03 CVP Analysis - Apuntes tema 3 PDF

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07/10/2019

Topic 3: Breakeven Point. Cost-Volume-Profit Analysis

Cost Accounting I Department of Economics and Business Universitat Pompeu Fabra

Topic 3: Breakeven Point. Cost-VolumeProfit Analysis - Outline  Cost-Volume-Profit (CVP) Analysis – Definition  CVP –Terminology and Assumptions  Breakeven Point  Equation Method  Contribution Margin Method  Graph Method

 Sensitivity Analysis – Margin of Safety  Cost planning and CVP 2

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Cost-Volume-Profit Analysis - Definition  … examines the behavior of total revenues, total costs, and

operating profit as changes occur in    

the output level, the selling price, the variable costs, or the fixed costs.

 CVP Analysis General case many many various (short-run, long-run, product life cycles)

CVP-Factors revenue drivers cost drivers time period

Special case single (output units) single (output units) short-run (typically less than 1 year, in which fixed costs do not change within the relevant range)

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CVP – Terminology  CVP-Terminology  Total costs = Variable costs + Fixed costs  Operating profit = Total revenues – Total costs  Net profit = Operating profit – Income Taxes  USP … unit selling price  UVC … unit variable cost  UCM … unit contribution margin (USP – UVC)  CM % … contribution margin percentage UCM  FC … fixed costs

USP

 Q … quantity of output units

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CVP – Assumptions  Main CVP-Assumptions  Total costs can be divided into fixed part and variable part depending on

level of output.  Total revenues and total costs are linear in relation to output units within

relevant range.  Unit selling price, unit variable costs and fixed costs are known.  Analysis for a single product or a constant sales-mix.  Number of output units is the only revenue and cost driver.

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The Breakeven Point  Definition  Quantity of output where total revenues and total costs are equal;

that is, where operating profit is zero.

 Calculation  Equation method  Contribution Margin Method  Graph Method

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The Breakeven Point – Equation Method  Revenues – Variable costs – Fixed Costs = Operating profit

(USP*Q) – (UVC*Q) – FC = OP;

at breakeven ponint OP = zero.

 Breakeven number of units

Q (USP – UVC) = FC Q=

FC (USP  UVC )

 Breakeven in revenue €

Breakeven number of units * USP FC *USP FC FC FC    UVC VC (USP  UVC) (USP  UVC) 1 1 Sales USP USP

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Graphical Illustration 

Revenues

Total revenues

1500

Breakeven point

Profits

1000

400

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Total costs

Losses

5

10

15

Activity

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The Breakeven Point – Contribution Margin Method  Revenues – Variable costs – Fixed Costs = Operating profit

(USP*Q) – (UVC*Q) – FC = OP;

at breakeven ponint the OP = zero.

 Breakeven number of units

Q (USP – UVC) = FC Q=

FC UCM

 Breakeven in revenue €

Breakeven number of units (Q) * USP = = 9

FC *USP UCM

FC FC  UCM CM % USP

Graphical Illustration  Profits

400 Breakeven point Profits 0 5

10

15

Activity

Losses

400

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•Slope = UCM •UCM = 0 => loss = FC •UCM is first used to cover the fixed costs. •After reaching the BP => profits = CM

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Graphical Illustration – Changes in VC  Profits

UCMa < UCMb 400

BP with UCMb

0 5

15

10

Activity

BP with UCMa

400

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Graphical Illustration – Changes in FC  Profits

UCMc < UCMd 400

BP with CMUd

0 5

10

15

Activity

BP with CMUc 400 450 12

• Scrutinize if changes in FC are accompanied by movements in VC. • FC increase • Larger losses at low activity levels. • UCM increase makes us recuperate FC faster.

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Sensitivity Analysis – Margin of Safety  Sensitivity Analysis  A “what-if ”-technique examining how a result will change if the original

predicted data are not achieved or if an assumption changes. Example: What will operating profit be if unit variable costs increase by 5 %?

 Margin of Safety  Indicates by how much sales may decrease before resulting in a loss.  Calculation  Absolute: Expected sales – breakeven sales  In %:

( Expected s ales  breakeven sales ) Expected sales

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The Breakeven Point in a multiproduct situation  There is no unique breakeven number of units for a multiple-

product situation.

 Two possible methods are: I. Assume a constant mix of sales II. Use the lowest and highest UCM product to give a range of sales  The first method (assuming no changes in budgeted sales mix at

different levels of total unit sales) can be done in two ways:  Equation method (Ia)  Contribution margin method (Ib)

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A simple example Pen

Marker

Pencil

USP

17

17

8

UVC

(11)

(12)

(5)

UCM

6

5

3

 FC = 35,000 €  For each box with markers, we sell 2 with pens and 3 with pencils.  BP = ? 15

Method Ia – equation method (mix unit)  We define a fictitious mix unit through the combination of sales => 2 /

1 / 3.  CM (mix) = (2 x 6) + (1 x 5) + (3 x 3) = 26 € / mix units  BP = FC / CM mix unit = 35,000 / 26 = 1,347 mix units

 This means that we must sell:  Pens: 1,347 x 2 = 2,694 boxes  Markers: 1,347 x 1 = 1,347 boxes  Pencils: 1,347 x 3 = 4,041 boxes

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Method Ia – equation method (mix unit) Pen

Marker

Pencil

Total

Revenues

17*2,694 =45,798

17*1,347 =22,899

8*4,041= 32,328

101,025

VC

(11)*2,694 =29,634

(12)*1,347 =16,164

(5)*4,041 =20,205

(66,003)

CM

16,164

6,735

12,123

~ 35,000

FC

(35,000)

OP

0

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Method Ia – equation method (mix unit)  To reach a targeted operating profit, say 30,000 €, we must sell the

following quantity (Q):

Q = (FC + OP) / CM (mix) = (35,000 + 30,000) / 26 = 2,500 mix units  This means that we must sell:  Pens: 2,500 x 2 = 5,000 boxes  Markers: 2,500 x 1 = 2,500 boxes  Pencils: 2,500 x 3 = 7,500 boxes

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Method Ib – contribution margin method  Calculate the weighted-average contribution margin per unit

for all products (A, B, …) together:  Breakeven point: (UCM * N o . of units sold )  (UCM * N o. of units sold )  (...) No . of units sold  No . of units sold  ... A

A

B

A

 Breakeven point for each product:

B

B

Fixed Costs Weighted average CM

 Ratio of units sold for each product x Breakeven point 19

Method Ib – contribution margin method  For the previous example:  CM weighted = (6 x 2/6) + (5 x 1/6) + (3 x 3/6) = 4.33 €/unit  BP = 35,000 / 4.33 = 8,083 units (total boxes to sell)  This means that we must sell:  Pens: 8,083 x 2/6 = 2,694 boxes  Markers: 8,083 x 1/6 = 1,347 boxes  Pencils: 8,083 x 3/6 = 4,041 boxes

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Method II – range of sales  We take the product with the lowest UCM  calculate “highest

breakeven sales”

 We take the product with the highest UCM  calculate “lowest

breakeven sales”

 Breakeven sales with a typical mix of sales will be in that range.

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Method II – range of sales  For previous example:  Lowest UCM: pencils (UCM =3)  BP = 35,000 / 3 = 11,666

pencils

 Highest UCM: pens (UCM =6)  BP = 35,000 / 6 = 5,833 pens

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Graphical Illustration Profits

35000 BP (if we only sell pens)

0

BP (if we only sell pencils)

5833

11666

Activity

Possible BP

35000

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Operating Leverage  Useful to express relationships between VC and FC.  OL = CM / OP

Firm 1 R VC

10,000 (5,000)

Firm 2 10,000 (3,000)

CM

5,000

7,000

FC OP

(3,000) 2,000

(5,000) 2,000

 OL (F1) = 5,000 / 2,000 = 2.5  OL (F2) = 7,000 / 2,000 = 3.5 o If sales increase by 10%: o Profit F1 increases by: 10% x 2.5 = 25% 24

o Profit E2 increases by: 10% x 3.5 = 35%

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Operating Leverage Firm 1

Firm 1 + 10% extra sales

R

10,000

11,000

VC CM

(5,000) 5,000

(5,500) 5,500

FC OP

(3,000) 2,000

(3,000) 2,500

 Profit F1 increases by: 10% x 2.5 = 25%  2,000 x 1.25 = 2,500

(VC also increase!) 25

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