Chapter 14 - Co.it Analysis

Larson, Wild, Chiapetta, Ropidah, Haslinda, Aryati, Liana © The McGraw-Hill Companies, Inc., 2007

Cost-Volume-Profit Analysis

Chapter

1414 100 Shares

$1 par value

CVP Analysis???


Describe different types of cost

behavior in relation to

production and sales volume.

Determine cost estimates using

three different methods.

Compute the break-even point

for a single product company.

Graphs costs and sales for a

single product company.

Learning ObjectivesLearning Objectives

Identify assumptions in cost

volume profit analysis and

explain their impact.

Describe several applications

of cost-volume–profit analysis.

Compute break-even point

for a multiproduct company.

Analyze changes in sales

using the degree of operating

leverage.


CVP analysis is used to answer questionssuch as:• How much must I sell to earn my desired

income?• How will income be affected if I reduce

selling prices to increase sales volume?• How will income be affected if I change the

sales mix of my products?

CVP analysis is used to answer questionssuch as:• How much must I sell to earn my desired

income?• How will income be affected if I reduce

selling prices to increase sales volume?• How will income be affected if I change the

sales mix of my products?

Questions Addressed byCost-Volume-Profit Analysis

Questions Addressed byCost-Volume-Profit Analysis


• Refers to the manner in which a cost changes as a related activity changes.

• 3 common classifications: Fixed Cost Variable Cost Mixed Cost

Identifying Cost BehaviorIdentifying Cost Behavior

Larson, Wild, Chiapetta, Ropidah, Haslinda, Aryati, Liana © The McGraw-Hill Companies, Inc., 2007Volume (units produced)

Cos

t ($)

• Total fixed costs remain unchanged when activity

changes.• Eg: Factory Insurance, Factory Rent

Your monthly rent for a factory buildings does not

change at any level of production.

Total Fixed CostTotal Fixed Cost


Volume (units produced)

Cos

t ($)

• Fixed costs per unit decline as activity increases.

Your average cost perunit decreases as

production increases.

Fixed Cost Per UnitFixed Cost Per Unit



Cos

t ($)

• Total variable costs change when activity changes.

• Eg: Direct materials, Direct labor

Your direct materials cost changes with the level of

productions

Total Variable CostTotal Variable Cost



Cos

t ($)

• Variable costs per unit do not change as activity

increases.

Variable Cost Per UnitVariable Cost Per Unit

Your average cost perunit doest not change at any level of production.


Mixed Cost Mixed Cost

• Mixed cost includes both fixed and variable cost components. It is greater than zero when volume is zero, but increases when production is increased.

• Eg: Utility charge

Facility costs is incurred even when facility is unused, and

increases with usage.


Variable

Utility Charge


Cos

t ($

)

Total mixed cost

Fixed Monthly

Utility Charge

Total Mixed CostsTotal Mixed Costs


Volume (unit produced)

Co

st

Total cost remainsconstant within anarrow range of

activity.

Step-Wise CostsStep-Wise Costs


Co

st

Total cost increases to a new higher cost for the next

higher range of activity.

Step-Wise CostsStep-Wise Costs

Volume (unit produced)


• Costs that increase when production increases, but in a nonlinear manner.


Cos

t ($)

Curvilinear CostsCurvilinear Costs


• The objective is to classify all costs as either fixed or variable.

• Analysis of past cost behavior is required in order to identify costs.

• 3 different methods can be used to determine cost estimates:

1. Scatter Diagram2. High-Low Method3. Least-Squares Regression

Measuring Cost BehaviorMeasuring Cost Behavior


Plot the data points on a graph (total cost vs. activity).

0 1 2 3 4

*

Tot

al C

ost

in1,

000’

s of

Dol

lars

10

20

0

***

**

**

*

*

Volume, 1,000’s of Units Produced

Scatter DiagramScatter Diagram

• The Scatter Diagram Method estimates costs on a visual fit on the cost line.


Draw a line through the plotted data points so that about equal numbers of points fall above and below the line.

Estimated fixed cost = 10,000

0 1 2 3 4

*

Tot

al C

ost

in1,

000’

s of

Dol

lars

10

20

0

***

**

**

*

*




Vertical distance

is the change in cost.

Horizontal distance is the change in activity.

Unit Variable Cost = Slope = in costin units

0 1 2 3 4

*

Tot

al C

ost

in1,

000’

s of

Dol

lars

10

20

0

***

**

**

*

*




High-Low MethodHigh-Low Method• The High-Low Method cost estimates from the high-low

method are based only on costs corresponding to the lowest and highest sales.

0 1 2 3 4

*

Tot

al C

ost

in1,

000’

s of

Dol

lars

10

20

0

***

**

**

*

*


High-Low line of cost behavior

Estimated fixed cost


The following relationships between salesand costs are observed:

Using these two levels of activity, compute: the variable cost per unit. the total fixed cost.

Sales Cost

High activity level 67,500$ 29,000$ Low activity level 17,500 20,500 Change 50,000$ 8,500$

High-Low MethodHigh-Low Method


Unit variable cost = = = $0.17 per unitin costin units

$8,500$50,000

Sales Cost


The High-Low MethodThe High-Low Method


Sales Cost


Unit variable cost = = =$0.17 per unit

Fixed cost = Total cost – Total variable

in costin units

$8,500$50,000



Sales Cost


Unit variable cost = = = $0.17 per unit

Fixed cost = Total cost – Total variable cost

Fixed cost = $29,000 – ($0.17 per sales $ × $67,500)

Fixed cost = $29,000 – $11,475 = $17,525

in costin units

$8,500$50,000



Least-Squares RegressionLeast-Squares Regression• The least-squares regression method is a statistical technique and uses all data

points.• It is commonly used with computer software because of the large number of

calculations required.

0 1 2 3 4

*

Tot

al C

ost

in1,

000’

s of

Dol

lars

10

20

0

***

**

**

*

*


Regression Line of Cost Behavior

Estimated fixed cost


• The break-even point (expressed in units of product or dollars of sales) is the unique sales level at which a company earns neither a profit nor incurs a loss which total revenues equal to total costs.

• To compute a break even point in terms of sales unit, we divide total fixed costs by the contribution margin per unit.

• To compute a break even point in terms of sales dollars, we divide total fixed costs by the contribution margin ratio.

Break Even AnalysisBreak Even Analysis


• Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue.

• Contribution margin can be expressed in 3 ways:

1.Total contribution margin in dollars.

2.Unit contribution margin (dollars per unit)

3.Contribution margin ratio (%)

• Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue.

• Contribution margin can be expressed in 3 ways:

1.Total contribution margin in dollars.

2.Unit contribution margin (dollars per unit)

3.Contribution margin ratio (%)

Contribution MarginContribution Margin


Contribution Margin Per UnitContribution Margin Per Unit

• Selling price per unit less unit variable cost.

• Dollar from each unit of sales available to cover

fixed cost and income from operation.

• Useful when increase / decrease in sales volume

is measured in sales unit (quantity)Contribution Margin per Unit = Selling price per unit –

Variable cost per unit.

Contribution Margin per Unit = Selling price per unit –

Variable cost per unit.


Contribution Margin RatioContribution Margin Ratio

• Contribution margin per unit divide by selling price per unit.• It measures the effect on income from operations of an increase or a decrease in sales volume.• Useful when sales volume is measured in sales dollars.

Contribution Margin = Unit Selling price – Variable cost per unit.

Ratio Selling price per unit

Contribution Margin = Unit Selling price – Variable cost per unit.

Ratio Selling price per unit


Computing Break-Even PointComputing Break-Even Point

We have just seen one of the basic CVP relationships – the break-even computation.

Break-even point in units = Fixed costs

Contribution margin per unit


The break-even formula may also be expressed sales dollars.


Break-even point in dollars = Fixed costs

Contribution margin ratio



Total Unit

Sales Revenue (2,000 units) 100,000$ 50$

Variable costs (60,000) (30)

Contribution margin 40,000$ 20$

Fixed costs (30,000)

Profit for the period 10,000$


How much contribution margin must this company have to cover its fixed costs (break even)?

Answer: $30,000


Total Unit







How many units must this company sell to cover its fixed costs (break even)?

Answer: $30,000 ÷ $20 per unit = 1,500 units


Total Unit







ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to

break even?

a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units


break even?

a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units

Computing Break-Even Point – Illustration 1




break even?

a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units


break even?

a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units

Unit contribution = $5.00 - $3.00 = $2.00

Fixed costsUnit contribution =

$200,000$2.00 per unit

= 100,000 units



Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; Selling price per unit is $5.00; and unit

variable cost is $3.00.

a. $200,000

b. $300,000

c. $400,000

d. $500,000



a. $200,000

b. $300,000

c. $400,000

d. $500,000






a. $200,000

b. $300,000

c. $400,000

d. $500,000



a. $200,000

b. $300,000

c. $400,000

d. $500,000

Unit contribution = $5.00 - $3.00 = $2.00

Contribution margin ratio = $2.00 ÷ $5.00 = .40

Break-even revenue = $200,000 ÷ .4 = $500,000



Volume in Units

Cos

ts a

nd R

even

uein

Dol

lars Total fixed costs

Total costs

Draw the total cost line with a slopeequal to the unit variable cost.

Plot total fixed costs on the vertical axis.

Preparing a CVP ChartPreparing a CVP Chart


Sales

Volume in Units

Cos

ts a

nd R

even

ue (

$) Starting at the origin, draw the sales line

with a slope equal to the Selling price per unit.

Preparing a CVP ChartPreparing a CVP Chart

Break-even Point

Total costsTotal fixed costs


A limited range of activity called the relevant range, where CVP relationships are linear. Selling price per unit remains constant.

Variable costs per unit remain constant.

Total fixed costs remain constant.

Production = sales (no inventory changes).

Assumptions of CVP AnalysisAssumptions of CVP Analysis


Profit (pretax) = Sales – Variable costs – Fixed costsProfit (pretax) = Sales – Variable costs – Fixed costs

Sensitivity AnalysisSensitivity Analysis

• Cost-Volume-Profit Analysis can be used to predict what can happen under alternatives strategies concerning sales volume, selling prices, variable costs or fixed costs.


Rydell expects to sell 1,500 units at $100 each next month. Fixed costs are $24,000 per month and the unit variable cost is $70. What amount of income should Rydell expect?

Profit (pretax) = Sales – Variable costs – Fixed costs

= [1,500 units × $100] – [1,500 units × $70] – $24,000

= $21,000

Profit (pretax) = Sales – Variable costs – Fixed costs

= [1,500 units × $100] – [1,500 units × $70] – $24,000

= $21,000

Computing Profit from Expected Sales – Illustration 1

Computing Profit from Expected Sales – Illustration 1


Unit sales = Fixed costs + Target profitContribution margin per unit

Dollar sales = Fixed costs + Target profit


Computing Sales for a Target ProfitComputing Sales for a Target Profit

Break-even formulas may be adjusted to show the sales volume needed to earn

any amount of income.



earn income of $40,000?

a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units



a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units

Computing Sales for a Target Profit – Illustration2

Computing Sales for a Target Profit – Illustration2




a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units



a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units = 120,000 units

Unit contribution = $5.00 - $3.00

= $2.00

Fixed costs + Target profit Unit contribution

$200,000 + $40,000 $2.00 per unit

Computing Sales for a Target ProfitComputing Sales for a Target Profit


Dollar sales =

Fixed Target Incomecosts profit taxes


+ +

Computing Sales (Dollars) for aTarget Profit


Target profit is income after income tax.


To convert target profit to before-tax profit, use the following formula:

Before-tax profit = Target profit

1 - tax rate




Rydell has a monthly target profit of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent.

What is Rydell’s before-tax profit andincome tax expense?

Computing Sales (Dollars) for aTarget Profit – Illustration 1



Before-tax profit = Target profit

1 - tax rate

Before-tax profit = = $24,000$18,000

1 - .25

Income tax = .25 × $24,000 = $6,000


What is Rydell’s before-tax profit andincome tax expense?





What monthly sales revenue will Rydellneed to earn the target profit?




Dollar sales =



+ +

Dollar sales = = $160,000

$24,000 + $18,000 + $6,00030%


What monthly sales revenue will Rydellneed to earn the target profit?




The formula for computing dollar sales may be used to compute unit sales by substituting contribution per

unit in the denominator.

The formula for computing dollar sales may be used to compute unit sales by substituting contribution per

unit in the denominator.

Contribution margin per unitUnit sales =


+ +

Unit sales = = 1,600 units$24,000 + $18,000 + $6,000

$30 per unit

Formula for Computing Sales (Units)for a Target Profit

Formula for Computing Sales (Units)for a Target Profit


• Margin of safety is the amount by which sales may decline before reaching break-even sales.

• Margin of safety may be expressed as a percentage of expected sales.

Computing the Margin of SafetyComputing the Margin of Safety

Margin of safety Expected sales - Break-even sales percentage Expected sales

=



=

If Rydell’s sales are $100,000 and break-even sales are $80,000, what is the margin of safety

in dollars and as a percentage?

Computing the Margin of Safety – Illustration

Computing the Margin of Safety – Illustration


If Rydell’s sales are $100,000 and break-even sales are $80,000, what is the margin of safety in dollars and as a percentage?

Margin of safety = $100,000 - $80,000 = $20,000


=

Margin of safety $100,000 - $80,000 percentage $100,000

= = 20%

Computing the Margin of SafetyComputing the Margin of Safety


The CVP formulas may be modified for use when a company sells more than one product. • The unit contribution margin is replaced with the

contribution margin for a composite unit.

• A composite unit is composed of specific numbers of each product in proportion to the product sales mix.

• Sales mix is the ratio of the volumes of the various products.

Computing MultiproductBreak-Even Point



The resulting break-even formula for composite unit sales is:

Break-even pointin composite units

Fixed costsContribution marginper composite unit

=

Consider the following example:




Hair-Today offers three cuts as shown below. Annual fixed costs are $96,000. Compute the break-even point in composite units and in number of units for

each haircut at the given sales mix.

Haircuts Basic Ultra Budget

Selling Price 10.00$ 16.00$ 8.00$ Variable Cost (6.50) (9.00) (4.00) Unit Contribution 3.50$ 7.00$ 4.00$ Sales Mix Ratio 4 2 1

Computing MultiproductBreak-Even Point - Illustration

Computing MultiproductBreak-Even Point - Illustration


Hair-Today offers three cuts as shown below. Annual fixed costs are $96,000. Compute the break-even point in composite units and in number of units for

each haircut at the given sales mix.

Haircuts Basic Ultra Budget

Selling Price 10.00$ 16.00$ 8.00$ Variable Cost (6.50) (9.00) (4.00) Unit Contribution 3.50$ 7.00$ 4.00$ Sales Mix Ratio 4 2 1

A 4:2:1 sales mix means that if there are 500 budget cuts, then there will be 1,000 ultra cuts,

and 2,000 basic cuts.




HaircutsBasic Ultra Budget

Selling Price $10.00 $16.00 $8.00Variable Cost (6.50) (9.00) (4.00) Unit Contribution $3.50 $7.00 $4.00Sales Mix Ratio × 4 × 2 × 1

14.00$ 14.00$ 4.00$

Step 1: Compute contribution margin per composite unit.




HaircutsBasic Ultra Budget

Selling Price $10.00 $16.00 $8.00Variable Cost (6.50) (9.00) (4.00) Unit Contribution $3.50 $7.00 $4.00Sales Mix Ratio × 4 × 2 × 1Weighted Contribution 14.00$ + 14.00$ + 4.00$ = 32.00$

Contribution margin per composite unit

Step 1: Compute contribution margin per composite unit.






=

Step 2: Compute break-even point in composite units.






=

Step 2: Compute break-even point in composite units.


$96,000$32.00 per

composite unit

=


= 3,000 composite units




Sales CompositeProduct Mix Cuts Haircuts

Basic 4 × 3,000 = 12,000Ultra 2 × 3,000 = 6,000

Budget 1 × 3,000 = 3,000

Step 3: Determine the number of each haircut that must be sold to break even.




Step 4: Verify the results.

Multiproduct Break-EvenIncome Statement

Multiproduct Break-EvenIncome Statement

HaircutsBasic Ultra Budget Combined

Selling Price 10.00$ 16.00$ 8.00$ Variable Cost (6.50) (9.00) (4.00) Unit Contribution 3.50$ 7.00$ 4.00$ Sales Volume × 12,000 × 6,000 × 3,000 Total Contribution 42,000$ 42,000$ 12,000$ 96,000$

Fixed Costs 96,000 Profit $ 0


Contribution margin ($) Pretax profit

= Degree of operating leverage

Degree of Operating LeverageDegree of Operating Leverage

• A measure of the extent to which fixed costs are being used in an organization.• Also used to measure the impact of changes in sales on income from operation.• A high operating leverage indicates that a small increase in sales will yield a large percentage increase in income


$48,000 $24,000

= 2.0

Contribution margin Profit

= Degree of operating leverage

If Rydell increases sales by 10percent, what will the percentage

increase in income be?

Operating Leverage - IllustrationOperating Leverage - Illustration

Rydell Company

Sales (1,600 units) 160,000$ Variable expenses (112,000)

Contribution margin 48,000 Fixed expenses (24,000)



Percent increase in sales 10%

Degree of operating leverage × 2

Percent increase in income 20%

Operating LeverageOperating Leverage

Rydell Company

Sales (1,600 units) 160,000$ Variable expenses (112,000)

Contribution margin 48,000 Fixed expenses (24,000)



End of Chapter 14End of Chapter 14

Chapter 14 - Co.it Analysis

Documents

Transcript of Chapter 14 - Co.it Analysis