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# Cost volume-profit relationship

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• In the cost volume profit analysis the relationship between costs and volume of sales is assumed to be linear. Fixed cost remains fixed irrespective of the volume and variable cost depends directly on the volume, which forms a straight line equation.
• Marginal cost represents the variable cost that depends on the production level of the company. Marginal costs relate to a change in output in the particular circumstances under consideration. It is the increase or decrease in total cost which results from producing or selling additional or fewer units of a product or from a change in the method of production or distribution such as the use of improved machinery addition or exclusion of a product or territory or selection of an additional sales channel. Marginal costing deals in the relationship between variable cost and production level and the impact on profit and loss. It is a technique of ascertaining marginal cost and of the effect on profit of changes in volume of out put by differentiating between fixed and variable costs. This costing technique can be incorporated into the accounting system. Marginal cost can be easily ascertained by adding variable overheads to prime cost.
• Managements use different mathematical tools to analyze how to get the maximum profit. Linear programming method can be used for ascertaining the optimum profit. Linear programming has been used in many situations that require thousands of decision variables and numerous constraints. Main drawback of this model is that very few characteristics of this model are being met in the practical world. Marginal costing does not consider fixed cost. Otherwise a problem may arise for allocating fixed cost for a particular period.
• B.E. analysis is used in both restricted and broad sense. In a broad sense B.E. analysis means an enquiry about inter-dependence among cost, volume of sales and profit at different levels of production. In a restricted sense we can measure the level of production and sales using this technique where the total of fixed and variable costs equal sales. It can be ascertained arithmetically or graphically. Arithmetically, it is called break even analysis and graphically, it is termed as break even chart. B.E. graphical method is applied by showing fixed cost along with total cost (traditional method) or comparing sales with contribution (contribution break even chart). Similarly mathematical B.E. method is applied by using P.V. ratio approach i.e. Fixed Cost/P.V. ratio or by using the following equation- NP=Px – (a +bx) Where, Np= net profit   X= units sold   P= selling price   b= unit variable cost   a= total fixed costs At the point of B.E.P. NP sets at 0
• In the given graph, the sales line and variable line starts from the ‘0’ point indicating variable cost is dependent on the sales. Fixed cost line is parallel to the horizontal axis denoting its fixed nature irrespective of the amount of production. Total cost line has been derived after adding variable cost line with the fixed cost. The point at which the sales line intersects the total cost line represents the B.E. Point. Area between total cost line and sales line is situated to the right side of the B.E.P. This denotes profit. Left side area of B.E.P. denotes loss. Right side area of the B.E.P. denotes the margin of safety i.e. sales over the B.E.P. and the angle between sales line and total cost line is known as angle of incidence.
• In the above graph, both the contribution line and sales line originate from the origin and the intersection point of the fixed cost and sales line is known as B.E.P. Production at this point represents the level of activity at which contribution is equal to fixed cost and there is no profit or loss. If the contribution exceeds the fixed cost line, it represents the profit position and vice versa.

### Transcript

• 1. Cost-Volume-Profit Relationship
• Nature of relationship
•   Linear
• Assumptions under this concept are as follows-
• Costs are classified under fixed and variable costs.
• Selling price remains constant.
• Only one product is manufactured.
• 2.
• 3.
• 4. What is Marginal Cost?
• “ 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” ICMA, London
• “ The ascertainment of marginal costs and of the effect on profit or changes in volume or type of output by differentiating between fixed costs and variable costs” ICMA, London
• 5. Characteristics of Marginal costing
• Difference between product and period cost.
• Considered only those manufacturing costs that are dependant on the production volume.
• Prices are determined by adding the contribution with the marginal cost.
• It is helpful in decision-making.
• 6. llustration
• Arrive at the marginal cost from the following information .
2,90,000 =  Total Cost 2,50,000 +(200 × 200) =   Rs. 2,50,000    = Fixed Cost Rs. 200/- unit.    = Variable Cost    200   = No. of units produced
• 7.
• If we increase the number of units to 201 , the variable costs will be = 201 × 200 = 40,200
Rs. 200/-     =    290200-290000 =  Marginal Cost 290200 =    40200+ 250000 =  Therefore, the total cost
• 8.
• 9.
• 10. Break Even Analysis
• 11. Traditional Break Even Chart
• 12. Contribution Break Even chart
• 13. Mathematical representation of BEP
• Mathematically B.E.P. can be calculated by using the following formulae:-
• BEP(Units) = (Fixed cost) / (Selling price per unit – Variable cost per unit)
• or
• (Fixed cost) / (Contribution per unit)
• or
• (Break-even sales (Rs) / (Selling price per unit)
• BEP (Rs) = (Fixed costs × Sales) / (Sales – Variable cost)
• or
• (Fixed cost × selling price per unit) / (Selling price per unit- variable cost per unit)
• or
• (Fixed cost × selling price per unit) / (contribution per unit)
• or
• Fixed cost/ PV ratio
• 14. Illustration
• Output: 6000 units
• Selling price per unit Rs.40
• Variable cost per unit Rs.30
• Total Fixed cost Rs.25000
• From the above information, calculate the break-even point in units and sales value