managerial accounting chapter 2 slides

© 2012 McGraw-Hill Education (Asia)

Cost Behaviour

Topic 3A

McGraw-Hill Education (Asia) Slide 2

Preview of This Week’s Class

Classify costs by behaviour and use it to answer the

following questions:

How will my profits change if I change my selling price,

volume, or costs?

Breakeven and target profit analysis (this week)

How can the income statement be presented for better

control purposes?

Variable costing vs. absorption costing (next week)


Topic 3A Learning Objectives

1. Understand various types of cost behaviour

Variable

Fixed

Mixed

2. Use various methods to analyze cost behaviour

Scattergraph Method

High-low Method

Least Squares Regression Method


Learning Objective 1

Understand Various Types

of Cost Behaviour:

Variable, Fixed and Mixed.


Cost Classifications for Predicting Cost

Behavior (Recap)

Behavior of Cost (within the relevant range)

Cost In Total Per Unit

Variable Total variable cost changes Variable cost per unit remains

as activity level changes. the same over wide ranges

of activity.

Fixed Total fixed cost remains Average fixed cost per unit goes

the same even when the down as activity level goes up.

activity level changes.


The Activity Base (also called a cost driver)

Activity Base:

A measure of what causes the incurrence of a variable

cost

Variable costs Activity base (cost driver)

Direct materials Number of units produced

Equipment maintenance cost Number of machine hours

Direct labor cost/Employee fringe

benefits

Number of labor hours

Delivery/Shipping cost Number of miles driven


Relevant

Range

A straight line

closely

approximates a

curvilinear

variable cost

line within the

relevant range.

Activity

Tota

l C

ost

Economist’s

Curvilinear Cost

Function

The Linearity Assumption and the Relevant Range

Accountant’s Straight-Line

Approximation (constant unit

variable cost)

A relevant range is the range of activity within which the assumptions

made about cost behaviors are reasonably valid


Volume

Cost

1a. True Variable Costs

The amount of a true variable cost used during the

period varies in direct proportion to the activity level.

The apps download charge on a cell phone bill was

one example of a true variable cost.

Direct material is

another example

of a cost that

behaves in a true

variable pattern.


1b. Step-Variable Costs

A step-variable cost is a resource that is obtainable only

in large chunks (such as maintenance workers) and

whose costs change only in response to fairly wide

changes in activity.

Volume

Cost

E.g., A maintenance worker is

required for every 1,000 units

of production



Small changes in the level of production are not

likely to have any effect on the number of

maintenance workers employed.

Volume

Cost



Volume

Cost

Only fairly wide changes

in the activity level will

cause a change in the

number of maintenance

workers employed.


Examples

Advertising and Research and Development

Examples

Depreciation on Buildings and Equipment and Real

Estate Taxes

2. Types of Fixed Costs

Discretionary

May be altered in the short-term by current managerial decisions

Committed

Long-term, cannot be significantly reduced in

the short term.


2. Fixed Costs and the Relevant Range

Fixed costs would increase

in a step fashion at a rate of

$30,000 for each additional

1,000 square feet.

For example, assume office space is available at

a rental rate of $30,000 per year in increments of

1,000 square feet.


Rent

Cost

in T

housands

of

Dolla

rs

0 1,000 2,000 3,000

Rented Area (Square Feet)

0

30

60


90

Relevant

Range

The relevant range

of activity for a fixed

cost is the range of

activity over which

the graph of the

cost is flat.


How does this

step-function

pattern differ from a

step-variable cost?

Step-variable costs can be adjusted more quickly as conditions

change and . . .

The width of the activity steps is much wider for

the fixed cost.



Is Labor a Variable or a Fixed Cost?

The behavior of wage and salary costs can differ

across countries, depending on labor regulations,

labor contracts, and custom.

In France, Germany, China, and Japan, management has

little flexibility in adjusting the size of the labor force.

Labor costs are more fixed in nature.

In the United States and the United Kingdom, management

has greater latitude. Labor costs are more variable in nature.

Within countries managers can view labor costs differently

depending upon their strategy. Most companies in the

United States continue to view direct labor as a variable cost.


Quick Check

Which of the following statements about

cost behavior are true?

a. Fixed costs per unit vary with the level of

activity.

b. Variable costs per unit are constant within the

relevant range.

c. Total fixed costs are constant within the

relevant range.

d. Total variable costs are constant within the

relevant range.


Fixed Monthly

Utility Charge

Variable

Cost per KW

Activity (Kilowatt Hours)

To

tal U

tilit

y C

ost

X

Y

A mixed cost (also called semi-variable cost)

contains both variable and fixed elements.

Consider the example of utility cost.

3.Mixed Costs


3.Mixed Costs

The total mixed cost line can be expressed

as an equation: Y = a + bX

Where: Y = The total mixed cost.

a = The total fixed cost (the

vertical intercept of the line).

b = The variable cost per unit of

activity (the slope of the line).

X = The level of activity.

Fixed Monthly

Utility Charge

Variable

Cost per KW

Activity (Kilowatt Hours)

To

tal U

tilit

y C

ost

X

Y


3.Mixed Costs – An Example

If your fixed monthly utility charge is $40, your

variable cost is $0.03 per kilowatt hour, and your

monthly activity level is 2,000 kilowatt hours, what is

the amount of your utility bill?


Analysis of Mixed Costs

In account analysis, each account is

classified as either variable or fixed based

on the analyst’s knowledge of how

the account behaves.

The engineering approach classifies

costs based upon an industrial

engineer’s evaluation of production

methods, and material, labor and

overhead requirements.

Account Analysis and the Engineering Approach



Use Various Methods to Analyze Cost

Behavior.

1. Scattergraph Method

2. High-Low Method

3. Least-Squares Regression

Method


Plot the data points on a graph

(Total Cost Y vs. Activity X).

0 1 2 3 4

*

Ma

inte

na

nce

Co

st

1,0

00’s

of

Dolla

rs

10

20

0

***

**

**

*

*

Patient-days in 1,000’s

X

Y

1. The Scattergraph Method



Draw a line through the data points with about an

equal numbers of points above and below the line.

0 1 2 3 4

*

Ma

inte

na

nce

Co

st

1,0

00’s

of

Dolla

rs

10

20

0

***

**

**

*

*


X

Y



Use one data point to estimate the total level of activity

and the total cost.

Intercept = Fixed cost: $10,000

0 1 2 3 4

*

Ma

inte

na

nce

Co

st

1,0

00’s

of

Dolla

rs

10

20

0

***

**

**

*

*


X

Y

Patient days = 800

Total maintenance cost = $11,000



Make a quick estimate of variable cost per unit and

determine the cost equation.

Variable cost per unit = $1,000

800= $1.25/patient-day

Y = $10,000 + $1.25X

Total maintenance at 800 patients 11,000$

Less: Fixed cost 10,000

Estimated total variable cost for 800 patients 1,000$

Total maintenance cost Number of patient days


2. The High-Low Method – An Example

Assume the following hours of maintenance work and the total maintenance costs for six months.

7,350



The variable cost

per hour of

maintenance is

equal to the change

in cost divided by

the change in hours.

= $6.00/hour$2,400

400

7,350



Total Fixed Cost = Total Cost – Total Variable Cost

Total Fixed Cost = $9,800 – ($6/hour × 850 hours)

Total Fixed Cost = $9,800 – $5,100

Total Fixed Cost = $4,700



Y = $4,700 + $6.00X

The Cost Equation for Maintenance


Quick Check 1

Sales salaries and commissions are $10,000 when

80,000 units are sold, and $14,000 when 120,000

units are sold. Using the high-low method, what is the

variable portion of sales salaries and commission?

a. $0.08 per unit

b. $0.10 per unit

c. $0.12 per unit

d. $0.125 per unit


Quick Check 2

Sales salaries and commissions are $10,000 when

80,000 units are sold, and $14,000 when 120,000

units are sold. Using the high-low method, what is

the fixed portion of sales salaries and commissions?

a. $ 2,000

b. $ 4,000

c. $10,000

d. $12,000


3. Least-Squares Regression Method

A method used to analyze mixed costs if a

scattergraph plot reveals an approximately linear

relationship between the X and Y variables.

This method uses all of the

data points to estimate

the fixed and variable

cost components of a

mixed cost.The goal of this method is

to fit a straight line to the

data that minimizes the

sum of the squared errors.



Software can be used to fit a

regression line through the data

points.

The cost analysis objective is

the same: Y = a + bX

𝑏 = 𝑖=1

𝑛 [(𝑋𝑖− 𝑋)∙(𝑌𝑖− 𝑌)

𝑖=1𝑛 (𝑋𝑖− 𝑋)2

; 𝑎 = 𝑌 − 𝑏 𝑋

Least-squares regression also provides a statistic, called

the R2, which is a measure of the goodness

of fit of the regression line to the data points.


0 1 2 3 4

Tota

l C

ost

10

20

0

Activity

*

***

**

****


R2 is the percentage of the variation in the dependent

variable (total cost) that is explained by variation in the

independent variable (activity).

R2 varies from 0% to 100%, and

the higher the percentage the better.

X

Y


Comparing Results From the Three Methods

The three methods just discussed provide

slightly different estimates of the fixed and

variable cost components of the mixed cost.

This is to be expected because each method

uses differing amounts of the data points to

provide estimates.

Least-squares regression provides the most

accurate estimate because it uses all the data

points.


End of Topic 3A

© 2012 McGraw-Hill Education (Asia)

Cost-Volume-Profit Analysis

Topic 3B


Topic 3B Learning Objectives

1. Prepare an income statement using the contribution

format

2. Understand cost-volume-profit (CVP) relations using

four approaches:

Equation Method

Formula Method

BE Percentage Method

Graphical Method

3. Understand the meaning of, and be able to deal with: Sensitivity Analysis

Margin of Safety

Operating Leverage

Multiple Products CVP



Prepare an income

statement using the

contribution format.


The Contribution Format

Total Unit

Sales Revenue 100,000$ 50$

Less: Variable costs 60,000 30

Contribution margin 40,000$ 20$

Less: Fixed costs 30,000

Net operating income 10,000$

The contribution margin format emphasizes cost

behavior. Contribution margin covers fixed costs

and provides for income.


The Contribution Format

Used primarily for

external reporting.

Used primarily by

management.



Understand cost-volume-profit (CVP)

relations using four approaches:

1) Equation Method

2) Formula Method

3) BE Percentage Method

4) Graphical Method


Basics of Cost-Volume-Profit Analysis

Contribution Margin (CM) is the amount remaining from sales revenue after

variable expenses have been deducted.

Sales (500 bicycles) 250,000$

Less: Variable expenses 150,000

Contribution margin 100,000

Less: Fixed expenses 80,000


Racing Bicycle Company

Contribution Income Statement

For the Month of June

The contribution income statement is helpful to managers in judging the impact

on profits of changes in selling price, cost, or volume. The emphasis is on cost

behavior.

CM is used first to cover fixed expenses. Any remaining CM contributes to

net operating income.


Total Per Unit

Sales (500 bicycles) 250,000$ 500$

Less: Variable expenses 150,000 300

Contribution margin 100,000 200$







Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. If Racing sells an additional bicycle, $200 additional CM will be generated

to cover fixed expenses and profit.


Total Per Unit

Sales (500 bicycles) 250,000$ 500$









Each month, RBC must generate at least $80,000 in total contribution margin to break-even (which is the level of sales at which profit is zero).


Total Per Unit

Sales (400 bicycles) 200,000$ 500$




Net operating income -$





If RBC sells 400 units in a month, it will be

operating at the break-even point.


Total Per Unit

Sales (401 bicycles) 200,500$ 500$




Net operating income 200$





If RBC sells one more bike (401 bikes), net

operating income will increase by $200.



We do not need to prepare an income statement to

estimate profits at a particular sales volume. Simply

multiply the number of units sold above break-even

by the contribution margin per unit.

If Racing sells

430 bikes, its net

operating income

will be $6,000.


CVP Relationships in Equation Form

The contribution format income statement can be

expressed in the following equation:

Profit = (Sales – Variable expenses) – Fixed expenses

= (SP x Q – VC x Q) – Fixed expenses

= (SP – VC) x Q – Fixed expenses

= Unit CM x Q – Fixed expenses

where:

Unit CM = Selling price per unit – Variable expenses per unit

= SP - VC


CVP Relationships in Equation Form

To compute RBC’s profit where 401 bikes are sold

using the equation method:


Break-even Analysis

Assume the following information for Racing Bicycle

Company (RBC). Determine the breakeven point in:

1) unit sales; 2) dollar sales

Total Per Unit Percent

Sales (500 bicycles) 250,000$ 500$ 100%

Less: Variable expenses 150,000 300 60%

Contribution margin 100,000 200$ 40%






VC Ratio

CM Ratio


Contribution Margin Ratio (CM Ratio)

The contribution margin ratio at Racing Bicycle is:

CM per unit

SP per unitCM Ratio = = 40%

$200

$500=

Total CM

Total SalesCM Ratio = = 40%

$100,000

$250,000=

The CM ratio indicates the change in contribution margin

for every dollar change in sales. For e.g. if sales increase

by $50,000, total contribution margin will increase by

$20,000 (40% x $50,000)

OR

The relationship between profit and the CM ratio can be

expressed using the following equation:

Profit = CM ratio × Sales – Fixed expenses


Quick Check

Coffee Klatch is an espresso stand in a downtown

office building. The average selling price of a cup of

coffee is $1.49 and the average variable expense per

cup is $0.36. The average fixed expense per month is

$1,300. 2,100 cups are sold each month on average.

What is the CM Ratio for Coffee Klatch?

a. 1.319

b. 0.758

c. 0.242

d. 4.139


Break-even in Unit Sales:

1. Equation Method

Profits = Unit CM × Q – Fixed expenses

Profits are zero at the break-even point, hence


Break-even in Unit Sales:

2. Formula Method

Let’s apply the formula method to solve for

the break-even point.

Fixed expenses

CM per unit =

Unit sales to

break even


Break-even in Dollar Sales:

1. Equation Method



Break-even in Dollar Sales:

2. Formula Method

Now, let’s use the formula method to calculate the

dollar sales at the break-even point.

Fixed expenses

CM ratio=

Dollar sales to

break even


Break-even:

3. The BE Percentage Method

Now, let’s use the 3rd method: the break-even percentage

(BE%) method to calculate the break-even point in units as

well as in sales $. This method also efficiently calculates

break-even for multiple products.

BE% =BE Sales $

Total Sales $x 100%

Since BE Sales $ =FE

CM%

BE% =FE

CM%

Total Sales $x 100% =

FE

CM%x

1

Total Sales $x 100%

Since CM% x Total Sales $ = CM

𝐁𝐄% =𝐅𝐄

𝐂𝐌𝐱 𝟏𝟎𝟎%


Break-even in Unit and Dollar Sales:


Applying the BE% formula to the same company RBC

𝐁𝐄% =𝐅𝐄

𝐂𝐌𝐗 𝟏𝟎𝟎%

𝐁𝐄% =$𝟖𝟎,𝟎𝟎𝟎

$𝟏𝟎𝟎,𝟎𝟎𝟎𝐗 𝟏𝟎𝟎% = 𝟖𝟎%

This means that the company requires 80% of its current

sales in order to break-even.

Currently, the company’s sales are $250,000 or 500 units.

A BE% of 80% means if the company sales are $200,000

($250,000 x 80%) or 400 units (500 units x 80%), the

company is break-even.

These figures are consistent with both the equation and

the formula methods.


Quick Check 1






What is the break-even sales dollars?

a. $1,300

b. $1,715

c. $1,788

d. $3,129


Quick Check 2






What is the break-even sales in units?

a. 872 cups

b. 3,611 cups

c. 1,200 cups

d. 1,150 cups


Target Profit Analysis in Unit Sales

1. Equation Method

Suppose Racing Bicycle management wants to

know how many bikes must be sold to earn a

target profit of $100,000.

Profit = Unit CM × Q – Fixed expenses


Target Profit Analysis in Unit Sales

2. Formula Method

Target profit + Fixed expenses

CM per unit =

Unit sales to attain

the target profit

Suppose Racing Bicycle management wants to

know how many bikes must be sold to earn a



Target Profit Analysis in Dollar Sales

1. Equation Method


Our goal is to solve for the unknown “Sales”

which represents the dollar amount of sales

that must be sold to attain the target profit.

Suppose RBC management wants to know the

sales volume that must be generated to earn a



Target Profit Analysis in Dollar Sales

2.Formula Method

We can calculate the dollar sales needed to

attain a target profit (net operating profit) of

$100,000 at Racing Bicycle.

Target profit + Fixed expenses

CM ratio=

Dollar sales to attain

the target profit


Target Profit Analysis:


Modifying the BE% formula to add target profit to FE

Target Profit% =𝐅𝐄+𝐓𝐚𝐫𝐠𝐞𝐭 𝐏𝐫𝐨𝐟𝐢𝐭

𝐂𝐌𝐱 𝟏𝟎𝟎%

Target Profit% =$𝟖𝟎,𝟎𝟎𝟎+$𝟏𝟎𝟎,𝟎𝟎𝟎

$𝟏𝟎𝟎,𝟎𝟎𝟎x 𝟏𝟎𝟎% = 𝟏𝟖𝟎%

This means that the company requires 180% of its current

sales in order to obtain the target profit.

Currently, the company’s sales are $250,000 or 500 units.

A Target Profit % of 180% means if the company sales

are $450,000 ($250,000 x 180%) or 900 units (500 units x

180%), the company has a target profit of $100,000.

These figures are consistent with both the equation and

the formula methods.


Quick Check 1

Coffee Klatch is an espresso stand in a downtown office

building. The average selling price of a cup of coffee is

$1.49 and the average variable expense per cup is

$0.36. The average fixed expense per month is $1,300.

Use the formula method to determine how many cups of

coffee would have to be sold to attain target profits of

$2,500 per month.

a. 3,363 cups

b. 2,212 cups

c. 1,150 cups

d. 4,200 cups


Quick Check 2

Coffee Klatch is an espresso stand in a downtown office

building. The average selling price of a cup of coffee is

$1.49 and the average variable expense per cup is

$0.36. The average fixed expense per month is $1,300.

Use the formula method to determine the sales dollars

that must be generated to attain target profits of $2,500

per month.

a. $2,550

b. $5,011

c. $8,458

d. $10,555


CVP Relationships in Graphic Form

The relationships among revenue, cost, profit and volume can be expressed graphically by preparing a CVP graph.

Racing Bicycle developed contribution margin income statements at 0, 200, 400, and 600 units sold. We will

use this information to prepare the CVP graph.

0 200 400 600

Sales -$ 100,000$ 200,000$ 300,000$

Total variable expenses - 60,000 120,000 180,000

Contribution margin - 40,000 80,000 120,000

Fixed expenses 80,000 80,000 80,000 80,000

Net operating income (loss) (80,000)$ (40,000)$ -$ 40,000$

Units Sold


$0

$50,000

$100,000

$150,000

$200,000

$250,000

$300,000

$350,000

0 100 200 300 400 500 600

Preparing the CVP Graph

Units

In a CVP graph, unit volume is usually

represented on the horizontal (X) axis

and dollars on the vertical (Y) axis.


$0

$50,000

$100,000

$150,000

$200,000

$250,000

$300,000

$350,000

0 100 200 300 400 500 600

Fixed expenses


Units

Draw a line parallel to the volume axis

to represent total fixed expenses.


$0

$50,000

$100,000

$150,000

$200,000

$250,000

$300,000

$350,000

0 100 200 300 400 500 600

Total expenses

Fixed expenses


Units

Choose some sales volume, say 400 units, and plot the point representing

total expenses (fixed and variable). Draw a line through the data point

back to where the fixed expenses line intersects the dollar axis.


$0

$50,000

$100,000

$150,000

$200,000

$250,000

$300,000

$350,000

0 100 200 300 400 500 600

Sales

Total expenses

Fixed expenses


Units

Choose some sales volume, say 400 units, and plot the point representing

total sales. Draw a line through the data point back to the point of origin.


$0

$50,000

$100,000

$150,000

$200,000

$250,000

$300,000

$350,000

0 100 200 300 400 500 600

Sales

Total expenses

Fixed expenses


Break-even point

(400 units or $200,000 in sales)

UnitsLoss Area

Profit Area


0 100 200 300 400 500 600

-$60,000

Number of bicycles sold

Pro

fit

60,000$

40,000$

20,000$

$0

-$20,000

-$40,000


Profit = Unit CM × Q – Fixed Costs

An even simpler form of

the CVP graph is called

the profit graph.


0 100 200 300 400 500 600

-$60,000

Number of bicycles sold

Pro

fit

60,000$

40,000$

20,000$

$0

-$20,000

-$40,000


Break-even point, where

profit is zero , is 400

units sold.



Understand the meaning of, and be

able to deal with:

1) Sensitivity Analysis

2) Margin of Safety

3) Operating Leverage

4) Multiple Products CVP


1. Sensitivity Analysis: Example 1

Changes in Fixed Costs and Sales Volume

What is the profit impact if Racing

Bicycle can increase unit sales from

500 to 540 by increasing the monthly

advertising budget by $10,000?


500 units 540 units

Sales 250,000$ 270,000$

Less: Variable expenses 150,000 162,000

Contribution margin 100,000 108,000

Less: Fixed expenses 80,000 90,000

Net operating income 20,000$ 18,000$



$80,000 + $10,000 advertising = $90,000

Sales increased by $20,000, but net operating

income decreased by $2,000.




A shortcut solution using incremental analysis

Increase in CM (40 units X $200) 8,000$

Increase in advertising expenses 10,000

Decrease in net operating income (2,000)$



Change in Variable Costs and Sales Volume

What is the profit impact if Racing

Bicycle can use higher quality raw

materials, thus increasing variable costs

per unit by $10, to generate an increase

in unit sales from 500 to 580?


500 units 580 units

Sales 250,000$ 290,000$

Less: Variable expenses 150,000 179,800


Less: Fixed expenses 80,000 80,000


1. Sensitivity Analysis:

Change in Variable Costs and Sales Volume

580 units × $310 variable cost/unit = $179,800

Sales increase by $40,000, and net operating income

increases by $10,200.


2. The Margin of Safety in Dollars

The margin of safety in dollars is the

excess of budgeted (or actual) sales over

the break-even volume of sales.

Margin of safety in dollars = Total sales - Break-even sales

Let’s look at Racing Bicycle Company and

determine the margin of safety.


2. The Margin of Safety in Units

The margin of safety can be expressed in terms of

the number of units sold. The margin of safety at

RBC is $50,000, and each bike sells for $500;

hence, RBC’s margin of safety is 100 bikes.

Margin of

Safety in units= = 100 bikes

$50,000

$500

Margin of

Safety in units= 500 – 400 = 100 bikes

OR


2. The Margin of Safety in Percentage

If we assume that RBC has actual sales of $250,000, given that

we have already determined the break-even sales to be

$200,000, the margin of safety is $50,000 as shown.

Break-even

sales

400 units

Actual sales

500 units

Sales 200,000$ 250,000$

Less: variable expenses 120,000 150,000


Less: fixed expenses 80,000 80,000

Net operating income -$ 20,000$

RBC’s margin of safety can be expressed as 20% of sales

($50,000 ÷ $250,000). This is also known as margin of

safety percentage or MoS%


Quick Check






What is the margin of safety expressed in cups?

a. 3,250 cups

b. 950 cups

c. 1,150 cups

d. 2,100 cups


Linking Margin of Safety % (to sales) and

Breakeven % (to sales)

Margin of safety in dollars

Total sales in dollars= Margin of safety percentage (MoS%)

= Total sales − Breakeven sales

Total sales

= 1 − Breakeven in dollars

Total sales in dollars

= 1 − Breakeven percentage

= 1 − BE%

Therefore: BE% = 1 − MoS %

Margin of safety in dollars = Total sales - Break-even sales


Calculate Breakeven given MOS (%)

RBC’s margin of safety = 20% of sales

Actual sales

500 units

Sales 250,000$

Less: variable expenses 150,000


Less: fixed expenses 80,000


Breakeven sales of RBC = 1 – 20% = 80% of sales (or BE%)

= $250,000 x 80%

= $200,000

= Breakeven Sales on slide 86


3. Operating Leverage:

Cost Structure and Profit Stability

Cost structure refers to the relative proportion

of fixed and variable costs in an organization.

Managers often have some latitude in

determining their organization’s cost structure.



Cost Structure and Profit Stability

There are advantages and disadvantages to high fixed cost

(or low variable cost) and low fixed cost (or high variable

cost) structures.

An advantage of a high fixed

cost structure is that income

will be higher in good years

compared to companies

with lower proportion of

fixed costs.

A disadvantage of a high fixed

cost structure is that income

will be lower in bad years

compared to companies

with lower proportion of

fixed costs.

Companies with low fixed cost structures enjoy greater

stability in income across good and bad years.



Managing fixed costs

Typical fixed costs: production facilities, rentals, employees

salaries and related benefits and utilities Converting them into variable may reduce risk of financial commitment

and provide flexibility of capacity utilization

Outsourcing - switching to variable costs

Business with fast and regular change and/or large varieties of

products most likely will benefit from this approach e.g. Nike and

Apple

Non-core business functions with lower value-add to majority

customers e.g. call centers for enquiries, 3rd party logistics, broker-

dealers’ securities back office operations

Offshoring - reducing fixed costs

Honda and Toyota Thailand plants

HSBC back office functions in China


3. Operating Leverage

Operating leverage is a measure of how sensitive net operating income is to percentage changes in sales. It is a measure, at any given level of sales, of how a percentage change in sales volume will affect profits.

** Profit Before Tax is a commonly used alternative to Net Operating Income in the degree of operating leverage calculation

**Income OperatingNet

Marginon Contributi Leverage Operating of DegreeDOL



Actual sales

500 Bikes

Sales 250,000$

Less: variable expenses 150,000


Less: fixed expenses 80,000

Net income 20,000$

Degree of

Operating

Leverage=

To illustrate, let’s revisit the contribution income statement

for RBC.



With an operating leverage of 5, if RBC

increases its sales by 10%, net operating

income would increase by 50%.

Percent increase in sales 10%

Degree of operating leverage × 5

Percent increase in profits 50%

Here’s the verification!



Actual sales

(500)

Increased

sales (550)

Sales 250,000$ 275,000$

Less variable expenses 150,000 165,000


Less fixed expenses 80,000 80,000


10% increase in sales from

$250,000 to $275,000 . . .

. . . results in a 50% increase in

income from $20,000 to $30,000.


Quick Check 1

Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the operating leverage?

a. 2.21

b. 0.45

c. 0.34

d. 2.92


Quick Check 2

At Coffee Klatch the average selling price of a cup of coffee is $1.49, the average variable expense per cup is $0.36, the average fixed expense per month is $1,300 and an average of 2,100 cups are sold each month.

If sales increase by 20%, by how much should net operating income increase?

a. 30.0%

b. 20.0%

c. 22.1%

d. 44.2%


What does higher value of Operating

Leverage mean?

High Operating Leverage ratio signals the existence of high fixed costs. increases risk of making loss in adverse market

conditions. increases opportunity to make profit when higher

demand exists. has lower margin of safety percentage (MoS%)

MoS%

1DOL

McGraw-Hill Education (Asia)

Proof of Operating Leverage and Profit

Movement Relationship

Benchmark Co. High F.C. Co.

Total Sales (Same) $3,200,000 $3,200,000

Unit selling price (Same) $800 $800

Unit variable costs ($300) ($150)

Unit Contribution margin $500 $650

Unit sales (Same) 4,000 4,000

Contribution margin (CM) $2,000,000 $2,600,000

Fixed costs ($1,500,000) ($2,100,000)

Net Operating Profit (Same) (P) 500,000 500,000

Degree of operating leverage (CM/P) 4.0 5.2

Slide 100

McGraw-Hill Education (Asia)

Proof of Operating Leverage and Profit

Movement Relationship


Increase in sales 12.5% 12.5%

Degree of operating leverage X 4.0 X 5.2

Increase in profits 50% 65%

Proof:

Unit contribution margin $500 $650

Unit change in sales (4,000 x 12.5%) x 500 x 500

Change in profits $250,000 $325,000

Percentage increase from the original $500,000 profit

50% 65%

Slide 101


Proof of Operating Leverage and MoS%

Relationship


Total Sales (Same) (S) $3,200,000 $3,200,000

Contribution margin (CM) $2,000,000 $2,600,000

Fixed costs (F) ($1,500,000) ($2,100,000)

Net Operating Profit (Same) (P) 500,000 500,000

Degree of operating leverage (CM/P) 4.0 5.2

Breakeven Sales Dollars [F/(CM/S)] 2,400,000 2,584,615

Breakeven % (to sales) 75% 80.77%

MoS% = 1 – BE% 25% 19.23%

1/MoS%

= Degree of operating leverage

4.0 5.2


4. The Concept of Sales Mix

Sales mix is the relative proportion in which a company’s products are sold.

Different products have different selling prices, cost structures, and contribution margins.

When a company sells more than one product, break-even analysis becomes more complex as the following example illustrates.


Multi-Product Break-Even Analysis

1. The BE% Method

Sales 20,000$ 80,000$ 100,000$

Variable expenses 15,000 40,000 55,000

Contribution margin 5,000 40,000 45,000

Fixed expenses 27,000


Le Louvre (200) Le Vin (400) Total

Virtual Journey’s Le Louvre and Le Vin sales and profit data are as follows:

%60%401MoS%1BE%

BE%1MoS%

%40000,45

000,18MoS%

Marginon Contributi

Income OperatingNet MoS%

MoS%

1

Income OperatingNet

Marginon ContributiDOL

Breakeven sales $12,000 $48,000

BE% = 60%

Sales $ 20,000 $80,000 x

Total breakeven sales = $60,000

Breakeven units 120 units 240 units

Total breakeven units = 360 units


Sales 20,000$ 100% 80,000$ 100% 100,000$ 100.0%

Variable expenses 15,000 75% 40,000 50% 55,000 55.0%

Contribution margin 5,000 25.0% 40,000 50% 45,000 45.0%



Sales mix 20,000$ 20% 80,000$ 80% 100,000$ 100%

Le Louvre (200 units) Le Vin (400 units) Total


2. The Weighted-Average CM Ratio Method

Le Louvre comprises 20% of Virtual Journey’s total sales revenue and Le Vin comprises the remaining 80%. Virtual

Journey provides the following information:

Weighted-average CM Ratio

= (20% x 25%) + (80% x 50%)

= 45%

Weighted-average CM Ratio

= 45,000/100,000

= 45%

OR



2. The Weighted-Average CM Ratio Method

Fixed expenses

CM ratio=

Dollar sales to

break even

Dollar sales to

break even

$27,000

45%= = $60,000

Sales 12,000$ 100% 48,000$ 100% 60,000$ 100.0%


Contribution margin 3,000 25% 24,000 50% 27,000 45.0%



Sales mix 12,000$ 20% 48,000$ 80% 60,000$ 100.0%



Sales 20,000$ 100% 80,000$ 100% 100,000$ 100.0%


Contribution margin 5,000 25.0% 40,000 50% 45,000 45.0%



Unit CM $25 $100

Sales mix (in units) 200 units 33.33% 400 units 66.66% 600 units 100%



3. The Weighted-Average CM Method

Le Louvre comprises 33.33% of Virtual Journey’s total unit sales and Le Vin comprises the remaining 66.66%. Virtual

Journey provides the following information:

Weighted-average CM

= (1/3 x $25) + (2/3 x $100)

= $75



3. The Weighted-Average CM Method

Fixed expenses

Unit CM =

Unit sales to

break even

Unit sales to

break even

$27,000

$75= = 360 units

Sales 12,000$ 100% 48,000$ 100% 60,000$ 100.0%


Contribution margin 3,000 25% 24,000 50% 27,000 45.0%



Sales mix (in units) 120 units 33% 240 units 67% 360 units 100.0%



Key Assumptions of CVP Analysis

Selling price is constant.

Costs are linear and can be accurately divided into

variable (constant per unit) and fixed (constant in

total) elements.

In multiproduct companies, the sales mix is

constant.

In manufacturing companies, inventories do not

change (units produced = units sold).


Quick Check


End of Topic 3B

managerial accounting chapter 2 slides

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