Accounting for Decn Making C-V-P Analysis L7 (1)

7/28/2019 Accounting for Decn Making C-V-P Analysis L7 (1)

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LECTURE 7

COST-VOLUME-PROFIT ANALYSIS

(BREAK-EVEN ANALYSIS)

14/06/2013 GIMPA BUSINESS SCHOOL MBA 1


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LEARNING OBJECTIVESAt the end of the lesson students should be able to:

Explain the objective of CVP analysis

Explain the concept of break-even

Calculate and explain the break-even point andrevenue, target profit, profit/volume ratio and marginof safety

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



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Cost-Volume-Profit Analysis The concept of c-v-p analysis examines the

inherent relationship that exists among sellingprice, cost structure, volume and profits.

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

It seeks to answer such questions as:1. Given existing prices and cost structure whatvolume of operation is needed to earn a certainlevel of profit.



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Cost-Volume-Profit Analysis2. If prices are cut by a certain percentage how much of an

increase in volume is needed to maintain the previouslevel of profits;

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

4. If variable costs increase by a certain percentage whathappens to profit assuming that volume will increase bya certain percentage



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Cost-Volume-Profit AnalysisAn understanding of cost behaviour and cost-

volume-profit relationship can help to answer

these questions as well as long-term questionssuch as the additional sales required to justify anincrease in profit.

The cost-volume-profit analysis is based on a

model of Income Statement using the MarginalCosting approach where Total Cost is divided intoFixed and Variable components.



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Cost-Volume-Profit Analysis Under Marginal Costing, Contribution Margin is the

difference between product revenue and variable cost.(C = TR VC).

It represents the amount available first for meetingfixed cost and then for contributing towards profitexpectation.

(C = FC + P)



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Cost-Volume-Profit Analysis Illustration

Asempa Ltd. manufactures a product which is soldfor GH20.00 per unit and has variable costs ofGH14.00 per unit. Fixed cost per annum isestimated at GH24,000.

Required:

Prepare summary statements showing the totalprofit/(loss) and profit/(loss) per unit where salesquantity may be 3,000, 4,000 and 5,000units.



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Cost-Volume-Profit Analysis Solution:

ASEMPA LTD. INCOME STATEMNTS

Sales Units 3,000 4,000 5,000

T U T U T U

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

Variable Cost 42,000 14 56,000 14 70,000 14

Contribution 18,000 6 24,000 6 30,000 6 Fixed Cost 24,000 8 24,000 6 24,000 4.80

Profit/(Loss) (6,000) (2) 0 0 6,000 1.20



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Cost-Volume-Profit Analysis Solution may be analysed as follows:

Fixed Cost remains constant at GH24,000irrespective of the sales volume.

Fixed cost per unit is an arbitrary measure which isobtained by dividing total cost by the number ofunits of sale. Fixed cost per unit falls as sales

volume increases.

Contribution is the difference between salesrevenue and variable cost.



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Cost-Volume-Profit Analysis Contribution per unit is a constant figure of

GH6.00 per unit (20 - 14) at all sales levels.

Total contribution increases as sales volumeincreases.

The point at which profit is zero is the break-evenpoint. At this point total contribution equals fixed

cost. Below 4,000 units of sales, fixed costs are greater

than total contribution and a loss results.



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Cost-Volume-Profit AnalysisAbove 4,000 units of sale, total contribution is

greater than fixed costs and a profit results.

Note that contribution increases by GH6,000(from 24,000 to 30,000) when sales volumeincreases from 4,000 to 5,000 units.

Profit also increases by GH6,000 for the same

sales volume range (0 to 6,000), whereas fixedcosts remain unchanged at GH24,000.



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Cost-Volume-Profit Analysis This indicates that the additional contribution

earned per unit is also the extra profit earned perunit.

This is a useful tool in profit planning.

For example, the increase in profit where sales risefrom 5,000 to 5,400 units can be measured as (400units x 6.00 = 2,400).

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



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Cost-Volume-Profit Analysis Check: Sales Units 5,400 T U Sales Revenue 108,000 20Variable Cost 75,600 14

Contribution 32,400 6 Fixed Cost 24,000 Profit 8,400



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Contribution/Sales Ratio (c/s) This ratio is an alternative to the contribution per

unit as a measure of the rate at which contribution

is being earned. Using the figures in the earlier example, it may be

calculated as: contribution per unit / selling price(c/s) (6/20 = 0.30 or 30%).

This ratio applies at any activity level as long as the basicassumptions of the model remain unchanged. (i.e.

constant selling price and variable cost per unit.)



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Contribution/Sales Ratio (c/s)Where business activity is expanding, the higher the

c/s ratio, the greater the rate at which additionalprofits will be earned.

Where business activity is declining, however, a higherc/s ratio means that profits will fall at a greater rate perunit of lost sales.



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Break-even Analysis Basic Assumptions: Cost can be segregated into two components:

fixedandvariable cost elements. Cost and Revenue behaviour is a linear

relationship over the relevant range of outputlevels. This implies that:Variable cost varies with the level of output. Increases in

output have identical effect on cost as on size per unit. The cost identified as fixed is constant within the range

of output levels considered. The selling price of the product remains unchanged

regardless of the level of sales.



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Break-even Analysis Efficiency in productivity remains unchanged. The analysis of break-even relates to one product

only or where multi-products are produced, it

relates to a constant mix of products. Sales and production units are equal implying that

stock level is zero.Volume is the only factor which affects cost

The prices paid for the resources used byenterprise will not change over the period.



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Break-even Analysis Illustration of Break-even charts.

Traditional Break-even Charts

Modified Break-even Chart Contribution/Volume Chart

Profit/Volume Chart



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Traditional Break-even Chart Example


S

FC

0

C

O

S

T

/

R

E

V

OUTPUT


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Modified Break-even Chart Example


S

0

C

OS

T

/

R

E

V

OUTPUT

FCC


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Profit/Volume Chart Example.


0

P

R

O

F

I

T

L

O

S

S

B/EP

OUTPUT


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Contribution/Volume Chart Example


C

FC

B/E

C

O

N

TR

I

B

U

T

I

O

N

OUTPUT0


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Break-even Analysis Calculating Sales units or value at Break-even and at

specific profit.

Two methods can be used:

Preparing Break-even chart and reading the requiredvalue from it.

Use a formula derived from the revenue function:(Sales Revenue (S) = Variable cost (V) + Fixed cost (F)

+ Profit (P).



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Break-even Analysis Steps in the preparation of Break-even chart:1. Choose suitable scales for the horizontal axis (activity units axis)

and the vertical axis (sales value and cost).2. Plot the point for the maximum sales revenue. Join this point to the

origin (when no units are sold sales revenue is zero). The resultingline is the Sales curve.3. Plot the point for fixed cost on the vertical axis. When sales units are

zero there is no variable cost.4. Plot the total cost point at the maximum units. This is variable cost

plus fixed cost.

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



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Break-even Analysis Deriving formulae from the sales function: S = V + F + P Hence S V = F + P But S V = C So C = F + P By dividing both sides of the equation by Sales

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



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Break-even Analysis From the equation, Sales revenue (S) for any desired level

of profit (P) can be calculated when fixed cost and c/s ratioare known.

For sales revenue at Break-even point,P = 0, hence, S = F / c/s.

C = F + P; but C = Q * c (Total Contribution is equal toQuantity multiplied by contribution per unit.)

To make Q the subject of the equation, C /c = Q; therefore

F + P/c = Q (i e. The Quantity at desired profit) S units = F / c per unit for Break-even quantity.



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ExampleA company has a budget summary as follows:

Fixed cost is GH50,000 Variable cost per unit is GH20

Selling price per unit is GH30

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

Required: Calculate the sales revenue and sales units atwhich the companys budget will show: (a) a break-even

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

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



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Solution (ii) Using formula: or

S at B/E = FC / C/S ratio or FC divided by CS ratio

Cont=sales-vc = 30-20=10

FC= 50,000, CS ratio= 10/30 x 100 =33.3% BE = 50,000/33.3%= 150,000 or 50,000 x 30 = 150,000

10

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

Q = 50,000 = 5,000 units10

S at Profit of 20,000: S = F + P / c/s ratio

S = (50,000 + 20,000) x 3 = 210,000



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

10 S at 10,000 Loss S = (F + P)/c/s ratio S = (50,000 10,000) x 3 = 20,000

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



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Margin of Safety Is the extent to which sales may fall below their

existing level before break-even point is reached.

It may be expressed in units, monetary value or asa percentage of the existing level.

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

It will help management to evaluate alternativeproposed strategies.



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Margin of Safety Example:

KK Ltd. has planned sales of GH600,000 (40,000 @

15 per unit). The variable cost per unit is 10 andthe fixed costs total 150,000.

Required: Calculate the margin of safety expressed interms of sales units, sales value and as a percentage of

current sales.



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Margin of Safety

Solution:

Contribution per unit: 15 - 10 = 5

S = F / c per unit

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

The Margin of Safety may be valued as:

40,000 units 30,000 units = 10,000units

600,000 - 450,000 = 150,000.

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



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Exercise The summary Income Statements of two

companies as at 31 December 2009 were:

A Co . Ltd. B Co. Ltd.

GH GH

Sales Revenue 100,000 100,000

Variable Cost 40,000 50,000

Contribution 60,000 50,000 Fixed Cost 45,000 35,000

Profit 15,000 15,000



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Exercise Required:

Calculate the Break-even Sales for each company.

Calculate the Margin of Safety and

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

times of

(i) high demand

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

produce the same product.

Documents

Accounting for Decn Making C-V-P Analysis L7 (1)