Financial and Management Accounting l7

7/31/2019 Financial and Management Accounting l7

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16/05/1216/05/12 GIMPA BUSINESS SCHOOL DBAGIMPA BUSINESS SCHOOL DBA 11

LECTURE 7LECTURE 7

COST-VOLUME-PROFIT ANALYSISCOST-VOLUME-PROFIT ANALYSIS(BREAK-EVEN ANALYSIS)(BREAK-EVEN ANALYSIS)


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At the end of the lesson students shouldAt the end of the lesson students shouldbe able to:be able to:

Explain the objective of CVP analysisExplain the objective of CVP analysis Explain the concept of break-evenExplain the concept of break-even

Calculate and explain the break-evenCalculate and explain the break-even

point and revenue, target profit,point and revenue, target profit,profit/volume ratio and margin of safetyprofit/volume ratio and margin of safety

Construct break-even, contribution, andConstruct break-even, contribution, andprofit/volume charts from given data.profit/volume charts from given data.


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The concept of c-v-p analysis examines theThe concept of c-v-p analysis examines theinherent relationship that exists among sellinginherent relationship that exists among sellingprice, cost structure, volume and profits.price, cost structure, volume and profits.

It involves considering the combined effect onIt involves considering the combined effect onboth cost and revenue functions of changes inboth cost and revenue functions of changes inthe level of output by examining the inter-the level of output by examining the inter-relation of cost, volume and profits.relation of cost, volume and profits.

It seeks to answer such questions as:It seeks to answer such questions as:1.1. Given existing prices and cost structure whatGiven existing prices and cost structure whatvolume of operation is needed to earn avolume of operation is needed to earn acertain level of profit.certain level of profit.


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2. If prices are cut by a certain percentage how much of an2. If prices are cut by a certain percentage how much of anincrease in volume is needed to maintain the previousincrease in volume is needed to maintain the previouslevel of profits;level of profits;

3. If variable costs are to be cut by the acquisition of some3. If variable costs are to be cut by the acquisition of someautomation machine (hence an increase in fixed cost),automation machine (hence an increase in fixed cost),how large a cut is required to provide a certain level ofhow large a cut is required to provide a certain level ofprofit assuming the existing level of operationprofit assuming the existing level of operationcontinues in the future.continues in the future.

4. If variable costs increase by a certain percentage what4. If variable costs increase by a certain percentage whathappens to profit assuming that volume will increasehappens to profit assuming that volume will increaseby a certain percentageby a certain percentage


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An understanding of cost behaviour and cost-An understanding of cost behaviour and cost-

volume-profit relationship can help to answervolume-profit relationship can help to answer

these questions as well as long-term questionsthese questions as well as long-term questionssuch as the additional sales required to justifysuch as the additional sales required to justify

an increase in profit.an increase in profit.

The cost-volume-profit analysis is based on aThe cost-volume-profit analysis is based on a

model of Income Statement using the Marginalmodel of Income Statement using the MarginalCosting approach where Total Cost is dividedCosting approach where Total Cost is divided

into Fixed and Variable components.into Fixed and Variable components.


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Under Marginal Costing, ContributionUnder Marginal Costing, Contribution

Margin is the difference between productMargin is the difference between product

revenue and variable cost. (C = TR revenue and variable cost. (C = TR VC).VC).

It represents the amount available first forIt represents the amount available first for

meeting fixed cost and then formeeting fixed cost and then forcontributing towards profit expectation.contributing towards profit expectation.

(C = FC + P)(C = FC + P)


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IllustrationIllustration

Asempa Ltd. manufactures a product which isAsempa Ltd. manufactures a product which issold for GHsold for GH20.00 per unit and has variable20.00 per unit and has variablecosts of GH14.00 per unit. Fixed cost percosts of GH14.00 per unit. Fixed cost perannum is estimated at GH24,000.annum is estimated at GH24,000.

Required:Required:

Prepare summary statements showing thePrepare summary statements showing thetotal profit/(loss) and profit/(loss) per unit wheretotal profit/(loss) and profit/(loss) per unit wheresales quantity may be 3,000, 4,000 andsales quantity may be 3,000, 4,000 and5,000units.5,000units.


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Solution:Solution:

ASEMPA LTD. INCOME STATEMNTSASEMPA LTD. INCOME STATEMNTS

Sales UnitsSales Units 3,0003,000 4,0004,000 5,0005,000

TT UU TT UU TT UU

Sales Rev. 60,000 20 80,000 20 100,000 20Sales Rev. 60,000 20 80,000 20 100,000 20

Variable CostVariable Cost 42,00042,000 1414 56,00056,000 1414 70,00070,000 1414

Contribution 18,000 6 24,000 6 30,000 6Contribution 18,000 6 24,000 6 30,000 6 Fixed CostFixed Cost 24,00024,000 88 24,00024,000 66 24,00024,000 4.804.80

Profit/(Loss)Profit/(Loss) (6,000)(6,000) (2)(2) 00 00 6,0006,000 1.201.20


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Solution may be analysed as follows:Solution may be analysed as follows:

Fixed Cost remains constant at GHFixed Cost remains constant at GH

24,000 irrespective of the sales volume.24,000 irrespective of the sales volume. Fixed cost per unit is an arbitrary measureFixed cost per unit is an arbitrary measure

which is obtained by dividing total cost by thewhich is obtained by dividing total cost by thenumber of units of sale. Fixed cost per unit fallsnumber of units of sale. Fixed cost per unit falls

as sales volume increases.as sales volume increases. Contribution is the difference between salesContribution is the difference between sales

revenue and variable cost.revenue and variable cost.


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Contribution per unit is a constant figure of GHContribution per unit is a constant figure of GH6.00 per unit (6.00 per unit (20 - 14) at all sales levels.20 - 14) at all sales levels.

Total contribution increases as sales volumeTotal contribution increases as sales volumeincreases.increases.

The point at which profit is zero is the break-The point at which profit is zero is the break-even point. At this point total contributioneven point. At this point total contribution

equals fixed cost.equals fixed cost.

Below 4,000 units of sales, fixed costs areBelow 4,000 units of sales, fixed costs aregreater than total contribution and a lossgreater than total contribution and a lossresults.results.


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Above 4,000 units of sale, total contribution isAbove 4,000 units of sale, total contribution is

greater than fixed costs and a profit results.greater than fixed costs and a profit results.

Note that contribution increases by GHNote that contribution increases by GH6,0006,000(from 24,000 to 30,000) when sales volume(from 24,000 to 30,000) when sales volume

increases from 4,000 to 5,000 units.increases from 4,000 to 5,000 units.

Profit also increases by GH6,000 for the sameProfit also increases by GH6,000 for the same

sales volume range (0 to 6,000), whereassales volume range (0 to 6,000), whereasfixed costs remain unchanged at GH24,000.fixed costs remain unchanged at GH24,000.


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This indicates that the additional contributionThis indicates that the additional contributionearned per unit is also the extra profit earnedearned per unit is also the extra profit earnedper unit.per unit.

This is a useful tool in profit planning.This is a useful tool in profit planning.

For example, the increase in profit where salesFor example, the increase in profit where salesrise from 5,000 to 5,400 units can be measuredrise from 5,000 to 5,400 units can be measuredas (400 units xas (400 units x 6.00 = 2,400).6.00 = 2,400).

This increases the total profit to GH8,400.This increases the total profit to GH8,400.(6,000 + 2,400).(6,000 + 2,400).


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Check:Check: Sales UnitsSales Units 5,4005,400 TT UU Sales RevenueSales Revenue 108,000108,000 2020 Variable CostVariable Cost 75,60075,600 1414

ContributionContribution 32,40032,400 66 Fixed CostFixed Cost 24,00024,000 ProfitProfit 8,4008,400


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This ratio is an alternative to the contributionThis ratio is an alternative to the contribution

per unit as a measure of the rate at whichper unit as a measure of the rate at which

contribution is being earned.contribution is being earned.

Using the figures in the earlier example, it mayUsing the figures in the earlier example, it may

be calculated as: contribution per unit / sellingbe calculated as: contribution per unit / selling

price (c/s) (price (c/s) (6/20 = 0.30 or 30%).6/20 = 0.30 or 30%).

This ratio applies at any activity level as long as theThis ratio applies at any activity level as long as thebasic assumptions of the model remain unchanged. (i.e.basic assumptions of the model remain unchanged. (i.e.

constant selling price and variable cost per unit.)constant selling price and variable cost per unit.)


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Where business activity is expanding, theWhere business activity is expanding, the

higher the c/s ratio, the greater the ratehigher the c/s ratio, the greater the rate

at which additional profits will be earned.at which additional profits will be earned. Where business activity is declining,Where business activity is declining,

however, a higher c/s ratio means thathowever, a higher c/s ratio means that

profits will fall at a greater rate per unit ofprofits will fall at a greater rate per unit oflost sales.lost sales.


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Basic Assumptions:Basic Assumptions: Cost can be segregated into two components:Cost can be segregated into two components:fixedfixedandand variablevariable cost elements.cost elements.

Cost and Revenue behaviour is a linearCost and Revenue behaviour is a linearrelationship over the relevant range of outputrelationship over the relevant range of outputlevels. This implies that:levels. This implies that: Variable cost varies with the level of output. IncreasesVariable cost varies with the level of output. Increases

in output have identical effect on cost as on size perin output have identical effect on cost as on size perunit.unit.

The cost identified as fixed is constant within the rangeThe cost identified as fixed is constant within the rangeof output levels considered.of output levels considered. The selling price of the product remains unchangedThe selling price of the product remains unchanged

regardless of the level of sales.regardless of the level of sales.


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Efficiency in productivity remains unchanged.Efficiency in productivity remains unchanged. The analysis of break-even relates to oneThe analysis of break-even relates to one

product only or where multi-products areproduct only or where multi-products are

produced, it relates to a constant mix ofproduced, it relates to a constant mix ofproducts.products.

Sales and production units are equal implyingSales and production units are equal implyingthat stock level is zero.that stock level is zero.

Volume is the only factor which affects costVolume is the only factor which affects cost The prices paid for the resources used byThe prices paid for the resources used by

enterprise will not change over the period.enterprise will not change over the period.


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Illustration of Break-even charts.Illustration of Break-even charts.

Traditional Break-even ChartsTraditional Break-even Charts

Modified Break-even ChartModified Break-even Chart

Contribution/Volume ChartContribution/Volume Chart

Profit/Volume ChartProfit/Volume Chart


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Calculating Sales units or value at Break-Calculating Sales units or value at Break-even at specific profit.even at specific profit.

Two methods can be used:Two methods can be used: Preparing Break-even chart and readingPreparing Break-even chart and reading

the required value from it.the required value from it.

Use a formula derived from the revenueUse a formula derived from the revenuefunction. (Sales Revenue (S) = Variablefunction. (Sales Revenue (S) = Variablecost (V) + Fixed cost (F) + Profit (P).cost (V) + Fixed cost (F) + Profit (P).


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Steps in the preparation of Break-even chart:Steps in the preparation of Break-even chart:

1.1. Choose suitable scales for the horizontal axis (activity unitsChoose suitable scales for the horizontal axis (activity unitsaxis) and the vertical axis (sales value and cost).axis) and the vertical axis (sales value and cost).

2.2. Plot the point for the maximum sales revenue. Join this point toPlot the point for the maximum sales revenue. Join this point to

the origin (when no units are sold sales revenue is zero). Thethe origin (when no units are sold sales revenue is zero). Theresulting line is the Sales curve.resulting line is the Sales curve.

3.3. Plot the point for fixed cost on the vertical axis. When salesPlot the point for fixed cost on the vertical axis. When salesunits are zero there is no variable cost.units are zero there is no variable cost.

4.4. Plot the total cost point at the maximum units. This is variablePlot the total cost point at the maximum units. This is variablecost plus fixed cost.cost plus fixed cost.

5.5. Join the points from 3 and 4 to give the straight line which is theJoin the points from 3 and 4 to give the straight line which is thetotal cost curve.total cost curve. The required information can then be read.The required information can then be read.


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Deriving formulae from the sales function:Deriving formulae from the sales function: S = V + F + PS = V + F + P Hence S V = F + PHence S V = F + P But S V = CBut S V = C So C = F + PSo C = F + P By dividing both sides of the equation by SalesBy dividing both sides of the equation by Sales

Revenue (S) gives:Revenue (S) gives: C/S = (F + P) / SC/S = (F + P) / S Re-arranging to make S the subject:Re-arranging to make S the subject: S = (F + P) / C/S.S = (F + P) / C/S.


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From the equation, Sales revenue (S) for any desiredFrom the equation, Sales revenue (S) for any desiredlevel of profit (P) can be calculated when fixed cost andlevel of profit (P) can be calculated when fixed cost andc/s ratio are known.c/s ratio are known.

For sales revenue at Break-even point,For sales revenue at Break-even point,

P = 0, hence, S = F / c/s.P = 0, hence, S = F / c/s. The answers obtained from the formula can beThe answers obtained from the formula can be

expressed in units by substituting contribution per unitexpressed in units by substituting contribution per unitfor c/s ratio in the denominator of the equation. Thisfor c/s ratio in the denominator of the equation. Thisgives:gives:

S units = (F + P)/ c per unit for quantity at specifiedS units = (F + P)/ c per unit for quantity at specifiedprofit.profit.

S units = F / c per unit for Break-even quantity.S units = F / c per unit for Break-even quantity.


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A company has a budget summary as follows:A company has a budget summary as follows:

Fixed cost is GHFixed cost is GH50,00050,000 Variable cost per unit is GH20Variable cost per unit is GH20

Selling price per unit is GH30Selling price per unit is GH30

Sales will be in the range up to 8,000 units.Sales will be in the range up to 8,000 units.

Required:Required: Calculate the sales revenue and sales unitsCalculate the sales revenue and sales unitsat which the companys budget will show: (a) a break-at which the companys budget will show: (a) a break-

even position, (b) a profit of GH20,000 and (c) a loss ofeven position, (b) a profit of GH20,000 and (c) a loss ofGH10,000, using:GH10,000, using:

(i) Break-even chart and (ii) the formula.(i) Break-even chart and (ii) the formula.


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(ii) Using formula:(ii) Using formula:

S at B/E = F / C/S ratioS at B/E = F / C/S ratio

S =S = 50,00050,000 == 150,000150,000

0.3330.333 S units at B/E = F / c per unitS units at B/E = F / c per unit

Q =Q = 50,00050,000 == 5,000 units5,000 units

1010

S at Profit ofS at Profit of20,000: S =20,000: S = F + P / c/s ratioF + P / c/s ratio S =S = (50,000 + 20,000)(50,000 + 20,000) == 210,000210,000

0.3330.333


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S units atS units at 20,000 Profit20,000 Profit Q = (F + P)/c per unitQ = (F + P)/c per unit Q =Q = (50,000 + 20,000)(50,000 + 20,000) == 7,000 units7,000 units

1010 S at 10,000 LossS at 10,000 Loss S = (F + P)/c/s ratioS = (F + P)/c/s ratio S =S = (50,000 10,000)(50,000 10,000) == 20,00020,000

0.3330.333 S units at 10,000 LossS units at 10,000 Loss Q = (F + P)/c per unitQ = (F + P)/c per unit Q = (50,000 10,000) / 10 =Q = (50,000 10,000) / 10 = 4,000 units4,000 units


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Is the extent to which sales may fall below theirIs the extent to which sales may fall below theirexisting level before break-even point isexisting level before break-even point isreached.reached.

It may be expressed in units, monetary value orIt may be expressed in units, monetary value oras a percentage of the existing level.as a percentage of the existing level.

The Margin of Safety is an additional usefulThe Margin of Safety is an additional usefulstatistic available as part of c-v-p analysis.statistic available as part of c-v-p analysis.

It will help management to evaluate alternativeIt will help management to evaluate alternativeproposed strategies.proposed strategies.


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Example:Example:

KK Ltd. has planned sales of GHKK Ltd. has planned sales of GH600,000600,000

(40,000 @ 15 per unit). The variable cost per(40,000 @ 15 per unit). The variable cost perunit is 10 and the fixed costs total unit is 10 and the fixed costs total 150,000.150,000.

Required:Required: Calculate the margin of safetyCalculate the margin of safety

expressed in terms of sales units, salesexpressed in terms of sales units, salesvalue and as a percentage of currentvalue and as a percentage of current

sales.sales.


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Solution:Solution: Contribution per unit:Contribution per unit: 15 - 10 = 515 - 10 = 5

S = F / c per unitS = F / c per unit

S units = 150,000 / 5 = 30,000 unitsS units = 150,000 / 5 = 30,000 units Break-even Sales = 30,000 x 15 = 450,000.Break-even Sales = 30,000 x 15 = 450,000.

The Margin of Safety may be valued as:The Margin of Safety may be valued as:

40,000 units 30,000 units = 10,000units40,000 units 30,000 units = 10,000units 600,000 - 450,000 = 150,000.600,000 - 450,000 = 150,000.

As percentage: 150,000/600,000 x 100 = 25%.As percentage: 150,000/600,000 x 100 = 25%.


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The summary Income Statements of twoThe summary Income Statements of two

companies as at 31 December 2009 were:companies as at 31 December 2009 were:

A Co . Ltd.A Co . Ltd. B Co. Ltd.B Co. Ltd.

GHGH GHGH

Sales RevenueSales Revenue 100,000100,000 100,000100,000

Variable CostVariable Cost 40,00040,000 50,00050,000

ContributionContribution 60,00060,000 50,00050,000

Fixed CostFixed Cost 45,00045,000 35,00035,000

ProfitProfit 15,00015,000 15,00015,000


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Required:Required:

Calculate the Break-even Sales for each company.Calculate the Break-even Sales for each company.

Calculate the Margin of Safety andCalculate the Margin of Safety and

Contribution/Sales Ratio for each company.Contribution/Sales Ratio for each company. In which of the two companies should one invest duringIn which of the two companies should one invest during

times oftimes of

(i) high demand(i) high demand

(ii) low demand(ii) low demand The two companies operate in the same market andThe two companies operate in the same market and

produce the same product.produce the same product.

Financial and Management Accounting l7

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