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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
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 break-even sales in units?
a. 872 bagels
b. 3,611 bagels
c. 1,200 bagels
d. 1,150 bagels
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 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
The Margin of Safety
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
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$
The Margin of Safety
The margin of safety can be expressed as 20% of sales.($50,000 ÷ $250,000)
Break-even sales
400 unitsActual sales
500 unitsSales 200,000$ 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
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$
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 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)
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