Marginal Costing & Absorption Costing

Marginal Costing and Absorption Costing

Learning Objectives

• To understand the meanings of marginal cost and marginal costing
• To distinguish between marginal costing and absorption costing
• To ascertain income under both marginal costing and absorption costing

IntroductionThe costs that vary with a decision should only be included in decision analysis. For many decisions that involve relatively small variations from existing practice and/or are for relatively limited periods of time, fixed costs are not relevant to the decision. This is because either fixed costs tend to be impossible to alter in the short term or managers are reluctant to alter them in the short term.

Marginal costing - definition

Marginal costing distinguishes between fixed costs and variable costs as convention ally classified.

The marginal cost of a product –“ is its variable cost”. This is normally taken to be; direct labour, direct material, direct expenses and the variable part of overheads.

Marginal costing is formally defined as:

‘the accounting system in which variable costs are charged to cost units and the fixed costs of the period are written-off in full against the aggregate contribution. Its special value is in decision making’. (Terminology.)

The term ‘contribution’ mentioned in the formal definition is the term given to the difference between Sales and Marginal cost. Thus

MARGINAL COST =

VARIABLE COST DIRECT LABOUR + DIRECT MATERIAL + DIRECT EXPENSE + VARIABLE OVERHEADS

CONTRIBUTION SALES - MARGINAL COST

The term marginal cost sometimes refers to the marginal cost per unit and sometimes to the total marginal costs of a department or batch or operation. The meaning is usually clear from the context.

Note

Alternative names for marginal costing are the contribution approach and direct costing In this lesson, we will study marginal costing as a technique quite distinct from absorption costing.

Theory of Marginal Costing

The theory of marginal costing as set out in “A report on Marginal Costing” published by CIMA, London is as follows:

In relation to a given volume of output, additional output can normally be obtained at less than proportionate cost because within limits, the aggregate of certain items of cost will tend to remain fixed and only the aggregate of the remainder will tend to rise proportionately with an increase in output. Conversely, a decrease in the volume of output will normally be accompanied by less than proportionate fall in the aggregate cost.

The theory of marginal costing may, therefore, by understood in the following two steps:

1.     If the volume of output increases, the cost per unit in normal circumstances reduces. Conversely, if an output reduces, the cost per unit increases. If a factory produces 1000 units at a total cost of $3,000 and if by increasing the output by one unit the cost goes up to $3,002, the marginal cost of additional output will be $.2.

2.     If an increase in output is more than one, the total increase in cost divided by the total increase in output will give the average marginal cost per unit. If, for example, the output is increased to 1020 units from 1000 units and the total cost to produce these units is $1,045, the average marginal cost per unit is $2.25. It can be described as follows:

Additional cost = Additional units

$ 45 = $2.25    20

The ascertainment of marginal cost is based on the classification and segregation of cost into fixed and variable cost. In order to understand the marginal costing technique, it is essential to understand the meaning of marginal cost.

Marginal cost means the cost of the marginal or last unit produced. It is also defined as the cost of one more or one less unit produced besides existing level of production. In this connection, a unit may mean a single commodity, a dozen, a gross or any other measure of goods.

For example, if a manufacturing firm produces X unit at a cost of $ 300 and X+1 units at a cost of $ 320, the cost of an additional unit will be $ 20 which is marginal cost. Similarly if the production of X-1 units comes down to $ 280, the cost of marginal unit will be $ 20 (300–280).

The marginal cost varies directly with the volume of production and marginal cost per unit remains the same. It consists of prime cost, i.e. cost of direct materials, direct labor and all variable overheads. It does not contain any element of fixed cost which is kept separate under marginal cost technique.

Marginal costing may be defined as the technique of presenting cost data wherein variable costs and fixed costs are shown separately for managerial decision-making. It should be clearly understood that marginal costing is not a method of costing like process costing or job costing. Rather it is simply a method or technique of the analysis of cost information for the guidance of management which tries to find out an effect on profit due to changes in the volume of output.

There are different phrases being used for this technique of costing. In UK, marginal costing is a popular phrase whereas in US, it is known as direct costing and is used in place of marginal costing. Variable costing is another name of marginal costing.

Marginal costing technique has given birth to a very useful concept of contribution where contribution is given by: Sales revenue less variable cost (marginal cost)

Contribution may be defined as the profit before the recovery of fixed costs. Thus, contribution goes toward the recovery of fixed cost and profit, and is equal to fixed cost plus profit (C = F + P).

In case a firm neither makes profit nor suffers loss, contribution will be just equal to fixed cost (C = F). this is known as break even point.

The concept of contribution is very useful in marginal costing. It has a fixed relation with sales. The proportion of contribution to sales is known as P/V ratio which remains the same under given conditions of production and sales.

The principles of marginal costing

The principles of marginal costing are as follows.

a.      For any given period of time, fixed costs will be the same, for any volume of sales and production (provided that the level of activity is within the ‘relevant range’). Therefore, by selling an extra item of product or service the following will happen.

§  Revenue will increase by the sales value of the item sold.

§  Costs will increase by the variable cost per unit.

§  Profit will increase by the amount of contribution earned from the extra item.

b.     Similarly, if the volume of sales falls by one item, the profit will fall by the amount of contribution earned from the item.

c.      Profit measurement should therefore be based on an analysis of total contribution. Since fixed costs relate to a period of time, and do not change with increases or decreases in sales volume, it is misleading to charge units of sale with a share of fixed costs.

d.     When a unit of product is made, the extra costs incurred in its manufacture are the variable production costs. Fixed costs are unaffected, and no extra fixed costs are incurred when output is increased.

Features of Marginal CostingThe main features of marginal costing are as follows:

1.     Cost Classification
The marginal costing technique makes a sharp distinction between variable costs and fixed costs. It is the variable cost on the basis of which production and sales policies are designed by a firm following the marginal costing technique.

2.     Stock/Inventory Valuation
Under marginal costing, inventory/stock for profit measurement is valued at marginal cost. It is in sharp contrast to the total unit cost under absorption costing method.

3.     Marginal Contribution
Marginal costing technique makes use of marginal contribution for marking various decisions. Marginal contribution is the difference between sales and marginal cost. It forms the basis for judging the profitability of different products or departments.

Advantages and Disadvantages of Marginal Costing TechniqueAdvantages

1.     Marginal costing is simple to understand.

2.     By not charging fixed overhead to cost of production, the effect of varying charges per unit is avoided.

3.     It prevents the illogical carry forward in stock valuation of some proportion of current year’s fixed overhead.

4.     The effects of alternative sales or production policies can be more readily available and assessed, and decisions taken would yield the maximum return to business.

5.     It eliminates large balances left in overhead control accounts which indicate the difficulty of ascertaining an accurate overhead recovery rate.

6.     Practical cost control is greatly facilitated. By avoiding arbitrary allocation of fixed overhead, efforts can be concentrated on maintaining a uniform and consistent marginal cost. It is useful to various levels of management.

7.     It helps in short-term profit planning by breakeven and profitability analysis, both in terms of quantity and graphs. Comparative profitability and performance between two or more products and divisions can easily be assessed and brought to the notice of management for decision making.

Disadvantages

1.     The separation of costs into fixed and variable is difficult and sometimes gives misleading results.

2.     Normal costing systems also apply overhead under normal operating volume and this shows that no advantage is gained by marginal costing.

3.     Under marginal costing, stocks and work in progress are understated. The exclusion of fixed costs from inventories affect profit, and true and fair view of financial affairs of an organization may not be clearly transparent.

4.     Volume variance in standard costing also discloses the effect of fluctuating output on fixed overhead. Marginal cost data becomes unrealistic in case of highly fluctuating levels of production, e.g., in case of seasonal factories.

5.     Application of fixed overhead depends on estimates and not on the actuals and as such there may be under or over absorption of the same.

6.     Control affected by means of budgetary control is also accepted by many. In order to know the net profit, we should not be satisfied with contribution and hence, fixed overhead is also a valuable item. A system which ignores fixed costs is less effective since a major portion of fixed cost is not taken care of under marginal costing.

7.     In practice, sales price, fixed cost and variable cost per unit may vary. Thus, the assumptions underlying the theory of marginal costing sometimes becomes unrealistic. For long term profit planning, absorption costing is the only answer.

Presentation of Cost Data under Marginal Costing and Absorption CostingMarginal costing is not a method of costing but a technique of presentation of sales and cost data with a view to guide management in decision-making.

The traditional technique popularly known as total cost or absorption costing technique does not make any difference between variable and fixed cost in the calculation of profits. But marginal cost statement very clearly indicates this difference in arriving at the net operational results of a firm.

Following presentation of two Performa shows the difference between the presentation of information according to absorption and marginal costing techniques:

MARGINAL COSTING PRO-FORMA

	£	£
Sales Revenue		xxxxx
Less Marginal Cost of Sales
Opening Stock (Valued @ marginal cost)	xxxx
Add Production Cost (Valued @ marginal cost)	xxxx
Total Production Cost	xxxx
Less Closing Stock (Valued @ marginal cost)	(xxx)
Marginal Cost of Production	xxxx
Add Selling, Admin & Distribution Cost	xxxx
Marginal Cost of Sales		(xxxx)
Contribution		xxxxx
Less Fixed Cost		(xxxx)
Marginal Costing Profit		xxxxx

ABSORPTION COSTING PRO-FORMA

	£	£
Sales Revenue		xxxxx
Less Absorption Cost of Sales
Opening Stock (Valued @ absorption cost)	xxxx
Add Production Cost (Valued @ absorption cost)	xxxx
Total Production Cost	xxxx
Less Closing Stock (Valued @ absorption cost)	(xxx)
Absorption Cost of Production	xxxx
Add Selling, Admin & Distribution Cost	xxxx
Absorption Cost of Sales		(xxxx)
Un-Adjusted Profit		xxxxx
Fixed Production O/H absorbed	xxxx
Fixed Production O/H incurred	(xxxx)
(Under)/Over Absorption		xxxxx
Adjusted Profit		xxxxx

Reconciliation Statement for Marginal Costing and Absorption Costing Profit

	$
Marginal Costing Profit	xx
ADD (Closing stock – opening Stock) x OAR	xx
= Absorption Costing Profit	xx

Where OAR( overhead absorption rate) =

Budgeted fixed production overhead Budgeted levels of activities

Marginal Costing versus Absorption Costing

After knowing the two techniques of marginal costing and absorption costing, we have seen that the net profits are not the same because of the following reasons:1. Over and Under Absorbed Overheads

In absorption costing, fixed overheads can never be absorbed exactly because of difficulty in forecasting costs and volume of output. If these balances of under or over absorbed/recovery are not written off to costing profit and loss account, the actual amount incurred is not shown in it. In marginal costing, however, the actual fixed overhead incurred is wholly charged against contribution and hence, there will be some difference in net profits.

2. Difference in Stock Valuation

In marginal costing, work in progress and finished stocks are valued at marginal cost, but in absorption costing, they are valued at total production cost. Hence, profit will differ as different amounts of fixed overheads are considered in two accounts.

The profit difference due to difference in stock valuation is summarized as follows:

a.      When there is no opening and closing stocks, there will be no difference in profit.

b.     When opening and closing stocks are same, there will be no difference in profit, provided the fixed cost element in opening and closing stocks are of the same amount.

c.      When closing stock is more than opening stock, the profit under absorption costing will be higher as comparatively a greater portion of fixed cost is included in closing stock and carried over to next period.

d.     When closing stock is less than opening stock, the profit under absorption costing will be less as comparatively a higher amount of fixed cost contained in opening stock is debited during the current period.

The features which distinguish marginal costing from absorption costing are as follows.

a.      In absorption costing, items of stock are costed to include a ‘fair share’ of fixed production overhead, whereas in marginal costing, stocks are valued at variable production cost only. The value of closing stock will be higher in absorption costing than in marginal costing.

b.     As a consequence of carrying forward an element of fixed production overheads in closing stock values, the cost of sales used to determine profit in absorption costing will:

                               i.            include some fixed production overhead costs incurred in a previous period but carried forward into opening stock values of the current period;

                             ii.            exclude some fixed production overhead costs incurred in the current period by including them in closing stock values.

In contrast marginal costing charges the actual fixed costs of a period in full into the profit and loss account of the period. (Marginal costing is therefore sometimes known as period costing.)

c.      In absorption costing, ‘actual’ fully absorbed unit costs are reduced by producing in greater quantities, whereas in marginal costing, unit variable costs are unaffected by the volume of production (that is, provided that variable costs per unit remain unaltered at the changed level of production activity). Profit per unit in any period can be affected by the actual volume of production in absorption costing; this is not the case in marginal costing.

d.     In marginal costing, the identification of variable costs and of contribution enables management to use cost information more easily for decision-making purposes (such as in budget decision making). It is easy to decide by how much contribution (and therefore profit) will be affected by changes in sales volume. (Profit would be unaffected by changes in production volume).In absorption costing, however, the effect on profit in a period of changes in both:

                               i.            production volume; and

                             ii.            sales volume;
is not easily seen, because behaviour is not analysed and incremental costs are not used in the calculation of actual profit.

Limitations of Absorption CostingThe following are the criticisms against absorption costing:

1.     You might have observed that in absorption costing, a portion of fixed cost is carried over to the subsequent accounting period as part of closing stock. This is an unsound practice because costs pertaining to a period should not be allowed to be vitiated by the inclusion of costs pertaining to the previous period and vice versa.

2.     Further, absorption costing is dependent on the levels of output which may vary from period to period, and consequently cost per unit changes due to the existence of fixed overhead. Unless fixed overhead rate is based on normal capacity, such changed costs are not helpful for the purposes of comparison and control.

The cost to produce an extra unit is variable production cost. It is realistic to the value of closing stock items as this is a directly attributable cost. The size of total contribution varies directly with sales volume at a constant rate per unit. For the decision-making purpose of management, better information about expected profit is obtained from the use of variable costs and contribution approach in the accounting system.Summary

Marginal cost is the cost management technique for the analysis of cost and revenue information and for the guidance of management. The presentation of information through marginal costing statement is easily understood by all mangers, even those who do not have preliminary knowledge and implications of the subjects of cost and management accounting.

Absorption costing and marginal costing are two different techniques of cost accounting. Absorption costing is widely used for cost control purpose whereas marginal costing is used for managerial decision-making and control.

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Chapter 3 – Breakeven Analysis

Learning Objectives

• To describe as to how the concepts of fixed and variable costs are used in C-V-P analysis
• To segregate semi-variable expenses in C-V-P analysis
• To identify the limiting assumptions of C-V-P analysis
• To work out the breakeven analysis, contribution analysis and margin of safety
• To understand how to draw a breakeven chart
• To compute breakeven point

IntroductionIn this lesson, we will discuss in detail the highlights associated with cost function and cost relations with the production and distribution system of an economic entity.

To assist planning and decision making, management should know not only the budgeted profit, but also:

• the output and sales level at which there would neither profit nor loss (break-even point)
• the amount by which actual sales can fall below the budgeted sales level, without a loss being incurred (the margin of safety)

MARGINAL COSTS, CONTRIBUTION AND PROFITA marginal cost is another term for a variable cost. The term ‘marginal cost’ is usually applied to the variable cost of a unit of product or service, whereas the term ‘variable cost’ is more commonly applied to resource costs, such as the cost of materials and labour hours.

Marginal costing is a form of management accounting based on the distinction between:

a.      the marginal costs of making selling goods or services, and

b.     fixed costs, which should be the same for a given period of time, regardless of the level of activity in the period.

Suppose that a firm makes and sells a single product that has a marginal cost of £5 per unit and that sells for £9 per unit. For every additional unit of the product that is made and sold, the firm will incur an extra cost of £5 and receive income of £9. The net gain will be £4 per additional unit. This net gain per unit, the difference between the sales price per unit and the marginal cost per unit, is called contribution.

Contribution is a term meaning ‘making a contribution towards covering fixed costs and making a profit’. Before a firm can make a profit in any period, it must first of all cover its fixed costs. Breakeven is where total sales revenue for a period just covers fixed costs, leaving neither profit nor loss. For every unit sold in excess of the breakeven point, profit will increase by the amount of the contribution per unit.

C-V-P analysis is broadly known as cost-volume-profit analysis. Specifically speaking, we all are concerned with in-depth analysis and application of CVP in practical world of industry management.

Cost-Volume-Profit (C-V-P) Relationship

We have observed that in marginal costing, marginal cost varies directly with the volume of production or output. On the other hand, fixed cost remains unaltered regardless of the volume of output within the scale of production already fixed by management. In case if cost behavior is related to sales income, it shows cost-volume-profit relationship. In net effect, if volume is changed, variable cost varies as per the change in volume. In this case, selling price remains fixed, fixed remains fixed and then there is a change in profit.

Being a manager, you constantly strive to relate these elements in order to achieve the maximum profit. Apart from profit projection, the concept of Cost-Volume-Profit (CVP) is relevant to virtually all decision-making areas, particularly in the short run.

The relationship among cost, revenue and profit at different levels may be expressed in graphs such as breakeven charts, profit volume graphs, or in various statement forms.

Profit depends on a large number of factors, most important of which are the cost of manufacturing and the volume of sales. Both these factors are interdependent. Volume of sales depends upon the volume of production and market forces which in turn is related to costs. Management has no control over market. In order to achieve certain level of profitability, it has to exercise control and management of costs, mainly variable cost. This is because fixed cost is a non-controllable cost. But then, cost is based on the following factors:

• Volume of production
• Product mix
• Internal efficiency and the productivity of the factors of production
• Methods of production and technology
• Size of batches
• Size of plant

Thus, one can say that cost-volume-profit analysis furnishes the complete picture of the profit structure. This enables management to distinguish among the effect of sales, fluctuations in volume and the results of changes in price of product/services.In other words, CVP is a management accounting tool that expresses relationship among sale volume, cost and profit. CVP can be used in the form of a graph or an equation. Cost-volume- profit analysis can answer a number of analytical questions. Some of the questions are as follows:

1.     What is the breakeven revenue of an organization?

2.     How much revenue does an organization need to achieve a budgeted profit?

3.     What level of price change affects the achievement of budgeted profit?

4.     What is the effect of cost changes on the profitability of an operation?

Cost-volume-profit analysis can also answer many other “what if” type of questions. Cost-volume-profit analysis is one of the important techniques of cost and management accounting. Although it is a simple yet a powerful tool for planning of profits and therefore, of commercial operations. It provides an answer to “what if” theme by telling the volume required to produce.Following are the three approaches to a CVP analysis:

• Cost and revenue equations
• Contribution margin
• Profit graph

Objectives of Cost-Volume-Profit Analysis

1.     In order to forecast profits accurately, it is essential to ascertain the relationship between cost and profit on one hand and volume on the other.

2.     Cost-volume-profit analysis is helpful in setting up flexible budget which indicates cost at various levels of activities.

3.     Cost-volume-profit analysis assist in evaluating performance for the purpose of control.

4.     Such analysis may assist management in formulating pricing policies by projecting the effect of different price structures on cost and profit.

Assumptions and TerminologyFollowing are the assumptions on which the theory of CVP is based:

1.     The changes in the level of various revenue and costs arise only because of the changes in the number of product (or service) units produced and sold, e.g., the number of television sets produced and sold by Sigma Corporation. The number of output (units) to be sold is the only revenue and cost driver. Just as a cost driver is any factor that affects costs, a revenue driver is any factor that affects revenue.

2.     Total costs can be divided into a fixed component and a component that is variable with respect to the level of output. Variable costs include the following:

o    Direct materials

o    Direct labor

o    Direct chargeable expenses

Variable overheads include the following:

o    Variable part of factory overheads

o    Administration overheads

o    Selling and distribution overheads

3.     There is linear relationship between revenue and cost.

4.     When put in a graph, the behavior of total revenue and cost is linear (straight line), i.e. Y = mx + C holds good which is the equation of a straight line.

5.     The unit selling price, unit variable costs and fixed costs are constant.

6.     The theory of CVP is based upon the production of a single product. However, of late, management accountants are functioning to give a theoretical and a practical approach to multi-product CVP analysis.

7.     The analysis either covers a single product or assumes that the sales mix sold in case of multiple products will remain constant as the level of total units sold changes.

8.     All revenue and cost can be added and compared without taking into account the time value of money.

9.     The theory of CVP is based on the technology that remains constant.

10. The theory of price elasticity is not taken into consideration.

Many companies, and divisions and sub-divisions of companies in industries such as airlines, automobiles, chemicals, plastics and semiconductors have found the simple CVP relationships to be helpful in the following areas:

• Strategic and long-range planning decisions
• Decisions about product features and pricing

In real world, simple assumptions described above may not hold good. The theory of CVP can be tailored for individual industries depending upon the nature and peculiarities of the same.For example, predicting total revenue and total cost may require multiple revenue drivers and multiple cost drivers. Some of the multiple revenue drivers are as follows:

• Number of output units
• Number of customer visits made for sales
• Number of advertisements placed

Some of the multiple cost drivers are as follows:

• Number of units produced
• Number of batches in which units are produced

Managers and management accountants, however, should always assess whether the simplified CVP relationships generate sufficiently accurate information for predictions of how total revenue and total cost would behave. However, one may come across different complex situations to which the theory of CVP would rightly be applicable in order to help managers to take appropriate decisions under different situations.Limitations of Cost-Volume Profit Analysis

The CVP analysis is generally made under certain limitations and with certain assumed conditions, some of which may not occur in practice. Following are the main limitations and assumptions in the cost-volume-profit analysis:

1.     It is assumed that the production facilities anticipated for the purpose of cost-volume-profit analysis do not undergo any change. Such analysis gives misleading results if expansion or reduction of capacity takes place.

2.     In case where a variety of products with varying margins of profit are manufactured, it is difficult to forecast with reasonable accuracy the volume of sales mix which would optimize the profit.

3.     The analysis will be correct only if input price and selling price remain fairly constant which in reality is difficulty to find. Thus, if a cost reduction program is undertaken or selling price is changed, the relationship between cost and profit will not be accurately depicted.

4.     In cost-volume-profit analysis, it is assumed that variable costs are perfectly and completely variable at all levels of activity and fixed cost remains constant throughout the range of volume being considered. However, such situations may not arise in practical situations.

5.     It is assumed that the changes in opening and closing inventories are not significant, though sometimes they may be significant.

6.     Inventories are valued at variable cost and fixed cost is treated as period cost. Therefore, closing stock carried over to the next financial year does not contain any component of fixed cost. Inventory should be valued at full cost in reality.

Sensitivity Analysis or What If Analysis and UncertaintySensitivity analysis is relatively a new term in management accounting. It is a “what if” technique that managers use to examine how a result will change if the original predicted data are not achieved or if an underlying assumption changes.

In the context of CVP analysis, sensitivity analysis answers the following questions:

a.      What will be the operating income if units sold decrease by 15% from original prediction?

b.     What will be the operating income if variable cost per unit increases by 20%?

The sensitivity of operating income to various possible outcomes broadens the perspective of management regarding what might actually occur before making cost commitments.A spreadsheet can be used to conduct CVP-based sensitivity analysis in a systematic and efficient way. With the help of a spreadsheet, this analysis can be easily conducted to examine the effect and interaction of changes in selling prices, variable cost per unit, fixed costs and target operating incomes.

Example

Following is the spreadsheet of ABC Ltd.,

Statement showing CVP Analysis for Dolphy Software Ltd.

		Revenue required at $. 200 Selling Price per unit to earn Operating Income of
Fixed cost	Variable cost per unit	0	1,000	1,500	2,000
2,000	100	4,000	6,000	7,000	8,000
	120	5,000	7,500	8,750	10,000
	140	6,667	10,000	11,667	13,333
2,500	100	5,000	7,000	8,000	9,000
	120	6,250	8,750	10,000	11,250
	140	8,333	11,667	13,333	15,000
3,000	100	6,000	8,000	9,000	10,000
	120	7,500	10,000	11,250	12,500
	140	10,000	13,333	15,000	16,667

From the above example, one can immediately see the revenue that needs to be generated to reach a particular operating income level, given alternative levels of fixed costs and variable costs per unit. For example, revenue of $. 6,000 (30 units @ $. 200 each) is required to earn an operating income of $. 1,000 if fixed cost is $. 2,000 and variable cost per unit is $. 100. You can also use exhibit 3-4 to assess what revenue the company needs to breakeven (earn operating income of Re. 0) if, for example, one of the following changes takes place:

• The booth rental at the ABC convention raises to $. 3,000 (thus increasing fixed cost to $. 3,000)
• The software suppliers raise their price to $. 140 per unit (thus increasing variable costs to $. 140)

An aspect of sensitivity analysis is the margin of safety which is the amount of budgeted revenue over and above breakeven revenue. The margin of safety is sales quantity minus breakeven quantity. It is expressed in units. The margin of safety answers the “what if” questions, e.g., if budgeted revenue are above breakeven and start dropping, how far can they fall below budget before the breakeven point is reached? Such a fall could be due to competitor’s better product, poorly executed marketing programs and so on.Assume you have fixed cost of $. 2,000, selling price of $. 200 and variable cost per unit of $. 120. For 40 units sold, the budgeted point from this set of assumptions is 25 units ($. 2,000 ÷ $. 80) or $. 5,000 ($. 200 x 25). Hence, the margin of safety is $. 3,000 ($. 8,000 – 5,000) or 15 (40 –25) units.

Sensitivity analysis is an approach to recognizing uncertainty, i.e. the possibility that an actual amount will deviate from an expected amount.

Marginal Cost Equations and Breakeven Analysis

From the marginal cost statements, one might have observed the following:

Sales – Marginal cost = Contribution ......(1)Fixed cost + Profit = Contribution ......(2)

By combining these two equations, we get the fundamental marginal cost equation as follows:

Sales – Marginal cost = Fixed cost + Profit ......(3)

This fundamental marginal cost equation plays a vital role in profit projection and has a wider application in managerial decision-making problems.The sales and marginal costs vary directly with the number of units sold or produced. So, the difference between sales and marginal cost, i.e. contribution, will bear a relation to sales and the ratio of contribution to sales remains constant at all levels. This is profit volume or P/V ratio. Thus,

P/V Ratio (or C/S Ratio) =	Contribution (c)	......(4)
	Sales (s)

It is expressed in terms of percentage, i.e. P/V ratio is equal to (C/S) x 100.

Or, Contribution = Sales x P/V ratio ......(5)

Or, Sales =	Contribution	......(6)
	P/V ratio

The above-mentioned marginal cost equations can be applied to the following heads:1. Contribution

Contribution is the difference between sales and marginal or variable costs. It contributes toward fixed cost and profit. The concept of contribution helps in deciding breakeven point, profitability of products, departments etc. to perform the following activities:

• Selecting product mix or sales mix for profit maximization
• Fixing selling prices under different circumstances such as trade depression, export sales, price discrimination etc.

2. Profit Volume Ratio (P/V Ratio), its Improvement and ApplicationThe ratio of contribution to sales is P/V ratio or C/S ratio. It is the contribution per rupee of sales and since the fixed cost remains constant in short term period, P/V ratio will also measure the rate of change of profit due to change in volume of sales. The P/V ratio may be expressed as follows:

P/V ratio =	Sales – Marginal cost of sales	=	Contribution	=	Changes in contribution	=	Change in profit
	Sales		Sales		Changes in sales		Change in sales

A fundamental property of marginal costing system is that P/V ratio remains constant at different levels of activity.

A change in fixed cost does not affect P/V ratio. The concept of P/V ratio helps in determining the following:

• Breakeven point
• Profit at any volume of sales
• Sales volume required to earn a desired quantum of profit
• Profitability of products
• Processes or departments

The contribution can be increased by increasing the sales price or by reduction of variable costs. Thus, P/V ratio can be improved by the following:

• Increasing selling price
• Reducing marginal costs by effectively utilizing men, machines, materials and other services
• Selling more profitable products, thereby increasing the overall P/V ratio

3. Breakeven PointBreakeven point is the volume of sales or production where there is neither profit nor loss. Thus, we can say that:

Contribution = Fixed cost

Now, breakeven point can be easily calculated with the help of fundamental marginal cost equation, P/V ratio or contribution per unit.a. Using Marginal Costing Equation

S (sales) – V (variable cost) = F (fixed cost) + P (profit) At BEP P = 0, BEP S – V = F

By multiplying both the sides by S and rearranging them, one gets the following equation:

S BEP = F.S/S-V

b. Using P/V Ratio

Sales S BEP =	Contribution at BEP	=	Fixed cost
	P/ V ratio		P/ V ratio

Thus, if sales is $. 2,000, marginal cost $. 1,200 and fixed cost $. 400, then:

Breakeven point =		400 x 2000		= $. 1000
		2000 - 1200
Similarly,	P/V ratio		= 2000 – 1200 = 0.4 or 40%
	800

So, breakeven sales = $. 400 / .4 = $. 1000c. Using Contribution per unit

Breakeven point =	Fixed cost	= 100 units or $. 1000
	Contribution per unit

4. Margin of Safety (MOS)

Every enterprise tries to know how much above they are from the breakeven point. This is technically called margin of safety. It is calculated as the difference between sales or production units at the selected activity and the breakeven sales or production.

Margin of safety is the difference between the total sales (actual or projected) and the breakeven sales. It may be expressed in monetary terms (value) or as a number of units (volume). It can be expressed as profit / P/V ratio. A large margin of safety indicates the soundness and financial strength of business.

Margin of safety can be improved by lowering fixed and variable costs, increasing volume of sales or selling price and changing product mix, so as to improve contribution and overall P/V ratio.

Margin of safety = Sales at selected activity – Sales at BEP =	Profit at selected activity
	P/V ratio

Margin of safety is also presented in ratio or percentage as follows:	Margin of safety (sales) x 100 %
	Sales at selected activity

The size of margin of safety is an extremely valuable guide to the strength of a business. If it is large, there can be substantial falling of sales and yet a profit can be made. On the other hand, if margin is small, any loss of sales may be a serious matter. If margin of safety is unsatisfactory, possible steps to rectify the causes of mismanagement of commercial activities as listed below can be undertaken.

a.      Increasing the selling price-- It may be possible for a company to have higher margin of safety in order to strengthen the financial health of the business. It should be able to influence price, provided the demand is elastic. Otherwise, the same quantity will not be sold.

b.     Reducing fixed costs

c.      Reducing variable costs

d.     Substitution of existing product(s) by more profitable lines e. Increase in the volume of output

e.      Modernization of production facilities and the introduction of the most cost effective technology

Problem 1A company earned a profit of $. 30,000 during the year 2000-01. Marginal cost and selling price of a product are $. 8 and $. 10 per unit respectively. Find out the margin of safety.

Solution

Margin of safety =	Profit
	P/V ratio

P/V ratio =	Contribution x 100
	Sales

Problem 2

A company producing a single article sells it at $. 10 each. The marginal cost of production is $. 6 each and fixed cost is $. 400 per annum. You are required to calculate the following:

• Profits for annual sales of 1 unit, 50 units, 100 units and 400 units
• P/V ratio
• Breakeven sales
• Sales to earn a profit of $. 500
• Profit at sales of $. 3,000
• New breakeven point if sales price is reduced by 10%
• Margin of safety at sales of 400 units

Solution Marginal Cost Statement

Particulars	Amount	Amount	Amount	Amount
Units produced	1	50	100	400
Sales (units * 10)	10	500	1000	4000
Variable cost	6	300	600	2400
Contribution (sales- VC)	4	200	400	1600
Fixed cost	400	400	400	400
Profit (Contribution – FC)	-396	-200	0	1200

Profit Volume Ratio (PVR) = Contribution/Sales * 100 = 0.4 or 40%

Breakeven sales ($.) = Fixed cost / PVR = 400/ 40 * 100 = $. 1,000

Sales at BEP = Contribution at BEP/ PVR = 100 units

Sales at profit $. 500

Contribution at profit $. 500 = Fixed cost + Profit = $. 900

Sales = Contribution/PVR = 900/.4 = $. 2,250 (or 225 units)

Profit at sales $. 3,000

Contribution at sale $. 3,000 = Sales x P/V ratio = 3000 x 0.4 = $. 1,200

Profit = Contribution – Fixed cost = $. 1200 – $. 400 = $. 800

New P/V ratio = $. 9 – $. 6/$. 9 = 1/3

Sales at BEP = Fixed cost/PV ratio =	$. 400	= $. 1,200
	1/3

Margin of safety (at 400 units) = 4000-1000/4000*100 = 75 %

(Actual sales – BEP sales/Actual sales * 100)

Breakeven Analysis-- Graphical Presentation

Apart from marginal cost equations, it is found that breakeven chart and profit graphs are useful graphic presentations of this cost-volume-profit relationship.

Breakeven chart is a device which shows the relationship between sales volume, marginal costs and fixed costs, and profit or loss at different levels of activity. Such a chart also shows the effect of change of one factor on other factors and exhibits the rate of profit and margin of safety at different levels. A breakeven chart contains, inter alia, total sales line, total cost line and the point of intersection called breakeven point. It is popularly called breakeven chart because it shows clearly breakeven point (a point where there is no profit or no loss).

Profit graph is a development of simple breakeven chart and shows clearly profit at different volumes of sales.

Construction of a Breakeven Chart

The construction of a breakeven chart involves the drawing of fixed cost line, total cost line and sales line as follows:

1.     Select a scale for production on horizontal axis and a scale for costs and sales on vertical axis.

2.     Plot fixed cost on vertical axis and draw fixed cost line passing through this point parallel to horizontal axis.

3.     Plot variable costs for some activity levels starting from the fixed cost line and join these points. This will give total cost line. Alternatively, obtain total cost at different levels, plot the points starting from horizontal axis and draw total cost line.

4.     Plot the maximum or any other sales volume and draw sales line by joining zero and the point so obtained.

Uses of Breakeven ChartA breakeven chart can be used to show the effect of changes in any of the following profit factors:

• Volume of sales
• Variable expenses
• Fixed expenses
• Selling price

ProblemA company produces a single article and sells it at $. 10 each. The marginal cost of production is $. 6 each and total fixed cost of the concern is $. 400 per annum.

Construct a breakeven chart and show the following:

• Breakeven point
• Margin of safety at sale of $. 1,500
• Angle of incidence
• Increase in selling price if breakeven point is reduced to 80 units

SolutionA breakeven chart can be prepared by obtaining the information at these levels:

Output units	40	80	120	200
Sales	$.	$.	$.	$.
	400	800	1,200	2,000
Fixed cost	400	400	400	400
Variable cost	240	480	400	720
Total cost	640	880	1,120	1,600

Fixed cost line, total cost line and sales line are drawn one after another following the usual procedure described herein:

This chart clearly shows the breakeven point, margin of safety and angle of incidence.

a.      Breakeven point-- Breakeven point is the point at which sales line and total cost line intersect. Here, B is breakeven point equivalent to sale of $. 1,000 or 100 units.

b.     Margin of safety-- Margin of safety is the difference between sales or units of production and breakeven point. Thus, margin of safety at M is sales of ($. 1,500 - $. 1,000), i.e. $. 500 or 50 units.

c.      Angle of incidence-- Angle of incidence is the angle formed by sales line and total cost line at breakeven point. A large angle of incidence shows a high rate of profit being made. It should be noted that the angle of incidence is universally denoted by data. Larger the angle, higher the profitability indicated by the angel of incidence.

d.     At 80 units, total cost (from the table) = $. 880. Hence, selling price for breakeven at 80 units = $. 880/80 = $. 11 per unit. Increase in selling price is Re. 1 or 10% over the original selling price of $. 10 per unit.

Limitations and Uses of Breakeven ChartsA simple breakeven chart gives correct result as long as variable cost per unit, total fixed cost and sales price remain constant. In practice, all these facto$ may change and the original breakeven chart may give misleading results.

But then, if a company sells different products having different percentages of profit to turnover, the original combined breakeven chart fails to give a clear picture when the sales mix changes. In this case, it may be necessary to draw up a breakeven chart for each product or a group of products. A breakeven chart does not take into account capital employed which is a very important factor to measure the overall efficiency of business. Fixed costs may increase at some level whereas variable costs may sometimes start to decline. For example, with the help of quantity discount on materials purchased, the sales price may be reduced to sell the additional units produced etc. These changes may result in more than one breakeven point, or may indicate higher profit at lower volumes or lower profit at still higher levels of sales.

Nevertheless, a breakeven chart is used by management as an efficient tool in marginal costing, i.e. in forecasting, decision-making, long term profit planning and maintaining profitability. The margin of safety shows the soundness of business whereas the fixed cost line shows the degree of mechanization. The angle of incidence is an indicator of plant efficiency and profitability of the product or division under consideration. It also helps a monopolist to make price discrimination for maximization of profit.

Multiple Product Situations

In real life, most of the firms turn out many products. Here also, there is no problem with regard to the calculation of BE point. However, the assumption has to be made that the sales mix remains constant. This is defined as the relative proportion of each product’s sale to total sales. It could be expressed as a ratio such as 2:4:6, or as a percentage as 20%, 40%, 60%.

The calculation of breakeven point in a multi-product firm follows the same pattern as in a single product firm. While the numerator will be the same fixed costs, the denominator now will be weighted average contribution margin. The modified formula is as follows:

Breakeven point (in units) =	Fixed costs
	Weighted average contribution margin per unit

One should always remember that weights are assigned in proportion to the relative sales of all products. Here, it will be the contribution margin of each product multiplied by its quantity.

Breakeven Point in Sales Revenue

Here also, numerator is the same fixed costs. The denominator now will be weighted average contribution margin ratio which is also called weighted average P/V ratio. The modified formula is as follows:

B.E. point (in revenue) =	Fixed cost
	Weighted average P/V ratio

Problem Ahmedabad Company Ltd. manufactures and sells four types of products under the brand name Ambience, Luxury, Comfort and Lavish. The sales mix in value comprises the following:

Brand name                      Percentage

Ambience                     33 1/3

Luxury                              41 2/3

Comfort                             16 2/3

Lavish                              8 1/3

                                    ------

                                     100

         

The total budgeted sales (100%) are $. 6,00,000 per month.The operating costs are:

Ambience     60% of selling price Luxury

Luxury       68% of selling price Comfort

Comfort      80% of selling price Lavish

Lavish       40% of selling price

The fixed costs are $. 1,59,000 per month.

a.      Calculate the breakeven point for the products on an overall basis.

b.     It has been proposed to change the sales mix as follows, with the sales per month remaining at $. 6,00,000:

Brand Name    Percentage

Ambience             25

Luxury               40

Comfort              30

Lavish              05

                    ---

                    100

    

Assuming that this proposal is implemented, calculate the new breakeven point.Solution

a.      Computation of the Breakeven Point on Overall Basis

b.     Computation of the New Breakeven Point

Profit GraphProfit graph is an improvement of a simple breakeven chart. It clearly exhibits the relationship of profit to volume of sales. The construction of a profit graph is relatively easy and the procedure involves the following:

1.     Selecting a scale for the sales on horizontal axis and another scale for profit and fixed costs or loss on vertical axis. The area above horizontal axis is called profit area and the one below it is called loss area.

2.     Plotting the profits of corresponding sales and joining them. This is profit line.

Summary

1.     Fixed and variable cost classification helps in CVP analysis. Marginal cost is also useful for such analysis.

2.     Breakeven point is the incidental study of CVP. It is the point of no profit and no loss. At this specific level of operation, it covers total costs, including variable and fixed overheads.

3.     Breakeven chart is the graphical representation of cost structure of business.

4.     Profit/Volume (P/V) ratio shows the relationship between contribution and value/volume of sales. It is usually expressed as terms of percentage and is a valuable tool for the profitability of business.

5.     Margin of safety is the difference between sales or units of production and breakeven point. The size of margin of safety is an extremely valuable guide to the financial strength of a business.