Cost Volume Profit Analysis

Introduction of Cost Volume Profit Analysis

Cost-Volume-Profit (CVP) analysis is a managerial accounting technique that studies how changes in sales volume, costs, and selling prices affect profit. It is one of the most important tools used by managers for decision-making, profit planning, and controlling operations.

CVP analysis helps managers answer key questions such as:

What products should we produce or sell?
What should be the selling price?
What sales volume is needed to avoid losses?
How will changes in cost or volume affect profit?
What is the most profitable sales mix?

Managers use CVP analysis to estimate future revenues, costs, and profits, and to monitor organizational performance. It also helps assess operational risk by evaluating alternative cost structures.

Elements of CVP Analysis

Cost-Volume-Profit (CVP) analysis examines how cost, sales volume, and profit behave and interact. It is based on the following five key elements:

Selling Price per Unit – The amount charged for each unit sold.
Sales Volume (Level of Activity) – The number of units produced or sold.
Variable Cost per Unit – Costs that change in direct proportion to the level of activity.
Total Fixed Costs – Costs that remain constant regardless of output within the relevant range.
Sales Mix – The relative proportion of different products sold (important when multiple products are involved).

Core Profit Components

The profit of any business is primarily determined by three interrelated components:

Cost
Volume
Profit

These components are strongly interconnected:

Profit depends on sales volume because higher sales typically generate higher revenue.
Selling price is influenced by cost since the price must cover all costs and provide a margin to earn profit.
Cost depends on production volume because:

Variable costs change with the number of units produced.
Fixed costs get distributed over more units as production increases, reducing the cost per unit.

Assumptions of CVP Analysis

CVP analysis is based on the following assumptions:

All costs can be classified as fixed or variable.
Costs and revenues behave in a linear manner within the relevant range.
Only volume of activity influences costs.
Selling price, variable cost per unit, and fixed costs remain constant.
All units produced are sold.
Mixed costs must be separated into fixed and variable components (e.g., High-Low Method, Scatter Plot, Regression).

CVP Income Statement (Marginal Costing Statement)

A CVP Income Statement presents the contribution approach:

Particulars	Amount
Sales	XXX
Less: Variable Cost	XXX
Contribution	XXX
Less: Fixed Cost	XXX
Profit	XXX

Contribution = Selling Price – Variable Cost
Contribution = Fixed Cost + Profit

CVP Analysis – Profit Equation

Profit=(P×Q) - (V×Q)-F

Where:

P = Selling price per unit
V = Variable cost per unit
(P – V) = Contribution per unit
Q = Quantity sold
F = Total fixed cost

The basic CVP formula: px=vx+FC+ Profit

Break Even Analysis

Widely use technique to study to CVP relationship.

Narrow interpretation – A system of determination of that level of activity where total cost is equal to total selling price.
Broader interpretation – That system of analysis which determines probable profit at any level of activity.

Break-Even Point (BEP)

Basic Terms

Contribution or Gross Margin – Excess of selling price over variable cost.

Contribution = Selling Price – Variable Cost
Contribution = Fixed Cost + Profit.

Profit / Volume Ratio (P/V Ratio) - Important for studying the profitability of operation of a business, also establishes a relationship between the contribution and the sale value is also called “Contribution or Sales Ratio”. Important for management to find out which product is more profitable.

P/V ration = Contribution ÷ Sales or (Sales – Variable Cost) ÷ Sales
C/S = (S – V) ÷ S or 1 – Variable Costs ÷ Sales

Break Even Point - The point which breaks the total cost & selling price evenly to show the level of output or Sales at which there shall be neither profit nor loss. At this point, income of business exactly equals its expenditure. At B.E.P total cost = Total Sale. Income = expenditure.

If production > B.E.P => Profit Shall Accrue
If production < B.E.P => Loss suffered by business
Formula

Break even point of output = fixed cost ÷ contribution per unit
Break even point of sales = (fixed cost ÷ contribution per unit) × selling price per unit.
Or (fixed cost ÷ total contribution) x total sales.
Fixed Cost ÷ (1 – Variable cost per unit ÷ Selling price per unit)
Fixed cost ÷ P/V ratio.

Desired profit - At B.E.P the desired profit is zero. In case the volume of output / sales is to be computed for a ‘desired profit’. The amount of ‘desired profit’ should be added to fixed cost in formula

Units for desired profit = (fixed cost + desired profit) ÷ contribution per unit
Sales for a desired profit = (fixed cost + desired profit) ÷ P/V ratio.

Margin of Safety

Total sales minus the sales at break even point

Margin Safety = T.S – B.E.S
Margin of Safety = Total sales – Break even sales
Margin of safety can also be computed according to the following formula
Margin of Safety = Net Profit ÷ P/V Ratio

MOS – Significance

If the margin of safety is large, it is a sign of soundness of the business since even with a substantial reduction in sales, profit shall be earned by the business. If the margin is small, reduction in sales, even to a small extent may affect the profit position very adversely and larger reduction of sales value may even result in losses. This, margin of safety serves as an indicator to the strength of the business.

Formula

Contribution = Selling Price – Variable Cost
Contribution = Fixed Cost + Profit
Break even point of output = Fixed Cost ÷ Contribution per unit
Break even point of sales = (Fixed Cost ÷ Contribution per unit) × Selling Price per unit.
Break even point of sales = (Fixed Cost ÷ Total Contribution) × Total Sales
Break even point of sales = Fixed Cost ÷ ((1 – Variable cost per unit) ÷ Selling price per unit)
Break even point of sales = Fixed Cost ÷ P/V Ratio
Units for a desired profit = (fixed cost + desired profit) ÷ Contribution per unit
Sales for desired profit = (fixed cost + desired profit) ÷ P/V Ratio
Margin of Safety = T.S – B.E.S
Margin of Safety = Total Sales – Break even Sales
Margin of safety can also be computed according to the following formula
Margin of safety = Net profit ÷ P/V ratio
P/V Ratio = Contribution ÷ Sales
P/V Ratio = (Sales – Variable Cost) ÷ Sales
C/S = (S -V) ÷ S
C/S = 1 – (Variable Costs ÷ Sales)

Numerical 1

Following data is given

Total fixed cost = Rs. 12,000 (FC)
Selling Price = Rs. 12 Per unit (SP)
Variable Cost = Rs. 9 per unit (VC)

Calculate B.E.P in term of unit and in term of Rs. And verify the solution

C = S.P – V.C = 12 -9 = 3
B.E.P (unit) = F ÷ C = 12,000 ÷ 3 = 4000 unit
B.E.P (Sales) = (F ÷ C) × Sales = (12,000 ÷ 3) × 12 = 48,000

Marginal Cost

The technique of marginal costing is concerned with “Marginal Cost”. Marginal cost represents the additional cost incurred when producing one more unit of a good or service. It’s the change in total cost when output increases by one unit.

Definition CIMA London – “Marginal cost is the amount at any given volume of output by which aggregate costs are changed, if the volume of output is increased or decreased by one unit.”

If refers to increase or decrease amount of cost on account of increase or decrease of production by single unit.

Example – if a business produces 100 units of a product at a total cost of 5,00,000, and producing an additional unit (101 units) costs 5,05,000. The marginal cost of that extra one unit is 5000 (the difference in total cost). Marginal cost refers to total variable cost because in organization increase of one unit in production will cause an increase in variable cost only.
Example – A factory produces 500 radio per annum. The variable cost per radio is 50. The fixed expenses are 10,000 p.a. the cost sheet of 500 radio will appear as follows:

Variable Cost (500 * 50)	25,000
Fixed Cost	10,000
	35,000

If production increase by one unit i.e. 501 radio per annum. Then cost will be.

Variable Cost (501 * 50)	25,050
Fixed Cost	10,000
	35,050

Marginal cost of one additional unit is 50.
Marginal cost is thus the total variable cost.

Formula

Marginal Cost = Total Variable
Direct Material	XXX
Add: Direct labour	XXX
Add: Direct Expenses	XXX
Add: Variable Overheads	XXX

Contribution

This amount represents the portion of sales revenue that contributes towards covering fixed costs and ultimately, generating profit. Contribution is the difference between selling price and variable cost of sales. It is the money remaining from sales once all variable expenses associated with producing a product are paid. This tells us how much money to pay for fixed expenses and anything left after is used as operating income. if the total contribution does not meet the entire fixed cost, there will be loss. At break even point, where profit is zero contribution = fixed costs. Contribution is also known as “Gross margin”.

Formula -

Sale	XXX
Less: Variable Cost	XXX
Contribution	XXXX
Less: Fixed Cost	XXX
Profit	XXXX

Total Contribution ( C) = Sales (S) – Variable Cost (VC)
Total contribution = fixed cost + profit
Profit = contribution – fixed cost
Sales – variable cost = fixed cost + profit (i.e. marginal cost equation)

Fintaxman

Cost Volume Profit Analysis

Introduction of Cost Volume Profit Analysis