desired ProfitContribution per Unit

**COMPOSITE BREAK EVEN POINT**

A company may have different production units, where they may produce the same product. In this case, the combined fixed cost of each productions unit and the combined total sales are taken into consideration to find out BEP.

● **Constant Product** – Mix Approach In this approach, the ratio is constant for the products of all production units.

● **Variable Product** – Mix Approach In this approach, the preference of products is based on bigger ratio.

### Margin of Safety

Excess of sale at BEP is known as margin of safety. Therefore,

Margin of safety = Actual Sales − Sales at BEP

Margin of safety may be calculated with the help of the following formula:

Margin of Safety =

Profit^{P}⁄_{V} Ratio

=

ProfitContribution per Unit