Marginal Costing – Contribution Margin – Cost / Volume / Profit Formulae

This article focuses on the basic and important formulae used in Contribution margin - cost/ volume/ profit in

marginal costing: Marginal cost, missing factor, contribution, units sold, break even point, break even sales,

calculation of sales for desired profit, profit/volume ratio, contibution/sales ratio, margin of safety, quantity, target

income etc.

Basic Equation:  

Variable Cost    =  Direct Materials + Direct Labor + Direct Expenses 

Variable cost per unit  =         Difference in cost            

Difference in Activity level 

Variable Cost is also called as Marginal Cost. 

 

Marginal Cost Equation: 

Sales (S) =  Variable Cost (V) + Fixed Expenses (F) + or – Profit (P) / Loss (L) 

      S    =   Sales

      V    =   Variable Cost

      F    =   Fixed Expenses

      +P  =   Profit

      -P  =   Loss 

Sales - Variable Cost   =   Fixed Expenses + or – Profit / Loss

      S  -  V   =   F  + or – P 

 

Contribution: 

Sales – Variable Cost    =  Contribution = S - V

Fixed Expenses + or – Profit / Loss   =   Contribution = F + or – P 

In simple form,    S – V  =  F + or – P 

 

Missing Factor: 

In the above four factors, if any three factors are known, the remaining one can be easily found out. 

Sales     =    Variable Cost  +  Fixed Expenses + Profit

Variable Cost  =    Sales – (Fixed Expenses + Profit)

Fixed Expenses  =    Sales – Variable Cost – Profit

Profit     =    Sales – Variable Cost – Fixed Expenses  

 

Units sold:  

Units sold = Contribution margin / Contribution margin per unit

 

Break Even Point: 

A business is said to break even when its total sales are equal to its total costs.

It is a point where

There is no profit or no loss.

Contribution is equal to Fixed Expenses.

Break Even Point  =                         Total Fixed Expenses                     

    (in Units)                  (Selling Price per Unit – Marginal Cost per Unit) 

The answer will be in units and not in value because break even point is based on unit cost. 

 

Break Even Sales: 

      S – V  =  F + P 

At Break Even Point Profit equals zero. 

Hence,  S – V  =  F 

For Break Even Point, the equation is S – V = F 

Dividing both sides by S – V, 

        S – V      =          F    

    (S – V)           (S – V) 

      i.e. 1    =       F    

                      (S – V) 

Multiplying both sides by S, 

      S x 1    =            F x S    

                           (S – V) 

Therefore, the formula for the calculation of break even sales is: 

                    F x S    

                 (S – V) 

 Calculation of Sales for a desired or expected Profit:

              (Fixed Expenses + Profit)                

(Selling Price per Unit – Marginal Cost per Unit)

                           Or

             (Fixed Expenses + Profit)         

               Contribution per Unit

The formula for the calculation of Sales to earn an expected or desired profit is: 

               (F + P) x S  

                  S – V 

 

Profit / Volume Ratio  or Contribution / Sales Ratio

(P/V Ratio) or (C/S Ratio)

P/V Ratio  

                     Contribution    i.e.      C  

                         Sales                S 

                           Or 

               (Sales – Variable Cost)   i.e.     S – V  

                          Sales                      S 

                          Or 

             (Fixed Expenses + Profit)  i.e.   F + P

                         Sales                         S 

                          Or  

             Changes in contribution in two periods  

                  Changes in Sales in two periods  

                                   Or 

               Changes in Profit in two periods    

              Changes in Sales in two periods 

The ratio can be shown in the form of percentage if the formula is multiplied by 100. 

This ratio can be used for the calculation of  

Break Even Point is   Fixed Costs    =         F        

                                P/V Ratio           P/V Ratio                 

 

For the calculation of sales to earn a desired or expected profit is 

                         Fixed Costs + Profit   =       F + P    

                              P/V Ratio                  P/V Ratio 

                            Contribution  

                             P/V Ratio  

Variable Costs =  Sales (1 – P/V Ratio) 

Contribution is  Sales  x  P/V Ratio 

 

Margin of Safety (M/S) 

It is the difference between the actual sales and the sales at break even point.

Sales or Output beyond break even point is known as margin of safety. 

 Margin of Safety (M/S) = Present Sales – Break Even Sales

                                   Or 

                        =       Profit    

                              P/V Ratio 

 

Break-Even and Target Income 

Sales   =   Total Variable Costs + Total Fixed Costs + Target Income 

Where Target Income is zero, then

Sales   =   Total Variable Costs + Total Fixed Costs 

Which is the Break even sales. 

Break-Even Point in Units  =  Total Fixed Costs / Contribution Margin Per Unit 

Break-Even Point in Sales  =  Total Fixed Costs / Contribution Margin Ratio 

Units to Achieve a Target Income   =   (Total Fixed Costs + Target Income)    

                                                                 Contribution Margin per Unit 

Sales to Achieve a Target Income  =     (Total Fixed Costs + Target Income)    

                                                                   Contribution Margin Ratio 

Break-even quantity  =                  Total fixed costs                

                                      (selling price - average variable costs). 

Explanation - in the denominator :  

"Price minus average variable cost" is the variable profit per unit, or contribution margin of each unit that is sold.  

This relationship is derived from the profit equation:  

Profit   =  Revenues - Costs

Where, 

Revenues  =  (selling price * quantity of product) and 

Costs   =  (average variable costs * quantity) + total fixed costs.  

Therefore, 

Profit = (selling price * quantity) - (average variable costs * quantity + total fixed costs). 

Solving for Quantity of product at the breakeven point when Profit equals zero, 

the quantity of product at breakeven is  

Break-even quantity  =                  Total fixed costs                

                                        (selling price - average variable costs)