Chapter 6 Cost-Volume-Profit Relationships

Chapter 6

Cost-Volume-Profit Relationships

The Contribution Format

Used primarily forexternal reporting.

Used primarily bymanagement.

Total Per UnitSales (500 ovens) 250,000$ 500$ Less: variable expenses 150,000 300 Contribution margin 100,000 200$

Less: fixed expenses 80,000 Operating income 20,000$

Micro Wave Co.Contribution Income Statement

For the Month of June

Practice…

(a) (b) (c) (d) (e) (f) Per Unit Var. Cost Total Total Total Operating Selling Per Units CM Fixed Income Price Unit Sold Costs $30 120,000 $720,000 $640,000

$10 $6 100,000 $320,000

$9 80,000 $160,000 $120,000

Total Per Unit PercentSales (500 ovens) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%

Less: fixed expenses 80,000 Operating Income 20,000$

Contribution-Margin Ratio

Sales revenue, variable expenses and contribution for Micro Wave can be expressed as a percentage of sales

Pop Quiz

Tasty Bagel is a snack shop in a strip mall. The average selling price of a bagel is $1.49 and the average variable expense per bagel is $0.36. The average fixed expense per month is $1,300. 2,100 bagels are sold each month on average.

What is the CM Ratio for Tasty Bagel?

a. 1.319

b. 0.758

c. 0.242

d. 4.139

Contribution Margin Method to Determine Break-even

The contribution margin method is a variation of the equation method.

Fixed expensesUnit contribution margin =

Break-even pointin units sold

Fixed expenses CM ratio

=Break-even point in

total sales dollars

Pop Quiz


What is the break-even sales in units?

a. 872 bagels

b. 3,611 bagels

c. 1,200 bagels

d. 1,150 bagels

Pop Quiz


What is the break-even sales in dollars?

a. $1,300

b. $1,715

c. $1,788

d. $3,129

-

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

- 100 200 300 400 500 600 700 800

CVP Graph

Fixed expenses

Units

Dol

lars Total Expenses

Total Sales

-

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

- 100 200 300 400 500 600 700 800

Units

Dol

larsCVP Graph

Break-even point

Profit Area

Loss Area

Break-even Reduction

Micro is currently selling 500 ovens per month. Break-even units are 400 per month under the current cost structure.

What would be the break-even units if fixed costs decrease to $70,000?

What would be the break-even units if variable costs were reduced to $250?

What would be the break-even units if selling price was increased to $513.33?

Target Operating Profit - CM Approach

Original contribution margin formula:

Target operating profit modification:

Units Sold to Earn Target Profit = Fixed Expenses +Target Op. Profit Unit Contribution Margin

Break Even Point in Units = Fixed Expenses Contribution Margin per Unit

Pop Quiz

Tasty Bagel is a snack shop in a strip mall. The average selling price of a bagel is $1.49 and the average variable expense per bagel is $0.36. The average fixed expense per month is $1,300.

How many bagels would have to be sold to attain target profits of $2,500 per month?

a. 3,363 bagels

b. 2,212 bagels

c. 1,150 bagels

d. 4,200 bagels

Sensitivity Analysis – Fixed Costs

Micro Wave Co. is currently selling 500 ovens per month

The sales manager believes that an increase of $10,000 in the monthly advertising budget would increase sales of ovens to 540 per month

Should the increase in advertising be made?

Change in Variable Costs and Sales Volume

Micro Wave management is contemplating the use of higher-quality components, which would increase variable costs by $15 per oven. However, the sales manager predicts that the overall higher quality would increase sales to 600 ovens per month. Should the higher quality components be used?

Change in Fixed Cost, Sales Price, and Sales Volume

To increase sales, the sales manager would like to cut the selling price by $40 per oven and increase the advertising budget by $30,000 per month. The sales manager believes that if these two steps are taken, unit sales will increase by 60% to 800 ovens per month. Should the changes be made?

Change in Variable Cost, Fixed Cost, and Sales Volume

The sales manager would like to place the sales staff on commission basis of $40 per oven sold, rather than on flat salaries that now total $10,000 per month. The sales manager is confident that the change will increase monthly sales by 15% to 575 ovens per month. Should the change be made?

Change in Regular Sales Price

The company has an opportunity to make a bulk sale of 200 ovens to a wholesaler if an acceptable price can be worked out. This sale would not have any effect on the company’s regular sales. What price per oven should be quoted to the wholesaler if Micro wants to increase its Operating profits by $5,000?

The Margin of Safety

Excess of budgeted (or actual) sales over the break-even volume of sales. The amount by which sales can drop before

losses begin to be incurred.

Margin of safety = Total sales - Break-even sales

Let’s calculate the margin of safety for Micro


Micro has a break-even point of $200,000. If actual sales are $250,000, the margin of safety is $50,000 or 100 ovens.

Break-even sales

400 unitsActual sales

500 unitsSales 200,000$ 250,000$ Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net operating income -$ 20,000$

Break-even sales




The margin of safety can be expressed as 20% of sales.($50,000 ÷ $250,000)

Break-even sales



Break-even sales



Pop Quiz


What is the margin of safety?

a. 3,250 bagels

b. 950 bagels

c. 1,150 bagels

d. 2,100 bagels

Cost Structure and Profitability

Alpha Beta Gamma

Amount % Amount % Amount %

Sales $800,000 100% $800,000 100% $800,000 100%

Variable Expenses

400,000 50% 300,000 37.5% 200,000 25%

Contribution Margin

400,000 50% 500,000 62.5% 600,000 75%

Fixed Expenses

300,000 400,000 500,000

Op. Income $ 100,000 $ 100,000 $ 100,000

Effect on Profit of 10% Increase in Sales Revenue

Increase in Sales

Revenue

Contribution Margin Ratio

Increase in Op.Income

Alpha $80,000 X 50% = $40,000 +40%

Beta $80,000 X 62.5% = $50,000 +50%

Gamma $80,000 X 75% = $60,000 +60%

Break-Even Points

Fixed Expenses

$300,000 /

$400,000 /

$500,000 /

Contribution Margin Ratio

50% =

62.5% =

75% =

Break-Even Sales Revenue

$600,000

$640,000

$666,667

Alpha

Beta

Gamma

Margin of Safety

Actual Sales Revenue

Break-Even Sales Revenue

Margin of

Safety

Alpha

Beta

Gamma

$800,000 -

800,000 -

800,000 -

$600,000 =

640,000 =

666,667 =

$200,000

160,000

133,333

Definition of Operating Leverage

The relative mix of a firm’s fixed and variable costs determines its operating leverage.

At a given level of sales: Degree of operating = Contribution Margin leverage Operating Income

The higher a firm’s fixed cost as compared to its variable cost, the greater its operating leverage.

Operating leverage acts like a multiplier. The greater the operating leverage, the greater the change in operating income for a given change in sales.

Let’s calculate the operating leverage for each firm.

Application of Operating Leverage

At a given level of sales, the operating leverage is a measure of how a given percentage change in sales will affect operating profits.

In fact, the operating profit will increase by the operating leverage times the percentage change in sales.

For a 10% increase in sales , Firm Alpha’s operating income increased 40% (4 times 10%).

For a 10% increase in sales , Firm Beta’s operating income increased 50% (5 times 10%).

For a 10% increase in sales , Firm Gamma’s operating income increased 60% (6 times 10%).

Pop Quiz

Tasty Bagel is an snack shop in a strip mall. The average selling price of a bagel is $1.49 and the average variable expense per bagel is $0.36. The average fixed expense per month is $1,300. 2,100 bagels are sold each month on average. What is the operating leverage?

a. 2.21

b. 0.45

c. 0.34

d. 2.92

Pop Quiz

At Tasty Bagel the average selling price of a bagel is $1.49, the average variable expense per bagel is $0.36, and the average fixed expense per month is $1,300. 2,100 bagels are sold each month on average.

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

a. 30.0%b. 20.0%c. 22.1%d. 44.2%

Break-even Analysis (in Units) with Multiple Products

Curl Company provides us with the following information:

Fixed cost is $120,000. What is the break-even point in units? What are the sales of Surfboards and Sailboards at the break-even point?

Mark Corporation produces two models of calculators. The Business model sells for $60, and the Math model sells for $40. The variable expenses are given below:

Business Math

Model Model

Variable production costs per unit $15 $16

Variable selling and administrative expenses per unit $9 $6

The fixed expenses are $75,000 per month. The expected monthly sales of each model are: Business, 1,000 units; Math, 500 units.

The break-even point for the expected sales mix is (round to nearest whole unit):

A) 833 of each B) 1,667 Business and 833 Math C) 1,667 of each D) 833 Business and 1,667 Math

POP QUIZ

Break-even Analysis (in Sales Dollars) with Multiple Products

Curl’s Contribution Margin income statement is shown below:

Surfboards Sailboards TotalSales 300,000$ 100% 150,000$ 100% 450,000$ 100.0%Var. exp. 210,000 70% 90,000 60% 300,000 66.7%Contrib. margin 90,000$ 30% 60,000$ 40% 150,000 33.3%

Fixed exp. 120,000 Operating income 30,000$

Sales mix 300,000$ 67% 150,000$ 33% 450,000$ 100.0%

$150,000 $450,000

= 33.3%

What is the break-even point in Sales? What are the sales of Surfboards and

Sailboards at the break-even point?

Break-even Analysis (in Sales Dollars) with Multiple Products

A Shift in Sales Mix

Surfboards Sailboards TotalSales 150,000$ 100% 300,000$ 100% 450,000$ 100.0%Var. exp. 105,000 70% 180,000 60% 285,000 63.3%Contrib. margin 45,000$ 30% 120,000$ 40% 165,000 36.7%

Fixed exp. 120,000 Operating income 45,000$

Sales mix 150,000$ 33% 300,000$ 67% 450,000$ 100.0%

$165,000 $450,000

= 36.7%

What is the break-even point in Sales? How does it compare with the previous amount?

Pop Quiz

Shirley’s Shoes sells two products. The controller provides you with the f ollowing information:

Low Heel High Heel I n Total Per Unit I n Total Per Unit Combined Sales Revenue $120,000 $1.20 $80,000 $0.80 $200,000 Variable Expenses 60,000 0.60 60,000 0.60 120,000 Contribution Margin $60,000 $0.60 $20,000 $0.20 80.000 Fixed Expenses 50,000 Net I ncome $30,000 What is Shirley’s Shoes breakeven point in dollars? (a) $66,667 (b) $100,000 (c) $125,000 (d) $180,000 (e) $300,000

Assumptions Underlying CVP Analysis

• Selling price is constant throughout the entire relevant range

• Costs are linear over the relevant range (costs can be divided

into variable and fixed)

• In multi-product companies, the sales mix is constant

• In manufacturing firms, inventories do not change (units

produced = units sold)

Chapter 6 Cost-Volume-Profit Relationships

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