Chapter 5 - Cost-Volume-Profit Relationships - completed outline PDF

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Cost-Volume-Profit Relationships

Cost-volume-profit (CVP) analysis helps managers make many important decisions such as what products and services to offer, what prices to charge, what marketing strategy to use, and what cost structure to maintain. CVP analysis expresses the relationships among costs, volume, and the company’s profit. It allows companies to determine the sales volume needed to just breakeven or the sales volume needed to earn a target profit. It also allows companies to see how changes, such as cost increases, impact the company’s profit and what adjustments can be made to offset those changes.

Assumptions of CVP Analysis:    

Selling price is constant Costs can be accurately divided into variable and fixed components Costs are linear o Variable costs are constant per unit o Fixed costs are constant in total Sales mix remains constant

Cost-volume-profit analysis uses the contribution margin income statement format:

Sales - Variable Expenses Contribution Margin - Fixed Expenses Operating Income

1

CVP Example: The Juicery is a juice bar that produces a variety of fresh juices and smoothies. Assume a local Juicery sells each juice for $3.00. The ingredients and cup for each juice costs an average of $0.75 per juice and other variable costs average $1.05 per juice. The fixed costs, including rent, a franchise fee, advertising, and the store manager’s salary, total $4,000 per month.

What is the contribution margin per unit? What does the contribution margin tell managers?

-

Sales price VC per unit CM per unit

$3.00 1.80 $1.20

Every juice sold “contributes” $1.20 towards paying for fixed costs and generating operating income

What are the variable cost ratio and the contribution margin ratio? What do these ratios tell managers?

Variable Cost Ratio: VC Sales

=

$1.80 $3.00

=

60%

=

40%

Contribution Margin Ratio: CM Sales

=

$1.20 $3.00

For every $1.00 of sales revenue, 60% pays for variable costs and 40% goes towards paying for fixed costs and generating operating income.

Because both the sales price per unit and the variable cost per unit are assumed to remain constant, this means the VC% and CM% will also remain constant, regardless of changes in volume.

Sales - Variable Expenses Contribution Margin

Per unit

100 units

$3.00 $1.80 $1.20

$300 $180 $120

200 units 500 units $600 $360 $240

$1,500 $900 $600

Ratios (% of Sales) 100% 60% 40%

2

Using the contribution margin income statement, calculate operating income if 3,000 juices are sold in a month. -

Sales revenue Variable expenses Contribution margin Fixed expenses Operating income

$3.00 x 3,000 = $1.80 x 3,000 = $1.20 x 3,000 = =

$9,000 5,400 $3,600 4,000 ($ 400)

Using the contribution margin income statement, calculate operating income if 3,500 juices are sold in a month. -

Sales revenue Variable expenses Contribution margin Fixed expenses Operating income

$3.00 x 3,500 = $1.80 x 3,500 = $1.20 x 3,500 = =

$10,500 6,300 $ 4,200 4,000 $ 200

Using the contribution margin income statement, calculate operating income if 4,000 juices are sold in a month. -

Sales revenue Variable expenses Contribution margin Fixed expenses Operating income

$3.00 x 4,000 = $1.80 x 4,000 = $1.20 x 4,000 = =

$12,000 7,200 $ 4,800 4,000 $ 800

Alternatively, if we know the operating income is $200 when 3,500 juices are sold, we could just calculate the additional contribution margin earned by selling 500 more units, as follows: CM per unit: x Additional Units: Additional CM:

$1.20 x 500 $ 600

Selling 500 additional juices generates $600 of additional contribution margin that goes towards profit. Our operating income went from $200 at 3,500 juices to $800 at 4,000 juices (a $600 increase). 3

Whenever unit data isn’t known, we can still calculate operating income if we know our variable cost ratio (VC%) and contribution margin ratio (CM%). Using the VC% and CM%, calculate operating income when sales are $15,000. -

Sales revenue Variable expenses Contribution margin Fixed expenses Operating income

60% x $15,000 40% x $15,000

= = =

$15,000 9,000 $ 6,000 4,000 $ 2,000

Cost-volume-profit (CVP) analysis is often used for predicting the number of units that need to be sold to 1) breakeven or 2) earn a target level of operating income. The contribution margin format of the income statement can help us to easily solve for these. It also leads to a short cut that can be used to quickly find the results. Sales – Variable Expenses – Fixed Expenses = Operating Income Contribution Margin – Fixed Expenses = Operating Income Contribution Margin = Fixed Expenses + Operating Income CM per unit (# units) = Fixed Expenses + Operating Income # units to sell

= Fixed Expenses + Operating Income CM per unit

Note that the “operating income” used in the calculation above is the target operating income. It represents the operating income the company wants to achieve. When calculating the break-even point, the operating income is set equal to zero ($0).

4

Before the local Juicery opened its store, the owners wanted to know how many juices they would need to sell each month just to breakeven. What must sales be (in units and in dollars) in order for the Juicery to breakeven?

Equation Method:

Sales – Variable Expenses – Fixed Expenses = Operating Income $3.00x - $1.80x - $4,000 $1.20x

= =

$0 $4,000

x

=

3,333 juices

=

$4,000 + $0 $1.20

Shortcut:

FC + Operating Income CM per unit

In dollars:

3,333 juices x $3.00 per juice =

=

3,333 juices

$10,000

5

$ Revenues Expenses

$10,000 Breakeven Point

0

3,333

# units

What must sales be (in units and in dollars) in order for the Juicery to earn $5,000 of operating income? Equation Method:

Sales – Variable Expenses – Fixed Expenses = Operating Income $3.00x - $1.80x - $4,000 $1.20x

= =

$5,000 $9,000

x

=

7,500 juices

=

$4,000 + $5,000 $1.20

Shortcut:

FC + Operating Income CM per unit

In dollars:

7,500 juices x $3.00 per juice =

=

7,500 juices

$22,500

6

Alternatively, if we know the breakeven point is 3,333 juices, we can figure out how many juices are needed to generate $5,000 of operating income and add that to the 3,333 juices needed to breakeven (or to cover fixed expenses), as follows: $5,000 / $1.20 CM per unit

=

4,167 juices + 3,333 juices 7,500 juices

To find the sales in dollars needed to break even or to reach a target profit when unit data is not available, the VC% and CM% can be used within the contribution margin format of the income statement. Sales – Variable Expenses – Fixed Expenses = Operating Income Contribution Margin – Fixed Expenses = Operating Income Contribution Margin = Fixed Expenses + Operating Income CM % (Sales Revenue) = Fixed Expenses + Operating Income Sales Revenue

= Fixed Expenses + Operating Income CM %

Calculate the sales revenue needed in order to breakeven. Does this answer match the answer above when calculating the breakeven point in units? Equation Method:

Shortcut:

Sales – Variable Expenses – Fixed Expenses = Operating Income S - 0.60 S - $4,000 0.40 S

= =

$0 $4,000

S

=

$10,000

=

$4,000 + $0 40%

FC + Operating Income CM %

=

$10,000

7

Calculate the sales revenue needed in order to earn $5,000 of operating income. Does this answer match the answer above when calculating the results in units? Equation Method:

Shortcut:

Sales – Variable Expenses – Fixed Expenses = Operating Income S - 0.60 S - $4,000 0.40 S

= =

$5,000 $9,000

S

=

$22,500

=

$4,000 + $5,000 40%

FC + Operating Income CM %

=

$22,500

What-if Analysis CVP analysis is very helpful for answering “what if” questions. Consider each of the examples below independently of one another. Assume a competitor opened up across the street, and the Juicery needs to discount their juices in order to retain customers. If the average sales price per juice is reduced to $2.60, what impact will this change have on the breakeven point? Equation Method:

Sales – Variable Expenses – Fixed Expenses = Operating Income $2.60x - $1.80x - $4,000 $0.80x

= =

$0 $4,000

x

=

5,000 juices

=

$4,000 + $0 $0.80

Shortcut:

FC + Operating Income CM per unit

In dollars:

5,000 juices x $2.60 per juice =

=

5,000 juices

$13,000

Breakeven point went up by 1,667 units. 8

Assume the Juicery is able to buy cheaper ingredients and is able to reduce the variable cost per unit to $1.40. What impact will this change have on the breakeven point? Equation Method:

Sales – Variable Expenses – Fixed Expenses = Operating Income $3.00x - $1.40x - $4,000 $1.60x

= =

$0 $4,000

x

=

2,500 juices

=

$4,000 + $0 $1.60

Shortcut:

FC + Operating Income CM per unit

In dollars:

2,500 juices x $3.00 per juice =

=

2,500 juices

$7,500

Breakeven point went down by 833 units.

Assume the Juicery has an unexpected increase in rent, which increased fixed expenses to $4,500 per month. What impact will this change have on the breakeven point? Equation Method:

Sales – Variable Expenses – Fixed Expenses = Operating Income $3.00x - $1.80x - $4,500 $1.20x

= =

$0 $4,500

x

=

3,750 juices

=

$4,500 + $0 $1.20

Shortcut:

FC + Operating Income CM per unit

In dollars:

3,750 juices x $3.00 per juice =

=

3,750 juices

$11,250

Breakeven point went up by 417 units. 9

Assume the Juicery is currently selling an average of 10,000 juices per month. Due to an unexpected increase in rent, fixed expenses increased from $4,000 to $4,500. However, the Juicery hopes to be able to offset the increase in rent by reducing variable costs. What reduction in the variable cost per unit is needed in order to offset the increase in rent? Savings in total variable expenses needed: Number of units: Savings in variable cost per unit needed: Original operating income: Sales – VC – FC = Operating Income $3.00 (10,000) - $1.80 (10,000) - $4,000 = x $30,000 - $18,000 - $4,000 = $8,000

$500 10,000 units $0.05 per unit New variable cost per unit: Sales – VC – FC = Operating Income $3.00 (10,000) – x (10,000) - $4,500 = $8,000 $30,000 – x (10,000) - $4,500 = $8,000 $17,500 = 10,000 x $1.75 = x

10

Sales Mix and Multiproduct CVP Analysis If a company sells more than one product, breakeven analysis is more complex because different products will have different sales prices, different costs, and different contribution margins. Therefore, the breakeven point will depend on the sales mix, which is the relative proportion of a company’s products that are sold.

Assume the Juicery has two products available for sale: fresh juices and pre-made, bottled juices that have a longer shelf life. The Juicery sells 3 fresh juices for every pre-made, bottled juice (3:1 ratio). The fixed costs are $4,000 per month, and additional data follows:

Fresh Juice Sales Price per Unit - VC per Unit CM per unit

$3.00 $1.80 $1.20

Pre-Made, Bottled Juice $2.80 $1.40 $1.40

Given the current sales mix, how many fresh juices and pre-made, bottled juices must the company sell to breakeven? Approach 1: Equation method (Sales – Variable Expenses) + (Sales – Variable Expenses) – Fixed Expenses = Op. Income For Fresh Juices

For Pre-Made, Bottled Juices

(Contribution Margin) + (Contribution Margin) –

For Fresh Juices ($1.20 * 3x) $3.60x

Fixed Expenses = Op. Income

For Pre-Made, Bottled Juices + +

($1.40 * x) $1.40x $5.00x $5.00x

-

$4,000 $4,000 $4,000 x

x= 3x =

Pre-made, Bottled Juice: Fresh Juice:

= = = =

$ 0 $ 0 $ 0 $4,000

=

800 units

800 pre-made, bottled juices 2,400 fresh juices 11

Approach 2: Weighted average contribution margin per unit method

CM per unit x # units in mix Total CM Total CM: Total units:

Fresh Juices $1.20 x 3 $3.60

Pre-Made, Bottled Juices $1.40 x 1 $1.40

$3.60 + $1.40 = $5.00 3 fresh juices + 1 pre-made, bottled juice = 4 units

Weighted Average CM per unit = $5.00 / 4 units = $1.25 per unit

FC + Operating Income WACM per unit

=

$4,000 + $0 $1.25

=

Fresh 3,200 x 3/4 2,400 Fresh Juices

3,200 juices

Pre-made, Bottled 3,200 x 1/4 800 Pre-made Bottled Juices

12

Margin of Safety The margin of safety is the excess of the current level of sales (actual or budgeted) over the breakeven volume of sales. It tells managers how far sales can drop before the company will incur a loss. Current Sales (actual or budgeted) - Breakeven Sales Margin of Safety The margin of safety can be calculated in dollars, in units, and as a percentage of current sales.

Assume the Juicery is currently selling an average of 10,000 juices per month. What is the margin of safety in units, dollars, and as a percentage? Current Sales

-

Breakeven Sales

=

Margin of Safety

In units:

10,000 units

-

3,333units

=

6,667 units

In dollars:

$30,000

-

$10,000

=

$20,000

=

6,667 units 10,000 units

Percentage: Margin of Safety Current Sales

or

$20,000 $30,000

=

67%

13

Operating Leverage Cost structure refers to the relative proportion of fixed and variable costs in an organization. Managers often have some latitude in trading off between these two types of costs. For example, a company may pay its sales team a fixed salary or a commission based on sales (which is variable). Which cost structure is better? More fixed costs and less variable costs? More variable costs and less fixed costs? Unfortunately, there is no right or wrong answer. The cost structure does affect a company’s operating leverage, which is a measure of how sensitive operating income is to a given percentage change in sales. The degree of operating leverage (also called the operating leverage factor) is a multiplier used to determine the impact an increase (or decrease) in sales revenue will have on operating income.

Degree of Operating Leverage

=

Contribution Margin Operating Income

To help us understand the operating leverage factor, let’s look at the two examples below. Note that a company with higher operating leverage has higher fixed costs in relation to variable costs. A company with lower operating leverage has lower fixed costs in relation to variable costs.

Example 1 Lower Operating Leverage 10% Decrease in Sales Sales

Original Data

Example 2 Higher Operating Leverage

10% Increase in Sales

$9,000

$10,000

$11,000

-VC

7,200

8,000

8,800

CM

$1,800

$2,000

-FC

1,000

Op. Inc.

$800

10% Decrease in Sales Sales

Original Data

10% Increase in Sales

$9,000

$10,000

$11,000

-VC

900

1,000

1,100

$2,200

CM

$8,100

$9,000

$9,900

1,000

1,000

-FC

8,000

8,000

8,000

$1,000

$1,200

Op. Inc.

$100

$1,000

$1,900

14

Using the original data (middle column), the degree of operating leverage is calculated as follows: Example 1: Degree of Operating Leverage

=

Contribution Margin Operating Income

=

$2,000 $1,000

=

2.0

=

Contribution Margin Operating Income

=

$9,000 $1,000

=

9.0

Example 2: Degree of Operating Leverage

Impact of 10% increase in sales on operating income (column on the right): Example 1:

2.0 x 10% = 20% increase in operating income From $1,000 to $1,200 = 20% increase

Example 2:

9.0 x 10% = 90% increase in operating income From $1,000 to $1,900 = 90% increase

Impact of 10% decrease in sales on operating income (column on the left): Example 1:

2.0 x 10% = 20% decrease in operating income From $1,000 to $800 = 20% decrease

Example 2:

9.0 x 10% = 90% decrease in operating income From $1,000 to $100 = 90% decrease

15

Characteristics of higher vs. lower operating leverage: HIGHER Operating Leverage

LOWER Operating Leverage

Relative degree of fixed costs

Higher

Lower

Relative degree of variable costs

Lower

Higher

Contribution Margin & CM%

Higher

Lower

Degree of Operating Leverage

Higher

Lower

Riskiness, if sales volume is low

Higher

Lower

Reward, if sales volume is high

Higher

Lower

Assume the Juicery is considering automating some of its processes, which would cause fixed costs to increase by $900, but direct labor costs (variable costs per unit) would decrease by $0.20 per unit. What level of sales is necessary to justify the automation?

Operating income before changes: Sales – Variable Expenses – Fixed Expenses $3.00 x - $1.80 x - $4,000 $1.20 x - $4,000 $900

= = = =

Operating income after changes: Sales – Variable Expenses – Fixed Expenses $3.00 x - $1.60 x - $4,900 $1.40 x - $4,900 $0.20 x

x

=

4,500 units

Operating Income at 4,500 units: Before the ch...