Chapter Four Cost-Volume-Profit Analysis: A Managerial Planning Tool COPYRIGHT © 2012 Nelson...

Chapter FourCost-Volume-Profit Analysis: A Managerial Planning Tool

Chapter FourCost-Volume-Profit Analysis: A Managerial Planning Tool

COPYRIGHT © 2012 Nelson Education Ltd.

Learning ObjectivesLearning Objectives

1. Determine the break-even point in units and sales dollars

2. Determine the number of units that must be sold, and the amount of revenue required to earn a targeted profit

3. Prepare a profit-volume graph and a cost-volume-profit graph and explain the meaning of each

4. Apply cost-volume-profit analysis in a multiple product setting

5. Explain the impact of risk, uncertainty and changing variables on cost-volume-profit analysis


4-2

Determine the break-even point in units and sales dollars

OBJECTIVE OBJECTIVE 11


4-3

Cost-Volume-Profit AnalysisCost-Volume-Profit Analysis

A powerful tool for planning and decision making It can be used to calculate:

The number of units that must be sold to

break-even

The impact of a given reduction in fixed

costs on the break-even point

The impact of an increase in price on

profit


4-4

Break-Even PointBreak-Even Point

Total Revenue = Total Cost

Or put it another way:

Total Revenue- Total Costs Zero Profit


4-5

Using Operating Income in Cost-Volume-Profit AnalysisUsing Operating Income in Cost-Volume-Profit Analysis

Contribution Margin

Sales - Variable Expense

=

Contribution Margin is then used to cover Fixed Costs and Operating Income

Contribution

Margin


4-6

Contribution Margin Income StatementContribution Margin Income Statement

• Divides costs based on behaviour• Costs are divided into variable and fixed

components• Important subtotal is contribution margin

– Sales revenue minus variable expenses


4-7

Using Operating Income in Cost-Volume-Profit AnalysisUsing Operating Income in Cost-Volume-Profit Analysis

Contribution Margin

Sales - Variable Costs

= Contribution

Margin

Break-even point is when Operating Income = 0

Contribution Margin

Fixed Costs

Operating Income

- =


4-8

Cornerstone 4-1Cornerstone 4-1

How to Prepare a Contribution Margin Income Statement


• Whittier Co. plans to sell 1,000 mowers at $400 each in the coming year. Product costs include:– Direct materials per mower $180– Direct labour per mower $100– Variable overhead per mower $25– Total fixed factory overhead $15,000

• Variable selling expense is a commission of $20 per mower; fixed selling and administrative expense totals $30,000

Information:

4-9

ExampleExample

• Calculate the total variable cost per unit• Calculate the total fixed expense for the year• Prepare a contribution margin income statement

for Whittier Co. for the coming year

Required:


4-10

+

Variable CostVariable Cost

Variable Cost Per

unit=

Direct Materials +

Direct Labour

Variable Overhead

Variable Selling

Expense+ +

Variable Cost Per

unit= $180 + $100 $25 $20+

Variable Cost Per

unit= $325


4-11

Fixed ExpensesFixed Expenses

Total Fixed Expenses =

Fixed Overhead +

Fixed Selling & Administrative

Expense

Total Fixed Expenses = $15,000 + $30,000

Total Fixed Expenses = $45,000


4-12

Whittier CompanyContribution Margin Income Statement

For the Coming Year


For the Coming Year

Total Per Unit

Sales ($400 × 1,000 mowers) $400,000 $400

Total variable expense ($325 × 1,000) 325,000 325

Total contribution margin $ 75,000 $ 75

Total fixed expense 45,000

$ 30,000Operating income

Each unit contributes $75 to cover fixed costs


4-13


How to Solve for the Break-Even Point in Units


• Whittier Co. plans to sell 1,000 mowers at $400 each in the coming year. Product costs include:– Direct materials per mower $180– Direct labour per mower $100– Variable overhead per mower $25– Total fixed factory overhead $15,000

• Variable selling expense is a commission of $20 per mower; fixed selling and administrative expense totals $30,000

Information:

4-14

ExampleExample

• Calculate the total variable cost per unit• Calculate the total fixed expense for the year• Calculate the number of mowers that Whittier Co. must

sell to break-even• Check the answer by preparing a contribution margin

income statement based on the break-even point

Required:


4-15

Variable & Fixed CostsVariable & Fixed Costs

Variable Cost Per

unit= $180 + $100 $25 $20+ +

Total Fixed Expenses = $15,000 + $30,000

These were computed in Cornerstone 4-1

= $325

= $45,000


4-16

Break-Even Number of MowersBreak-Even Number of Mowers

Break-even units =

Total Fixed Cost

Contribution Margin per unit

Formula can be simplified down to:

Selling Price – Variable cost per unit


Break-even units =

$45,000

($400 – $325)

Break-even units = 600 mowers

4-17


For the Coming Year based on sales of 600 mowers


For the Coming Year based on sales of 600 mowers

Total Per Unit

Sales ($400 × 600 mowers) $240,000 $400

Total Variable Expense ($325 × 600) 195,000 325

Total Contribution Margin $ 45,000 $ 75

Total Fixed Expense 45,000

$ 0Operating Income

Operating income is zero when 600 units are sold. The break-even calculation is correct!


4-18


How to Calculate the Variable Cost Ratio and the Contribution Margin Ratio


• Whittier Co. plans to sell 1,000 mowers at $400 each in the coming year

• Variable cost per unit is $325

• Total fixed cost is $45,000

Information:

4-19

ExampleExample

• Calculate the variable cost ratio• Calculate the contribution margin ratio using unit

figures• Prepare a contribution margin income statement

based on the budgeted figures for next year– In a column next to the income statement, show the

percentages based on sales for:• Sales• Total variable costs• Total contribution margin

Required:


4-20

Variable Cost RatioVariable Cost Ratio

Variable Cost Ratio =

Variable Cost

Sales

Variable Cost Ratio

=$325$400

Variable Cost Ratio = 81.25%


4-21

Contribution Margin RatioContribution Margin Ratio

Contribution Margin per unit = Sales Variable Cost-

Contribution Margin per unit

= $75 per unit

Sales

Contribution Margin

18.75%Contribution Margin Ratio

Contribution Margin Ratio

=

$75$400= =


4-22


For the Coming Year


For the Coming Year

Total% of Sales

Sales ($400 ×1,000 mowers) $400,000 100.00

Total Variable Exp. (0.8125 × $400,000) 325,000 81.25

Total Contribution Margin $ 75,000 18.75


$ 30,000Operating Income


4-23


How to Solve for the Break-Even Point in Sales Dollars


• Whittier Co. plans to sell 1,000 mowers at $400 each in the coming year

• Variable cost per unit is $325• Total fixed cost is $45,000

Information:

4-24

ExampleExample

• Calculate the contribution margin ratio• Calculate the sales revenue that Whittier Co. must make

to break-even by using the break-even point in sales equation

• Prepare a contribution margin income statement based on the break-even point in sales dollars

Required:


4-25

Contribution Margin RatioContribution Margin Ratio

Contribution Margin per unit = $400 $75 per unit–

18.75%Contribution Margin Ratio

$75$400

= =

$325 =

These were computed in Cornerstone 4-1


4-26

Break-Even Point in Sales DollarsBreak-Even Point in Sales Dollars

Break-even sales =

Total fixed expenses

Contribution margin ratio

Break-even sales = $45,000

0.1875

Break-even sales = $240,000


4-27


For the Coming Year


For the Coming Year

Sales $240,000

Total Variable Exp. (0.8125 × $240,000) 195,000

Total Contribution Margin $ 45,000


Operating Income

Operating Income is zero when sales are $240,000 The break-even calculation is correct!


4-28

$ 0


Determine the number of units that must be sold and the

amount of revenue required to earn a targeted profit


Units to Be Sold to Achieve a Target IncomeUnits to Be Sold to Achieve a Target Income

1. Using Operating Income equation

2. Using the Basic Break-even equation

Two Ways:

Cornerstone 4-5 will walk us through these computations


4-30


How to Solve for the Number of Units to Be Sold to Earn a Target Operating Income


• Whittier Co. sells mulching mowers at $400 each • Variable cost per unit is $325 and total fixed cost is $45,000

Information:

• Calculate the number of units that Whittier Co. must sell to earn operating income of $37,500

• Prepare a contribution margin income statement based on the number of units calculated

Required:

4-31

Units to Be Sold to Achieve a Target IncomeUnits to Be Sold to Achieve a Target Income

Number of units to earn

target income=

Total fixed expense + Target income

Price – Variable cost per unit


target income= $45,000 + $37,500

$400 - $325


target income= 1,100


4-32


For the Coming Year


For the Coming Year

Sales ($400 ×1,100) $440,000

Total variable expense ($325 × 1,100) 357,500

Total contribution margin $ 82,500



The calculation is correct! The operating income is $37,500


4-33


How to Solve for the Sales Needed to Earn a Target Operating Income


• Whittier Co. sells mulching mowers at $400 each • Variable cost per unit is $325 and Total fixed cost is $45,000

Information:

• Calculate the contribution margin ratio• Calculate the sales that Whittier Co. must make to earn an

operating income of $37,500• Prepare a contribution margin income statement based on

the sales dollars calculated

Required:

4-34

Sales Revenue to Achieve a Target IncomeSales Revenue to Achieve a Target Income

Sales dollars to earn target

income=

Fixed Cost + Target Income

Contribution margin ratio


income= $45,000 + $37,500

0.1875


income= $440,000


4-35


For the Coming Year


For the Coming Year

Sales $440,000

Total variable exp. (0.8125 × $440,000) 357,500

Total contribution margin $ 82,500



The calculation is correct! The operating income is $37,500


4-36

Prepare a profit-volume graph and a cost-volume-profit graph

and explain the meaning of each



Profit-Volume GraphProfit-Volume Graph

• Visually portrays the relationship between profits and units sold

• Operating Income is the dependent variable• Units sold is the independent variable


4-38

Cost-Volume-Profit GraphCost-Volume-Profit Graph

• Depicts relationship among cost volume and profits

• Graph two separate lines:– Total revenue– Total cost

• Vertical axis: measured in dollars• Horizontal axis: measured in units sold


4-39

Assumptions of Cost-Volume-Profit AnalysisAssumptions of Cost-Volume-Profit Analysis

• Revenue and cost functions are linear• Price, total fixed costs, and unit variable costs

can be identified and remain constant over relevant range

• All units produced are sold –no changes in inventory levels

• Sales mix is constant• Selling prices and costs are known with certainty


4-40

Linear Cost and Revenue FunctionsLinear Cost and Revenue Functions

Cost-Volume-Profit assumes that cost and revenue functions are linear

In other words they are straight lines


4-41

Production Equal to SalesProduction Equal to Sales

• Cost-Volume-Profit assumes that what is produced is actually sold

• Inventory levels do not change over period• CVP focuses on current costs by excluding

inventory costs of previous periods


4-42

Constant Sales MixConstant Sales Mix

Multiple product break-even analysis requires a constant sales mix

Relative combination of products being sold by a firm

Sales mix is difficult to predict with certainty


4-43

Linear Cost and Revenue FunctionsLinear Cost and Revenue Functions

Firms seldom know prices, variable costs, and fixed costs with certainty

There are formal ways of explicitly building uncertainty into the Cost-Volume-Profit model


4-44

Apply cost-volume-profit analysis in a multiple-product setting



Multiple-Product AnalysisMultiple-Product Analysis

Cost-Volume-Profit analysis becomes more complex with multiple products

We need to adapt the single-product formulas


4-46

Direct & Common Fixed ExpensesDirect & Common Fixed Expenses

Fixed costs that can be traced to each

segment and would be avoided if the

segment did not exist


Direct Fixed Expenses

Fixed costs that are not traceable to the

segments and would remain even if one of

the segments was eliminated

Common Fixed Expenses

4-47

Multiple-Product AnalysisMultiple-Product Analysis

Break-even point in units

Key: identify expected sales mix


• Measured in units sold• Reduced to the smallest possible whole numbers• Required in order to determine break-even point in

units

Sales Mix:

4-48


How to Calculate the Break-Even Units for a Multiple-Product Firm


• Whittier Co. sells two products:– Mulching mowers priced at $400– Riding mowers priced at $800

• The variable costs per unit are:– $325 per mulching mower– $600 per riding mower

• Total fixed expense is $96,250• Whittier’s expected sales mix is three mulching mowers to

two riding mowers

Information:

4-49

ExampleExample

• Form a package of mulching and riding mowers, based on the sales mix, and calculate the package contribution margin

• Calculate the break-even point in units for mulching mowers and for riding mowers

• Check calculations by preparing a contribution margin income statement

Required:


4-50

Package Contribution MarginPackage Contribution Margin

Product

Riding

Price

200

Unit Variable

Cost

Sales Mix

Pkg. Unit Contrib. Margin

Mulching

800

$400 $ 75 3 $225

Package Total $625

Unit Contrib. Margin

$325

600 2 400


4-51

Break-Even Point in UnitsBreak-Even Point in Units

Break-even packages =

Fixed Cost

Package contribution margin

Break-even packages = $96,250

$625

Break-even packages

= 154


4-52

Break-Even Point in UnitsBreak-Even Point in Units

154 Break-even packages

Each package contains:3 mulching mowers, 2 riding mowers

Mulching mowers break-even units

Riding mowers break-even units

= 154 × 3 = 462

= 154 × 2 = 308


4-53

462 × $325


For the Coming Year


For the Coming Year

Sales

Riding TotalMulching

$184,800 $246,400

Total Variable Expense 150,150

$431,200

184,800 334,950

Total Contribution Margin $ 34,650 $ 61,600 $ 96,250

Total Fixed Expense $ 96,250

Operating Income $ 0


308 × $800

462 × $400

4-54


How to Calculate the Break-Even Sales Dollars for a Multiple-Product Firm


• Whittier Co. sells two products that are expected to produce:– Total revenue next year of $1,120,000– Total variable costs of $870,000

• Total fixed costs are expected to equal $96,250

Information:

• The break-even point in sales dollars for Whittier Co.• Check calculations by preparing a contribution margin

income statement

Required:

4-55

CVP AnalysisCVP Analysis


=Expected Contribution Margin

Total Sales Revenue


= $250,000

$1,120,000


= 0.22*

Break-even point in sales dollars

*RoundedCOPYRIGHT © 2012 Nelson Education Ltd.

4-56

CVP AnalysisCVP Analysis

Break-Even Sales =

Fixed Cost


Break-Even Sales = $96,250

0.22

Break-Even Sales

= $437,500

Break-even sales


4-57


For the Coming Year


For the Coming Year

Sales $437,500

Total Variable Exp. (0.78 × 437,500) 341,250

Total Contribution Margin $ 96,250


$ 0Operating Income

Operating income is zero when sales are $437,500 The break-even calculation is correct!


4-58

Explain the impact of risk, uncertainty, and changing variables

on cost-volume-profit analysis



CVP Analysis: Risk and UncertaintyCVP Analysis: Risk and Uncertainty

• The break-even point can be affected by changes in:– Price– Unit Contribution Margin– Fixed Cost


Changes in any of the above will affect the sales mix

4-60

Risk and Uncertainty Effects on ManagersRisk and Uncertainty Effects on Managers

• Must realize the uncertain nature of future prices, costs, and quantities

• Move from consideration of a break-even point to what might be called a “break-even band”

• May engage in sensitivity or what-if analysis


4-61

Margin of SafetyMargin of Safety

• Units sold or revenue earned above break-even volume

• Crude measure of risk– When there is a downturn in sales, the risk of

suffering losses will be less if the firm’s margin of safety is large than if the margin of safety is small


4-62


How to Compute the Margin of Safety


• This year, Whittier Co. plans to sell 1,000 mowers at $400 ea.• Variable costs are $325• Fixed costs are $45,000• Break-even units were previously calculated as 600

Information:

• Calculate the margin of safety for Whittier Co. in units• Calculate the margin of safety for Whittier Co. in sales

revenue

Required:

4-63

Margin of Safety in UnitsMargin of Safety in Units

Margin of safety in units =

Sales in units

- Break-even units

Margin of safety in units = 1,000 600

Margin of safety in units = 400

-


4-64

Margin of Safety in Sales RevenueMargin of Safety in Sales Revenue

Margin of safety in sales revenue = Sales - Break-even

units

Margin of safety in sales revenue = $400(1,000) $400(600)

Margin of safety in sales revenue = $160,000

-


4-65

Operating LeverageOperating Leverage

• Relative mix of fixed costs to variable costs• Higher proportions of fixed costs to the amount of

variable costs create higher operating leverage• The greater the degree of operating leverage, the

larger the effect on operating income when sales change

Degree of operating leverage

=Contribution margin

Operating income


4-66


How to Compute the Degree of Operating Leverage


• This year, Whittier Co. plans to sell 1,000 mowers at $400 ea.• Variable costs are $325• Fixed costs are $45,000• Operating Income at 1,000 units is $30,000

Information:

Required:• Calculate the degree of operating leverage for Whittier Co.

4-67

Operating LeverageOperating Leverage

Degree of operating leverage

=Contribution Margin

Operating Income

Degree of operating leverage = ($400 - $325)(1,000 units)

$30,000

Degree of operating leverage = 2.5

Degree of operating leverage (DOL) can be measured for a given level of sales


4-68


How to Compute the Impact of Increased Sales on Operating Income Using the DOL


• Whittier Co. plans to sell 1,000 mowers and earn operating income equal to $30,000 next year

• Whittier’s degree of operating leverage is equal to 2.5• Now, the company plans to increase sales by 20 percent

next year

Information:

4-69

ExampleExample

• Calculate the percent change in operating income expected by Whittier Co. for the next year using the degree of operating leverage

• Calculate the operating income expected by Whittier Co. next year using the percent change in operating income calculated in the above requirement

Required:


4-70

Percentage Change in Operating LeveragePercentage Change in Operating Leverage

Percent change in operating leverage = DOL × Percent change

in sales

Percent change in operating leverage = 2.5 20%

Percent change in operating leverage = 50%

×


4-71

Expected Operating IncomeExpected Operating Income

Expected operating income

=Original

operating income

+ (percent change × original operating income)


= $30,000 (0.50 × $30,000)


= $45,000

+


4-72

Chapter Four Cost-Volume-Profit Analysis: A Managerial Planning Tool COPYRIGHT © 2012 Nelson...

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Transcript of Chapter Four Cost-Volume-Profit Analysis: A Managerial Planning Tool COPYRIGHT © 2012 Nelson...