CHAPTER 4 Cost-Volume-Profit Analysis Purpose of Budgeting Planning How many units of input do I need to support a budgeted output? Control Are operations

CHAPTER 4CHAPTER 4CHAPTER 4CHAPTER 4

Cost-Volume-Profit AnalysisCost-Volume-Profit Analysis

Purpose of BudgetingPurpose of Budgeting

Planning• How many units of input do I need

to support a budgeted output? Control• Are operations effective and

efficient? Decision making• How do we decide on a price, and

choose quantity given constraints?

Learning objective 1: Identify common cost behavior patterns

Variable Costs Costs which change directly in

proportion to changes in quantity or activity

Fixed Costs Costs which do not change when

quantity or activity volume changes

Common Cost Behavior Patterns



Mixed Costs Costs that have both variable and

fixed elements

Step Costs Fixed for a range of output, but

increase when upper bound of range is exceeded




Variable CostsVariable Costs

Costs that change in proportion to changes in volume or activity

An automobile manufacturer will need 400 tires to make 100 cars, but 4,000 tires to make 1,000 cars

A bakery will need 2 eggs to make 1 cake and 20 eggs to make 10 cakes

If activity increases by 10%, cost increases by 10%



A company has decided that direct labor costs are 100% variable. Last month total direct labor costs were $125,000 and total direct labor hours worked were 10,000.1.What is the direct labor cost per hour?

$125,000 / 10,000 hours = $12.50 per hour

2.Predict labor costs in a month when 12,000 labor hours are worked

$12.50 per hour × 12,000 hours = $150,000



Total Variable Cost = $91 × Units produced


Fixed CostsFixed Costs

Do not change in response to changes in activity level

Typical fixed costs are depreciation, supervisory salaries, and building maintenance• Rent for a bakery will not double if

output increases from 100 to 200 cakes

Activity increases by 10%, costs remain unchanged



Total fixed cost = $94,000



Discretionary Fixed Costs Management can easily change Advertising, research and

development• Many companies cut back on these costs

when sales drop. This can be shortsighted. Why?

Committed Fixed Costs Cannot be easily changed Rent, insurance



1.What happens to cost per unit when fixed costs remain the same but volume or activity declines?

2.Can you think of another way to set rates to make ratepayers less angry?


LINK TO PRACTICE

Using Less Water but Paying Higher Rates!

Mixed CostsMixed Costs

Contain both variable and fixed cost elements

Can separate mixed costs into variable and fixed components

Salesperson with base salary (fixed) and commission on sales (variable)

Base salary included with fixed costs Commission included with variable

costsLearning objective 1: Identify common cost behavior patterns

Mixed CostsMixed Costs

Total cost = ($91 × Units produced) + $94,000


Step CostsStep Costs

Fixed cost for a specific range

Increases to higher level when upper bound of range is exceeded• Use correct cost when budgeting for a

particular relevant range

Company adds third production shift, cost increase includes supervisory salary


Step CostsStep Costs

Total step costs = $94,000 for relevant range 0 – 3,000 units

produced$144,000 for relevant range 3,001 – 6,000 units$194,000 for relevant range 6,001 – 9,000 units


Direct LaborDirect Labor

Q Is direct labor always a variable cost?

•Are you willing to lay off workers when production declines?•What if the decline is temporary? •What if the decline is permanent?

•Does the degree of automation make a difference in whether direct labor is fixed or variable?


Cost Estimation MethodsCost Estimation Methods

Account Analysis-Classify costs into variable and fixed

pools Scattergraphs

-Can see cost relationships visually High-Low Method

-Linear estimation connects high and low volume observations

Regression Analysis-Linear estimation is best fit to observed

valuesLearning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

Account AnalysisAccount Analysis

Most common approach Requires professional judgment

of management Management classifies costs as

fixed, variable, or mixed• Total variable costs divided by

activity equals variable cost per unit• Variable cost per unit and total fixed

costs can be used in cost equation

Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method



Total cost = ($81.50 Variable cost per unit × Units produced) + $102,000 Fixed costsExpected cost of 2,500 units = ($81.50 × 2,500) + $102,000 = $305,750



ScattergraphsScattergraphs

Utilization of cost information from previous periods

Weekly, monthly, or quarterly cost reports

Plot the actual costs at the observed activity levels• Look for relationship between cost

and activity, linear is ideal• Use relationship to predict future

costsLearning objective 2: Estimate the relation between cost and activity using account analysis and the

high-low method

ScattergraphsScattergraphs

Is there a relationship between units produced and production costs? Describe the relationship.


High-Low MethodHigh-Low Method

Utilization of cost information from previous periods

Connect straight line from lowest activity level to highest activity level• Slope of the line (change in cost

divided by change in activity) equals variable cost per unit

• Total cost at lowest or highest activity level minus variable cost at that level equals fixed cost



Total cost at high

activity level

Total cost at low activity

level






Regression AnalysisRegression Analysis

Statistical technique Estimates the slope and intercept

of a cost equation• Finds the best straight line fit to the

observations Typically statistical software

packages are utilized• Spreadsheet applications like Excel®

typically include statistical operations





Input Y range are the costs. Input X range is the production.




The Relevant RangeThe Relevant Range

Range of activity for which estimates and predictions are expected to be accurate- Accuracy expected only for

production levels within range Difficult to assess costs outside

the relevant range

Learning objective 3: Perform cost-volume profit analysis for single products

The Relevant RangeThe Relevant Range



The Profit Equation

Profit = SP(x) – VC(x) – TFC

Where: x = Quantity of units produced and

sold SP = Selling price per unit VC = Variable cost per unitTFC = Total fixed cost

Fundamental to CVP analysis



Break-Even Point• Number of units sold that allow the company

to neither earn a profit nor incur a loss• $0 = SP(x) – VC(x) – TFC

CodeConnect has the following cost structure

• Selling price $200.00 per unit• Variable cost $90.83 per unit• Total fixed cost $160,285

Find CodeConnect’s break-even point



Break-Even Point$0 = SP(x) – VC(x) – TFC$0 = [$200.00 (x)] – [$90.83(x)] – $160,285$0 = [($200.00 – $90.83)(x)] – $160,285$0 = $109.17(x) – $160,285$109.17(x) = $160,285x = $160,285 / $109.17x = 1,468.21 units Break-even point is 1,469 units (always round

up)


Break-Even PointBreak-Even Point


Gabby’s Wedding Cakes creates elaborate wedding cakes. Each cake sells for $500. The variable cost of baking the cakes is $200 and the fixed cost per month is $6,000

1.Calculate the break-even point in units

$6,000 / ($500 - $200) = 20 cakes

2. How many cakes must be sold to earn a profit of $9,000?

($9,000 + $6,000) / ($500 - $200) = 50 cakes


Margin of SafetyMargin of Safety

The margin of safety is the difference between the expected level of sales and break-even sales

• If breakeven sales for Model DX375 is $293,600 and expected sales are $350,000, calculate the margin of safety.

• The margin of safety is:

$350,000 - $293,600 = $56,400.


3. At Winford Corp., the selling price per lawn mower is $120, variable cost per lawn mower is $55. Fixed costs are $130,000. Expected sales are 4,200 units. The Margin of Safety is?a. $264,000b. $384,000c. $143,000d. $121,000Answer a:Expected sales = 4,200 units X $120 = $504,000Break even sales = 2,000 units X $120 = $240,000Margin of safety = $504,000 – $240,000 = $264,000


http://www.accountingformanagement.com/margin_of_safety.htm

4. At Winford Corp., the selling price per lawn mower is $120, variable cost per lawn mower is $55. Fixed costs are $130,000. Expected sales are 4,200 units. What is profit expected to be?

Answer here: _________________

Margin of safety in units = 4,200 – 2,000 = 2,200

2,200 units × $65 unit CM = $143,000

$143,000


Contribution MarginContribution Margin

Difference between revenue and variable costs

Contribution margin =Total revenue minus total variable costs

Unit contribution margin =Selling price minus variable cost per unit

- The unit contribution margin measures the amount of incremental profit generated by selling an additional unit


Contribution Margin RatioContribution Margin Ratio

The contribution margin ratio measures the amount of incremental profit generated by an additional dollar of sales

Two methods to calculate the contribution margin ratio1. Contribution margin divided by

sales revenue (Sales – TVC) / Sales2. Unit contribution margin divided by

selling price (SP – VC) / SP


Rhetorix, Inc. produces stereo speakers. The selling price per pair of speakers is $800. The variable cost of production is $300 and the fixed cost per month is $50,000.

1.Calculate the unit contribution margin associated with a pair of speakers

$800 – $300 = $500 2.Calculate the contribution margin ratio

for Rhetorix associated with a pair of speakers

($800 – $300) / $800 = 0.625


Contribution MarginContribution Margin Using the contribution margin and the

contribution margin ratioSP = $200.00, VC = $90.83, CM = 200 – 90.83 = $109.17, TFC = 160,285, profit = $40,000

Units to produce = (Profit + TFC) / Unit contribution margin

($40,000 + $160,285) / 109.17 = 1,835 units

Sales required (in dollars) = (Profit + TFC) / Contribution margin ratio

CM ratio = $109.17 / $200.00 = 0.5459($40,000 + $160,285) / 0.5459 = $366,890


Rhetorix, Inc. produces stereo speakers. The selling price per pair of speakers is $800. The variable cost of production is $300 and the fixed cost per month is $50,000.

1.If the company sells five more speakers than planned, what is the expected effect on profit of selling the additional speakers?5 speakers × $500 unit CM = $2,500 profit

2.If the company has sales that are $5,000 higher than expected, what is the expected effect on profit?$5,000 × 0.625 = $3,125Learning objective 3: Perform cost-volume profit analysis for single products

1. At Winford Corp., the selling price per lawn mower is $120, variable cost per lawn mower is $55. Fixed costs are $130,000. Contribution Margin per unit is?

a. $65

b. $75

c. $175

d. $30

Answer a: $120 – $55 = $65


http://www.investorwords.com/1092/contribution_margin.html

2. At Winford Corp., the selling price per lawn mower is $120, variable cost per lawn mower is $55. Fixed costs are $130,000. Break-Even Point in units is?

a. 1,000 units

b. 1,083 units

c. 2,000 units

d. None of these

Answer c: $130,000 / ($120 – $55) = 2,000 units


http://www.investorwords.com/575/break_even_point.html


“What If” Analysis Utilize profit equation to determine

impact of managerial decisions • Change in Fixed and Variable Costs• Change in Selling Price

Taxes in CVP Analysis After tax profit =

[SP(x) – VC(x) – TFC](1 – t)


Multiproduct AnalysisMultiproduct Analysis

Contribution Margin Approach Used if products are similar Identify number of units needed to

be sold to break even• Calculate weighted average contribution

margin based on expected units sold and product mix

• Assume product mix to calculate break-even point and target profit



Learning objective 4: Perform cost-volume profit analysis for multiple products

Rohr Watch CompanyModel A Model B Total

Selling price $2,000 $3,000 Variable cost 800 1,200 Contribution margin $1,200 $1,800 Units produced and sold 4,000 2,000 6,000 Weight 4,000 / 6,000 2,000 / 6,000

Weighted average contribution margin is [(2 × $1,200) + (1 × $1,800)]/3 = $1,400 per unitBreak-even is $3,500,000 / $1,400 = 2,500 unitsBreak-even is 2,500 × (4,000 / 6,000) = 1,667 Model A units (Whole units.)Break-even is 2,500 × (2,000 / 6,000) = 834 Model B units (Whole units.)


Contribution Margin Ratio Approach- Products are substantially different

Calculate total company contribution margin ratio

Use total company contribution margin ratio to compute required sales in dollars



A company with 4 divisions has the following information available:Total sales $6,450,000Total variable costs$4,706,000Total direct fixed costs $1,260,000Total common fixed costs $1,120,0001.Calculate total company contribution

margin($6,450,000 – $4,706,000) / $6,450,000 = .2704

2.Calculate total company break-even sales in dollars.($1,260,000 + $1,120,000) / .2704 = $8,801,775


Assumptions in CVP Analysis

Assumptions in CVP Analysis

Assumptions can affect the validity of the analysis1. Costs can be separated into fixed

and variable components2. Total fixed cost and unit variable

cost do not change over the levels of interest

3. Multiproduct analysis assumes the product mix does not change

Despite assumptions, CVP is useful


Operating LeverageOperating Leverage

Level of fixed versus variable costs in a company

High level of fixed costs has a high operating leverage- Companies with high operating

leverage have large fluctuations in profit when sales increase or decrease

Learning objective 5: Discuss the effect of operating leverage

Fixed vs. Variable CostsFixed vs. Variable Costs

1.Can you think of any ways other than incentive compensation and outsourcing to turn fixed costs into variable costs?

2.Would you rather have fixed or variable costs when revenues are increasing? When revenues are decreasing?

Learning objective 5: Discuss the effect of operating leverage

LINK TO PRACTICE

Fixed Costs Too High—Make Them Variable!

ConstraintsConstraints Constraints on how many items can

be produced- Shortage of space, equipment, or labor

Utilize contribution margin per unit to analyze situations- Calculate contribution margin per unit of

constraint- Produce product with highest contribution

margin per unit of constraint

Linear programming can solve multiple constraints

Learning objective 6: Use the cost per unit of the constraint to analyze situations involving a resource constraint

ConstraintsConstraints

A company can produce Product A or Product B using the same machinery. Only 1,000 machine hours are available

Product A Product BSelling price $500 $300Variable cost 300 200Contribution margin $200 $100Machine hours toproduce one unit 10 hours 2 hoursContribution marginper machine hour $20 $50

Product A has the higher contribution margin, but Product B has the higher contribution margin per machine hour

Learning objective 6: Use the cost per unit of the constraint to analyze situations involving a resource constraint

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CHAPTER 4 Cost-Volume-Profit Analysis Purpose of Budgeting Planning How many units of input do I need to support a budgeted output? Control Are operations