Marginal Costing

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 = Profit

=

Sales – Variable Cost – 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 = (in Units)

Total Fixed Expenses (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

=

(S – V) i.e. 1

F (S – V)

=

F (S – V)

Multiplying both sides by S, Sx1

=

FxS (S – V)

Therefore, the formula for the calculation of break even sales is: FxS (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. Sales

C S

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

S

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

S

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

P/V Ratio

=

F

P/V Ratio

For the calculation of sales to earn a desired or expected profit is Fixed Costs + Profit = P/V Ratio

F+P

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)