Cost Volume Profit Analysis Paper Presentation

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COST-VOLUME-PROFIT

ANALYSIS

Managerial Accountancy CIA II Cost-Volume-Profit Analysis.

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A

PAPER PRESENTATION

ON

“COST-VOLUME-PROFIT

ANALYSIS”

UNDER THE GUIDANCE OF

PROF. RAMKESH GUPTA

SUBMITTED BY:

AMIT PRAKASH 1021204

APOORV JHUDELEY 1021207

HEMANTH V. 1021218

DELIA REYNAL DSOUZA 1021240

JAYA LAKHANI 1021241

KAVITHA PRABHATH RAMAN 1021242

STEFFI LEE JAMES 1021254


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CONTENTS

Particulars Page No.

Introduction 3

Cost-Volume-Profit Analysis 5

Assumptions of Cost-Volume-Profit Analysis. 7

Concepts Used 15

Break-Even Point Analysis 18

Incremental Analysis 20

Margin Of Safety (MOS) 21

Income statement Approach 22

Mathematical Calculations 24

Application 26

Limitations 27

Bibliography 28


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INTRODUCTION

COST-VOLUME-PROFIT ANALYSIS

A cost-volume-profit (CVP) analysis is a systematic method of examining the effects of

changes in an organization’s volume of activity on its costs, revenue and profit. It is useful

for the management in knowing how profit is influenced by sales volume, sales price,

variable expenses and fixed expenses.

Break-even point

Break-even point is the level of sales at which profit is zero. According to this definition, at break-even point sales are equal to fixed cost plus variable cost. This concept is further explained by the following equation:

[Break even sales = fixed cost + variable cost]

The break-even point can be calculated using either the equation method or contribution method. These two methods are equivalent.

Contribution

Contribution margin is a measure of operating leverage: the higher the contribution margin is (the lower variable costs are as a percentage of total costs), faster the profits increase with sales. In the linear CVP analysis Model, contribution margin is a fixed quantity, and does not change with Sales. Contribution = Sales - Variable Cost

Margin of Safety

The margin of safety is a tool to help management understand how far sales could

change before the company would have a net loss. It is computed by subtracting break-

even sales from budgeted or forecasted sales. To state the margin of safety as a percent,

the difference is divided by budgeted sales. Margin of safety is the difference between the

intrinsic value of a stock and its market price.

In Breakeven analysis margin of safety is how much output or sales level can fall before a

business reaches its breakeven point.

Applications

1. CVP simplifies the computation of breakeven point in break-even analysis.

2. Allows simple computation of Target Income Sales.

3. It simplifies analysis of short run trade-offs in operational decisions.


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Limitations

a. Profit Maximization--cost-volume-profit relationship is not a profit maximization technique

because it does not place any limitations upon the number of units a business can produce and sell.

b. Multiple Products--cost-volume-profit relationship requires simplifying assumptions to apply

it to a business that manufactures more than one product


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COST-VOLUME-PROFIT ANALYSIS

A cost-volume-profit (CVP) analysis is a systematic method of examining the effects of

changes in an organization’s volume of activity on its costs, revenue and profit. It is useful

for the management in knowing how profit is influenced by sales volume, sales price,

variable expenses and fixed expenses.

A critical part of CVP analysis is the point where total revenues equal total costs (both fixed

and variable costs). At this breakeven point (BEP), a company will experience no income or

loss. This BEP can be an initial examination that precedes more detailed CVP analysis.

Cost-volume-profit (CVP) analysis is a technique that examines changes in profits in response to changes in sales volumes, costs, and prices. Accountants often perform CVP analysis to plan future levels of operating activity and provide information about:

• Which products or services to emphasize.

• The volume of sales needed to achieve a targeted level of profit.

• The amount of revenue required to avoid losses.

• Whether to increase fixed costs.

• How much to budget for discretionary expenditures.

• Whether fixed costs expose the organization to an unacceptable level of risk.

Cost-Volume-Profit Relationship

A. Cost Classification

1. Variable Costs--variable costs are those costs that vary proportionately with changes in

the level of activity (such as direct materials, direct labor, salesmen’s commissions, etc.)

a. Relevant Range--even though variable cost per unit may vary throughout the entire

range of possible activity, the variable cost per unit is assumed to remain constant over the

range of activity over which the business expects to operate.

2. Fixed Costs--fixed costs are those costs that do not change with changes in the level of

activity (such as depreciation, property taxes, executive salaries, etc.)

a. Relevant Range-even though fixed costs may vary throughout the entire range of

possible activity, fixed costs are assumed to remain constant over the range of activity over

which the business expects to operate

3. Mixed Costs--mixed costs are those costs that have both a variable and a fixed

component (such as utility costs, costs of operating a truck, etc.)

a. Allocation--mixed costs must be classified into variable and fixed components for

cost-volume-profit relationship purposes


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B. Formula Approach

1. Derivation

a. Units--the net income of a business can be described by the following equation

SP x U – VC x U – FC = NI

where

SP = selling price per unit

U = number of units sold

VC = variable cost per unit

FC = fixed costs

NI = net income

Factoring out the common term, units, from the first two terms in the equation results in the

following equation.

U x (SP – VC) – FC = NI

Adding fixed costs to both sides of the equation results in the following equation.

U x (SP – VC) = NI + FC

Dividing both sides of the equation by (SP – VC) results in the following equation.

U = (NI + FC) / (SP – VC)


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Assumptions of Cost-Volume-Profit Analysis.

1. All costs can be analysed into their fixed and variable elements.

When we talk about fixed and variable costs, we usually assume that it is possible to take a

look at individual or total costs and split them into their fixed and variable elements.

However, if we look at any organisation of a reasonably large size we will quickly appreciate

that not only might there be several hundred costs comprising total cost but also there are

many forces acting on those costs (cost drivers in activity based costing

parlance). Consequently, it cannot be a simple matter of a few minutes' analysis and the

fixed and variable split has been fully explained.

Splitting out fixed and variable costs can be a long, time consuming process; and techniques

such as the inspection of accounts method really are not suitable if the analysis is to be

realistic. At the very least, some kind of statistical or mathematical analysis will have to be

undertaken. I have undertaken this kind of an exercise in a wide variety of companies and

industries; and it takes many man hours to research the organisation, set up and work a spread

sheet, analyse the results and then present my findings.

This is not to suggest that the splitting of fixed and variable costs is too difficult for the

average student or practitioner. Consider diagram one below (which we can assume for the

sake of the discussion is the regression line derived from an analysis of a business's total

costs) and suggest the level of fixed costs and hence calculate a variable cost per unit:

The graph is suggesting a regression equation of:

y = a + bx = 1,000 + 3x


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Which, in the present context, will be interpreted as: the fixed cost for the business is £1,000;

and the variable cost per unit is £3.

It should be remembered that this graph refers to the whole business and, as we have already

agreed, a reasonably large business is complex: consequently, although a statistical analysis

can be carried out, its results will not always be as simple to interpret as the assumptions on

which CVP analysis, and the example surrounding diagram one, would have us believe.

Imagine the problems which must be faced by the analyst trying to cope with the kind of cost

portrayed in diagram five: no longer a straight line at all; and such cost profiles are likely to

be the normal: as opposed to straight lines, that is.

More than all of this, though: it is frequently the case that even the people working in an

organisation will have little or no idea

a) Of their fixed/variable cost split; and

b) How to split their total costs into their fixed and variable components if asked!

It is these two aspects that often cause management accountants to assume linearity and/or

spend many hours analysing total costs.

Assessing the fixed and variable cost split can be fraught with difficulties and can be

time consuming.

2. Fixed costs remain fixed even over a wide range of activity.

Another simplifying assumption which helps to keep the arithmetic of CVP analysis simple

but which does not help those of us who wish to apply the techniques.

The common view of fixed costs is given in diagram two:

However, the major error contained in such charts is that it ignores (or merely assumes

away) the importance of the relevant range.


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The relevant range is the range of levels of activity over which the business has direct

experience. That is, it has probably produced at or over that range of outputs; or it has

studied such levels of output carefully. Hence, no business will know with certainty what its

fixed costs will be outside its relevant range; and there is no guarantee that fixed costs will

remain fixed if the business produces at a level of output outside its relevant range: whether

through expansion or contraction. Diagram three illustrates a more realistic scenario: where a

fixed cost can change as a result of a change in output level to a level outside the relevant

range. The relevant range in diagram three is represented as 401 units to 800 units.

The reasons why fixed costs will change in such a way include, for a reduction in

output: managers and supervisors being laid off as no longer required at reduced levels of

output; machinery sold; buildings sold or not rented any more. A similar analysis applies to

an increase in output and fixed costs.

Fixed costs behaving in this step cost fashion is another cause for concern over glibly trying

to apply CVP analysis. We may not, in fact, know how our fixed costs will behave outside

our relevant range unless and until we carry out detailed cost analysis of extra relevant range

scenarios.

3. Variable costs always vary directly with activity.

It is possible for a cost to be truly variable and behave in a perfectly linear way: think of

examples such as making one standard design of wooden tables and chairs. However, it is

still useful to explore here the more likely exceptions to that behaviour.

Diagram four demonstrates how a perfectly variable cost behaves:


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In reality, of course, a whole host of forces can act upon a cost which is deemed to be

variable. For example, once a business grows beyond a certain size it can then enjoy the

benefits of greater volume: such benefits are known as economies of scale and include being

awarded trade discounts, being offered cash discounts now that it can obtain credit; and

quantity discounts because it can now buy in greater bulk. Consequently, even though the

quantity of components in a product remains standard and fixed, their cost per unit can fall as

a result of these economies of scale.

These changes to the basic assumption of linearity mean that when diagram four shows a

perfectly straight line, reality could be more like diagram five where we can easily be dealing

with a situation where variable costs are essentially variable but which are not perfectly

variable. In the case of diagram five, we see a true curve; and any analysis of an estimation

of a precise relationship between variable cost and output will yield a solution but not a linear

one. Again, since any reasonably large business will have many such costs, isolating the

variability of all such costs can be a major task.

There are many variations on the possible shapes which a variable cost curve might

assume. For example, it might be the case that at higher levels of output a variable cost curve


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starts to slope upwards again, having initially behaved like the curve in diagram five: such a

situation would hold when diseconomies of scale or increasing import tariffs were being

imposed.

4. Selling prices are constant per unit.

A very similar series of arguments holds for selling prices as held for variable costs. There

is no reason why any business needs to sell to all of its customers at the same price for all

products. We could easily demonstrate that different prices are offered for different levels of

purchasing: for example, discounts for bulk buying. The hypothesis of supply and demand

also dictates that the higher the price the fewer will be sold; and the lower the price the more

will be sold. Diagram six combines the basic assumed sales curve and a more realistic sales

curve based on the arguments just put forward:

Again, when we consider the realistic side of total sales a true curve emerges; and again, this

means that any analysis of sales immediately becomes more difficult than the basic

assumptions of CVP analysis would have us believe.

As with the variable cost curve, there are potentially many shapes which the sales curve could

take on: diagram six gives only one variation from the usually assumed straight line.

5. Only levels of activity affect costs and revenues

This, to some extent, is the worst of all of the assumptions from the point of view of a

realistic application of CVP analysis. It is the worst because it denies there being such things

as labour efficiency and changes to labour efficiency: the learning effect is ignored, or

assumed away, by this assumption, of course.


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Along with all of the discussion so far, there are many reasons why a total cost or a cost per

unit might change; and changes in the level of output is only one. Consider your own

environment: why might any one of the costs with which you are associated change?

In the case of a manufacturer, costs might change because someone has improved the way an

operation is performed. A friend of mine, John, has a good eye for helping people to work

more efficiently. One day he Noticed that an operative in a factory was working on making

components for a Poly Tunnel (greenhouse type thing!) and was working on a bench but

keeping his metal rods on the floor. John brought a stand around to where the operative was

working and put the metal rods on there … the operative then completed his jobs in half the

time it used to take! The consequences of this relate to time, productivity, possibly better

quality output and the cost per unit will have improved. None of the reason for this change in

cost is due to the restrictive assumption of output being the only determinant of cost.

6. Usually only one product can be effectively dealt with

One product business

The reason for this assumption rests on the mathematics involved if more than one product is

assumed to be made. Although it is not the purpose of this paper to go too deeply into such

issues, we should be aware that trying to model a multi product business in terms of CVP

analysis can become very frustrating indeed. Consider diagram seven, which represents a ten

product business: all products have different characteristics, as we can see from the three

products included in the graph.

Within this multiproduct business, there are six prices, all of which are subject to varying

levels of variability.

The purpose of the graph is to demonstrate that simply by analysing the total sales curve, and

ignoring its constituent parts, is likely to lead to serious errors of judgement or decision


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making: the total sales curve is almost a straight line, but any one of the individual sales

curves for any product can be significantly different to a straight line; as is the case,

especially, with products three and ten.

Any simplistic attempt at unravelling this business is destined to fail. The mathematical

model even for this relatively simple ten product business could run to several complete lines

across an A4 page. Such a model is not too unmanageable for most of us, but it is unwieldy

and cannot be readily simplified just for the sake of argument; and the same arguments would

apply equally well to the variable and fixed costs (although they have been excluded from

diagram seven).

Sales mix issues

The sales mix argument is a straightforward one and it deals with the contribution to sales

ratio (the C/S ratio). If a business makes two products: one with a C/S ratio of 80% and the

other with a C/S ratio of 70%, the average C/S ratio will not be 75% (which would be

the simple average of the two C/S ratios). The average C/S ratio has to be based on

the weighted average of the two; and the value of this weighted average varies as the sales

mix varies.

Consider the weighted averages in each of the following cases for the business just

introduced:

Sales mix (i) Product 1 Product 2

Sales (units) 100,000 200,000

Sales (£) 500,000 300,000

C/S ratio (as given above) 80% 70%

The weighted average C/S ratio is:

Total Contribution = (£500,000 x 80%) + (£300,000 x 70%)

Total Sales £500,000 + £300,000

= 76.25%

Sales mix (ii) Product 1 Product 2

Sales (units) 300,000 350,000

Sales (£) 1,500,000 525,000

C/S ratio 80% 70%


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The weighted average C/S ratio is:

Total Contribution = (£1,500,000 x 80%) + (£525,000 x 70%)

Total Sales £1,500,000 + £525,000

= 77.41%

By changing the sales mix, in a situation where the values of the C/S ratio change from

product to product, the weighted average value of all C/S ratios also changes; and unless this

point is appreciated, the results of any CVP analysis could easily be invalidated.

7. Uncertainty does not exist.

The final assumption underlying CVP analysis is that there is no such thing as

uncertainty. Everything is known and knowable to 100% certainty levels. Prices are sure;

variability of cost is certain; and there is nothing as certain as the level of fixed cost.


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Concepts of Cost Accountancy used in COST-VOLUME-PROFIT Analysis

Before starting with explanation of Cost Volume Profit Analysis, we would like to briefly

explain a few basic concepts which are important while understanding CVP analysis.

Fixed Cost

These costs remain fixed in ‘total’ and do not increase or decrease when the volume of

production increases or decreases.

But the fixed cost ‘per unit’ increases when the volume of production decreases and

decreases when the volume of production increases.

Fixed cost per unit cannot be zero.

Examples – Rent, Insurance

Variable Cost

These costs fluctuate in proportion to the volume of production. In other words when volume

of output increases total variable cost also increases and when volume of output decreases the

variable cost also decreases.

But the variable cost ‘per unit’ remains fixed.

Example – Direct Material cost, direct wages

Direct Cost

These are the costs which are incurred for and can be conveniently identified with, a

particular product, process or department.

Example- cost of leather in manufacturing a pair of shoes.

Indirect Cost

These are general costs and are incurred for the benefits of a number of cost units, processes

or departments. These costs cannot be conveniently identified with a particular product.

Example – Power, Insurance

Total Revenue

Total revenue is the total money received from the sale of any given quantity of output.

The total revenue is calculated as the selling price of the firm's product times the quantity sold, i.e.

Total revenue = Price × Quantity


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Total costs

Total cost is the sum of fixed costs, variable costs, and semi-variable costs.

In other words it can also be explained as the sum of the Direct Cost plus the Indirect Cost.

Cost centre

A location, a person or an item of equipment (or group of these) for which costs may be

ascertained and used for purpose of cost control

Cost unit

A unit of product, service or time in relation to which costs may be ascertained or expressed

Sales mix

The term sale mix refers to the relative proportion in which a company's products are sold.

The concept is to achieve the combination that will yield the greatest amount of profits. Most

companies have many products, and often these products are not equally profitable. Hence,

profits will depend to some extent on the company's sales mix. Profits will be greater if high

margin rather than low margin items make up a relatively large proportion of total sales.

Selling Price per Unit

The amount of money charged to the customer for each unit of a product or service.

Target Profit

Target profit is the amount of net operating income or profit that management desires to

achieve at the end of a business period. Management needs to know the required level of

business activities to get target profits. Cost volume profit (CVP) equations and formulas can

be used to determine the sales volume needed to achieve a target profit. The two methods of

doing so are-

1) Equation Method

Sales = Variable expenses + Fixed expenses + Profits

2) Contribution Margin Method:

[(Fixed expenses + Target profit) / Contribution margin per unit]


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BREAK-EVEN POINT ANALYSIS

Break-even point is the point at which the gains equal the losses. A break-even point defines when an investment will generate a positive return. The point when sales or revenue equal expenses or also the point where the total cost equals the total revenue. There is no profit made or loss incurred at the break-even point. This is important for anyone that manages a business, since the break-even point is the lower limit of profit when prices are set and margins are determined. Therefore the break-even point is that quantity of output where the total revenue =total cost i.e. the operating income is zero

Break-even point is calculated by the following methods:

• Equation Method

• Contribution margin method

• Graphical method

I. Equation Method:

The income statement can be expressed in equation form as follows:

Revenues-Variable Costs-Fixed Costs= Operating Income

The equation provides the most general approach to any CVP situation.

Let N be the No. of units sold to break even, Let P be the price at which the units are sold, VC be the cost of the product (product related expense) and FC be the cost for the product not directly related to the product.

Setting Operating income= 0 we have;

N*P-VC*N-FC=0

Therefore, N=FC/ (P-VC)

If the company sells fewer than FC/ (P-VC) units of commodity, it will make a loss. If it sells more, it will make a profit and if it sells FC/ (P-VC) units, it will make no profit and no loss.

II. Contribution Margin:

Contribution margin is the revenue minus all costs that vary with respect to an output-related cost driver. This method uses the fact that:

P*N – VC*N-FC = operating income (OI)

N (P-VC) = OI+FC

Unit contribution margin * N = FC + OI

Since at the break-even point, operating income is by definition zero, we obtain;


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Unit contribution margin * Break even No. of units = FC

Therefore, Break even no. of units= FC/ Unit contribution margin

A contribution income statement groups individual line items to highlight the contribution margin, which is the difference between revenues and all costs that may vary with respect to an output-related driver.

III. Graphical calculation:

A break-even chart is one in which sales revenue, variable costs, and fixed costs are plotted on the vertical axis while volume is plotted on the horizontal axis. The Break-Even Point is the point at which the total sales revenue line intersects the total cost line. The chart below shows the calculation of break-even point graphically:

Here, the firm is at break-even at the point of intersection of the total revenue curve and the

total cost curve. The break-even point occurs when 1000 units of the commodity are

produced. The important concepts to be understood in this method are Variable costs, fixed

costs and total revenue. These concepts have already been explained in the previous sections.

The main advantages of break-even analysis are that it explains the relationship between

costs, production volume and returns. It can be extended to show how changes in fixed costs-

variable costs relationship will affect the profit levels of a company and the break even

points. Break even analysis is most useful when used with partial budgeting or capital

budgeting. Major benefit to using break even analysis is that it indicates the lowest output to

prevent a loss.

Operating income area

Operating Loss area


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Limitations of break-even analysis include:

• It is best suited to the analysis of one product at a time

• May be difficult to classify a cost as all variable or all fixed cost

• It may be a tendency to continue to use a break even analysis after the cost and

income function have changed.


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INCREMENTAL ANALYSIS

Incremental analysis is a technique used to assist decision making by assessing the impact of small or marginal changes. Its origins are linked to the principles of marginal analysis The most important principle of incremental analysis is that the only items relevant to a decision are those that will be different as a result of the decision. A second and related tenet is that if a past cost or negative is not recoverable or removable, it is irrelevant to a future decision. Those two principles have universal application. Incremental analysis guides many decisions in nearly every discipline including engineering, architecture, management, medicine, demography, sociology, consumer behaviour and investment management. Incremental analysis is applicable to both short- and long-run issues, but is particularly suited to short-run decisions. In the short run, production capacity remains unchanged so, by definition, fixed costs do not vary due to capacity shifts. In the long run, production capacity is changeable; more elements will thus generally be required to be incorporated into an incremental analysis. A simple situation in everyday life provides an example of incremental analysis. Consider a worker leaving work to travel home. Groceries are required and can be purchased at slightly higher prices at a store on the way from the work place to the home, or at lower prices by driving to a store 3 miles (4.82 km) from home. The worker decides to purchase the groceries on the way home since no incremental travel costs are involved, and the incremental difference in grocery prices will be less than the value the worker places on the time and other costs required to drive to the more distant store. In business, firms routinely use incremental analysis to assist a large range of decisions, including leasing versus purchasing of new assets, acquisitions and divestments, capacity expansions and additional raw material processing decisions. A key issue usually is determining the incremental impact on capital outlays, costs, and revenues. This is not always clear cut before the event and judgments are often required.


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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


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INCOME STATEMENT APPROACH OF CVP ANALYSIS FOR MULTI PRODUCT FIRM

INPUT SECTION Youth

Bikes Road Bikes

Mountain

Bikes

Expected sales volume-units 10,000 18,000 12,000

Price per unit (in Dollars) 200 700 800

Variable cost per unit 75 250 300

Fixed costs 1,47,00,000 (enter zero for breakeven)

Desired after-tax profit $100,000

Income tax rate 30%

Contribution Margin

Youth

Bikes Road Bikes Mtn. Bikes Total Bikes

Units 10,000 18,000 12,000 40,000

Revenue (in Dollars) 20,00,000 1,26,00,000 96,00,000 2,42,00,000

Variable costs 7,50,000 45,00,000 36,00,000 88,50,000

Contribution margin 12,50,000 81,00,000 60,00,000 1,53,50,000

Contrib. margin per unit 125 450 500 383.75

Contrib. margin ratio 62.50% 64.29% 62.50% 63.43%

Expected sales mix in units 25.00% 45.00% 30.00% 100.00%

Expected sales mix in revenues 8.26% 52.07% 39.67% 100.00%

Expected Income

Contribution margin (above) 1,53,50,000

Fixed costs 1,47,00,000

Pretax income 6,50,000

Income taxes 1,95,000

After-tax income 4,55,000

Preliminary CVP Calculations

Target pretax profit for CVP analysis 1,42,857

Fixed costs plus target pretax profit 1,48,42,857

CVP analysis in units

Youth


CVP calculation in units 9,669.61 17,405.30 11,603.54 38,678

Revenue 19,33,923 1,21,83,713 92,82,829 2,34,00,465

Variable costs 7,25,221 43,51,326 34,81,061 85,57,608

Contribution margin 12,08,702 78,32,387 58,01,768 1,48,42,857



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Income taxes 42,857

After-tax income $100,000

CVP analysis in revenues

Youth


CVP calculation in revenues $1,933,923 $12,183,713 $9,282,829 $23,400,465

Variable costs 7,25,221 43,51,326 34,81,061 85,57,608

Contribution margin $1,208,702 $7,832,387 $5,801,768 1,48,42,857



Income taxes 42,857

After-tax income $100,000


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MATHEMATICAL CALCULATIONS

Profit Equation and Contribution Margin

CVP analysis begins with the basic profit equation.

Profit =Total revenue - Total costs

Separating costs into variable and fixed categories, we express profit as:

Profit = Total revenue - Total variable costs- Total fixed costs

The contribution margin is total revenue minus total variable costs. Similarly, the contribution Margin per unit is the selling price per unit minus the variable cost per unit. Both contribution margin and contribution margin per unit are valuable tools when considering The effects of volume on profit. Contribution margin per unit tells us how much revenue from all fixed costs, then the contribution margin per unit from all remaining sales becomes profit.

Profit =P * Q - V * Q - F = (P - V ) * Q - F

where,

P - Selling price per unit

V - Variable cost per unit

(P - V ) - Contribution margin per unit Q - Quantity of product sold (units of goods or services)

F - Total fixed costs

We use the profit equation to plan for different volumes of operations. CVP analysis

can be performed using either:

Units (quantity) of product sold

Revenues

CVP Analysis in Units We begin with the preceding profit equation. Assuming that fixed costs remain constant, we

solve for the expected quantity of goods or services that must be sold to achieve a target

level of profit.

Profit equation: Profit = (P - V ) *Q - F


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Solving for Q:

Q=(F+profit)/(P-V)

For Eg:

Suppose that Magik Bicycles wants to produce a new mountain bike called Magikbike

III and has forecast the following information.

Price per bike - $800

Variable cost per bike - $300 Fixed costs related to bike production - $5,500,000

Target profit - $200,000

Estimated sales - 12,000 bikes We determine the quantity of bikes needed for the target profit as follows: Quantity = ($5,500,000+ $200,000) / ($800 - $300)

=11,400 bikes


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APPLICATION

Application to investing

Using margin of safety, one should buy a stock when it is worth more than its price on the market. This is the central thesis of value investing philosophy which espouses preservation of capital as its first rule of investing. One should also analyse financial statements and footnotes to understand whether companies have hidden assets (e.g., investments in other companies) that are potentially unnoticed by the market.

The margin of safety protects the investor from both poor decisions and downturns in the market. Because fair value is difficult to accurately compute, the margin of safety gives the investor room for error.

A common interpretation of margin of safety is how far below intrinsic value one is paying for a stock. For high quality issues, value investors typically want to pay 90 cents for a dollar (90% of intrinsic value) while more speculative stocks should be purchased for up to a 50 percent discount to intrinsic value (pay 50 cents for a dollar).

Application to accounting

In investing parlance, margin of safety is the difference between the expected (or actual) sales level and the break-even sales level. It can be expressed in the equation form as follows:

Margin of Safety = Expected (or) Actual Sales Level (quantity or dollar amount) - Breakeven sales Level (quantity or dollar amount).


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Limitations

1. For an organisation of a reasonably large size, it is not possible to take a look at total costs

and split them into their fixed and variable elements. Not only might there be several hundred

costs comprising total cost but also there are many forces acting on those costs.

2. It ignores the importance of the relevant range in fixed costs.

3. Variable costs do not always vary directly with activity.

4. Selling prices per unit are not always constant.

5. It doesn’t consider the effect of labour efficiency on costs and revenues.

6. It is difficult to apply this analysis to multi product businesses because simply by analysing

the total sales curve, and ignoring its constituent parts, is likely to lead to serious errors of

judgement or decision making


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BIBLIOGRAPHY

• http://www.accountingformanagement.com/cost_volume_profit_analysis.htm

• www.osun.org

• http://business.fortunecity.com/discount/29/cvpass.htm

• http://en.wikipedia.org/wiki/Cost-Volume-Profit_Analysis

• www.wiley.com/college/sc/eldenburg/ch03.pdf

• www.accountingformanagement.com/cost_volume_profit.htm

• Robbins, S. M. 1961. Emphasizing the marginal factor in the break-even analysis. N.A.A.

Bulletin (October): 53-60.

• Suver, J. D. and B. R. Neumann. 1977. Patient mix and breakeven analysis. Management

Accounting (January): 38-40.

• Stettler, H. F. 1962. Break-even analysis: Its uses and misuses. The Accounting Review (July):

460-463.

• Martin, J. R. 1989. Capital budgeting analysis with curvilinear cost and revenue functions: A

microcomputer application. Kent/Bentley Journal of Accounting and Computers Volume (V):

118-129.

• Fehr, F. W. 1960. Some points to watch in studying the fluctuation of cost with

volume. N.A.A. Bulletin (March): 67-76. • Battista, G. L. and G. R. Crowningshield. 1966. Cost behavior and breakeven analysis - A

different approach. Management Accounting (October): 3-14.

Documents

Cost Volume Profit Analysis Paper Presentation