Chapter 6 Cost-Volume-Profit Relationships Learning Objectives LO1. Explain how changes in activity affect contribution margin and net operating income. LO2. Prepare and interpret a cost-volume-profit (CVP) graph. LO3. Use the contribution margin ratio (CM ratio) to compute changes in contribution margin and net operating income resulting from changes in sales volume. LO4. Show the effects on contribution margin of changes in variable costs, fixed costs, selling price, and volume. LO5. Compute the break-even point in unit sales and sales dollars. LO6. Determine the level of sales needed to achieve a desired target profit. LO7. Compute the margin of safety and explain its significance. LO8. Compute the degree of operating leverage at a particular level of sales, and explain how the degree of operating leverage can be used to predict changes in net operating income. LO9. Compute the break-even point for a multiple product company and explain the effects of shifts in the sales mix on contribution margin and the break-even point. New in this Edition • Several new In Business boxes have been added. • A number of new exercises have been added, each of which focuses on a single learning objective. Chapter Overview 333
Transcript
Chapter 6
Cost-Volume-Profit Relationships
Learning Objectives
LO1.Explain how changes in activity affect contribution margin and net operating income.LO2.Prepare and interpret a cost-volume-profit (CVP) graph.LO3.Use the contribution margin ratio (CM ratio) to compute changes in contribution margin
and net operating income resulting from changes in sales volume.LO4.Show the effects on contribution margin of changes in variable costs, fixed costs, selling
price, and volume.LO5.Compute the break-even point in unit sales and sales dollars.LO6.Determine the level of sales needed to achieve a desired target profit.LO7.Compute the margin of safety and explain its significance.LO8.Compute the degree of operating leverage at a particular level of sales, and explain how the
degree of operating leverage can be used to predict changes in net operating income.LO9.Compute the break-even point for a multiple product company and explain the effects of
shifts in the sales mix on contribution margin and the break-even point.
New in this Edition• Several new In Business boxes have been added.• A number of new exercises have been added, each of which focuses on a single learning
objective.
Chapter Overview
A. The Basics of Cost-Volume-Profit (CVP) Analysis. (Exercises 6-1, 6-10, 6-14, and 6-15.) Cost-volume-profit (CVP) analysis is a key step in many decisions. CVP analysis involves specifying a model of the relations among the prices of products, the volume or level of activity, unit variable costs, total fixed costs, and the sales mix. This model is used to predict the impact on profits of changes in those parameters.
1. Contribution Margin. Contribution margin is the amount remaining from sales revenue after variable expenses have been deducted. It contributes towards covering fixed costs and then towards profit.
2. Unit Contribution Margin. The unit contribution margin can be used to predict changes in total contribution margin as a result of changes in the unit sales of a product. To do this, the unit contribution margin is simply multiplied by the change in unit sales. Assuming no change in fixed costs, the change in total contribution margin falls directly to the bottom line as a change in profits.
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3. Contribution Margin Ratio. The contribution margin (CM) ratio is the ratio of the contribution margin to total sales. It shows how the contribution margin is affected by a given dollar change in total sales. The contribution margin ratio is often easier to work with than the unit contribution margin, particularly when a company has many products. This is because the contribution margin ratio is denominated in sales dollars, which is a convenient way to express activity in multi-product firms.
B. Some Applications of CVP Concepts. (Exercises 6-4, 6-10, 6-11, 6-12, 6-13, and 6-16.) CVP analysis is typically used to estimate the impact on profits of changes in selling price, variable cost per unit, sales volume, and total fixed costs. CVP analysis can be used to estimate the effect on profit of a change in any one (or any combination) of these parameters. A variety of examples of applications of CVP are provided in the text.
C. CVP Relationships in Graphic Form. (Exercises 6-2 and 6-11.) CVP graphs can be used to gain insight into the behavior of expenses and profits. The basic CVP graph is drawn with dollars on the vertical axis and unit sales on the horizontal axis. Total fixed expense is drawn first and then variable expense is added to the fixed expense to draw the total expense line. Finally, the total revenue line is drawn. The total profit (or loss) is the vertical difference between the total revenue and total expense lines. The break-even occurs at the point where the total revenue and total expenses lines cross.
D. Break-Even Analysis and Target Profit Analysis. (Exercises 6-5, 6-6, 6-11, 6-12, and 6-15.) Target profit analysis is concerned with estimating the level of sales required to attain a specified target profit. Break-even analysis is a special case of target profit analysis in which the target profit is zero.
1. Basic CVP equations. Both the equation and contribution (formula) methods of break-even and target profit analysis are based on the contribution approach to the income statement. The format of this statement can be expressed in equation form as:
Profits = Sales Variable expenses Fixed expenses
In CVP analysis this equation is commonly rearranged and expressed as:
2. Break-even point using the equation method. The break-even point is the level of sales at which profit is zero. It can also be defined as the point where total sales equals total expenses or as the point where total contribution margin equals total fixed expenses. Break-even analysis can be approached either by the equation method or by the contribution margin method. The two methods are logically equivalent.
a. The Equation Method—Solving for the Break-Even Unit Sales. This method involves following the steps in section (1a) above. Substitute the selling price, unit variable cost and fixed expense in the first equation and set profits equal to zero. Then solve for the unit sales.
b. The Equation Method—Solving for the Break-Even Sales in Dollars. This method involves following the steps in section (1b) above. Substitute the variable expense ratio and fixed expenses in the first equation and set profits equal to zero. Then solve for the sales.
3. Break-even point using the contribution method. This is a short-cut method that jumps directly to the solution, bypassing the intermediate algebraic steps.
a. The Contribution Method—Solving for the Break-Even Unit Sales. This method involves using the final formula for unit sales in section (1a) above. Set profits equal to zero in the formula.
Break-even unit sales = =
b. The Contribution Method—Solving for the Break-Even Sales in Dollars. This method involves using the final formula for sales in section (1b) above. Set profits equal to zero in the formula.
Break-even sales = =
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4. Target profit analysis. Either the equation method or the contribution margin method can be used to find the number of units that must be sold to attain a target profit. In the case of the contribution margin method, the formulas are:
Unit sales to attain target profits =
Dollar sales to attain target profits =
Note that these formulas are the same as the break-even formulas if the target profit is zero.
E. Margin of Safety. (Exercises 6-7 and 6-15.) The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. It is the amount by which sales can drop before losses begin to be incurred. The margin of safety can be computed in terms of dollars:
Margin of safety in dollars = Total sales – Break-even sales
or in percentage form:
Margin of safety percentage =
F. Cost Structure. Cost structure refers to the relative proportion of fixed and variable costs in an organization. Understanding a company’s cost structure is important for decision-making as well as for analysis of performance.
G. Operating Leverage. (Exercises 6-8 and 6-16.) Operating leverage is a measure of how sensitive net operating income is to a given percentage change in sales.
1. Degree of operating leverage. The degree of operating leverage at a given level of sales is computed as follows:
2. The math underlying the degree of operating leverage. The degree of operating leverage can be used to estimate how a given percentage change in sales volume will affect net income at a given level of sales, assuming there is no change in fixed expenses. To verify this, consider the following:
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=
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= Percentage change in net operating income
Thus, providing that fixed expenses are not affected and the other assumptions of CVP analysis are valid, the degree of operating leverage provides a quick way to predict the percentage effect on profits of a given percentage increase in sales. The higher the degree of operating leverage, the larger the increase in net operating income.
3. Degree of operating leverage is not constant. The degree of operating leverage is not constant as the level of sales changes. For example, at the break-even point the degree of operating leverage is infinite since the denominator of the ratio is zero. Therefore, the degree of operating leverage should be used with some caution and should be recomputed for each level of starting sales.
4. Operating leverage and cost structure. Richard Lord, “Interpreting and Measuring Operating Leverage,” Issues in Accounting Education, Fall 1995, pp. 31xx-229, points out that the relation between operating leverage and the cost structure of the company is contingent. It is difficult, for example, to infer the relative proportions of fixed and variable costs in the cost structures of any two companies just by comparing their operating leverages. We can, however, say that if two single-product companies have the same profit, the same selling price, the same unit sales, and the same total expenses, then the company with the higher operating leverage will have a higher proportion of fixed costs in its cost structure. If they do not have the same profit, the same unit sales, the same selling price, and the same total expenses, we cannot safely make this inference about their cost structure. All of the statements in the text about operating leverage and cost structure assume that the companies being compared are identical except for the proportions of fixed and variable costs in their cost structures.
H. Structuring Sales Commissions. Students may have a tendency to overlook the importance of this section due to its brevity. You may want to discuss with your students how salespeople are ordinarily compensated (salary plus commissions based on sales) and how this can lead to dysfunctional behavior. For example, would a company make more money if its salespeople steered customers toward Model A or Model B as described below?
Which model will salespeople push hardest if they are paid a commission of 10% of sales revenue?
I. Sales Mix. (Exercises 6-9, 6-14, and 6-17.) Sales mix is the relative proportions in which a company’s products are sold. Most companies have a number of products with differing contribution margins. Thus, changes in the sales mix can cause variations in a company’s profits. As a result, the break-even point in a multi-product company is dependent on the sales mix.
1. Constant sales mix assumption. In CVP analysis, it is usually assumed that the sales mix will not change. Under this assumption, the break-even level of sales dollars can be computed using the overall contribution margin (CM) ratio. In essence, it is assumed that the company has only one product that consists of a basket of its various products in a specified proportion. The contribution margin ratio of this basket can be easily computed by dividing the total contribution margin of all products by total sales.
Overall CM ratio =
2. Use of the overall CM ratio. The overall contribution margin ratio can be used in CVP analysis exactly like the contribution margin ratio for a single product company. For a multi-product company the formulas for break-even sales dollars and the sales required to attain a target profit are:
Break-even sales =
Sales to achieve target profits =
Note that these formulas are really the same as for the single product case. The constant sales mix assumption allows us to use the same simple formulas.
3. Changes in sales mix. If the proportions in which products are sold change, then the overall contribution margin ratio will change. Since the sales mix is not in reality constant, the results of CVP analysis should be viewed with more caution in multi-product companies than in single product companies.
J. Assumptions in CVP Analysis. Simple CVP analysis relies on simplifying assumptions. However, if a manager knows that one of the assumptions is violated, the CVP analysis can often be easily modified to make it more realistic.
1. Selling price is constant. The assumption is that the selling price of a product will not change as the unit volume changes. This is not wholly realistic since unit sales and the selling price are usually inversely related. In order to increase volume it is often necessary to drop the price. However, CVP analysis can easily accommodate more realistic assumptions. A number of examples and problems in the text show how to use CVP analysis to investigate situations in which prices are changed.
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2. Costs are linear and can be accurately divided into variable and fixed elements. It is assumed that the variable element is constant per unit and the fixed element is constant in total. This implies that operating conditions are stable. It also implies that the fixed costs are really fixed. When volume changes dramatically, this assumption becomes tenuous. Nevertheless, if the effects of a decision on fixed costs can be estimated, this can be explicitly taken into account in CVP analysis. A number of examples and problems in the text show how to use CVP analysis when fixed costs are affected.
3. The sales mix is constant in multi-product companies. This assumption is invoked so as to use the simple break-even and target profit formulas in multi-product companies. If unit contribution margins are fairly uniform across products, violations of this assumption will not be important. However, if unit contribution margins differ a great deal, then changes in the sales mix can have a big impact on the overall contribution margin ratio and hence on the results of CVP analysis. If a manager can predict how the sales mix will change, then a more refined CVP analysis can be performed in which the individual contribution margins of products are computed.
4. In manufacturing companies, inventories do not change. It is assumed that everything the company produces is sold in the same period. Violations of this assumption result in discrepancies between financial accounting net operating income and the profits calculated using the contribution approach. This topic is covered in detail in the chapter on variable costing.
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Assignment Materials
Assignment TopicLevel of
DifficultySuggested
TimeExercise 6-1 Preparing a contribution margin format income statement.................Basic 20 min.Exercise 6-2 Prepare a cost-volume-profit (CVP) graph.........................................Basic 30 min.Exercise 6-3 Computing and using the CM ratio.....................................................Basic 10 min.Exercise 6-4 Changes in variable costs, fixed costs, selling price, and
volume............................................................................................Basic 20 min.Exercise 6-5 Compute the break-even point............................................................Basic 20 min.Exercise 6-6 Compute the level of sales required to attain a target profit...............Basic 10 min.Exercise 6-7 Compute the margin of safety.............................................................Basic 10 min.Exercise 6-8 Compute and use the degree of operating leverage............................Basic 20 min.Exercise 6-9 Compute the break-even point for a multi-product company.............Basic 20 min.Exercise 6-10 Using a contribution format income statement...................................Basic 20 min.Exercise 6-11 Break-even analysis and CVP graphing.............................................Basic 30 min.Exercise 6-12 Break-even and target profit analysis.................................................Basic 30 min.Exercise 6-13 Break-even and target profit analysis.................................................Basic 30 min.Exercise 6-14 Missing data; basic CVP concepts......................................................Basic 20 min.Exercise 6-15 Break-even analysis; target profit; margin of safety; CM
safety; operating leverage..............................................................Difficult 90 min.Case 6-33 Cost structure; break-even; target profits............................................Difficult 75 min.Case 6-34 Break-even analysis with step fixed costs..........................................Difficult 75 min.Case 6-35 Break-evens for individual products in a multi-product
company.........................................................................................Difficult 60 min.
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Essential Problems: Problem 6-18 or Problem 6-25, Problem 6-19 or Problem 6-20, Problem 6-21, Problem 6-24
Supplementary Problems: Problem 6-22, Problem 6-23, Problem 6-26, Problem 6-27, Problem 6-28, Problem 6-29, Problem 6-30, Case 6-31, Case 6-32, Case 6-33, Case 6-34, Case 6-35
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Chapter 6Lecture Notes
Helpful Hint: Before beginning the lecture, show students the sixth segment from the first tape of the McGraw-Hill/Irwin Managerial/Cost Accounting video library. This segment introduces students to many of the concepts discussed in chapter 6. The lecture notes reinforce the concepts introduced in the video.
Chapter theme: Cost-volume-profit (CVP) analysis helps managers understand the interrelationships among cost, volume, and profit by focusing their attention on the interactions among the prices of products, volume of activity, per unit variable costs, total fixed costs, and mix of products sold. It is a vital tool used in many business decisions such as deciding what products to manufacture or sell, what pricing policy to follow, what marketing strategy to employ, and what type of productive facilities to acquire.
I. The basics of cost-volume-profit (CVP) analysis
A. The contribution income statement is helpful to managers in judging the impact on profits of changes in selling price, cost, or volume. For example, let's look at a hypothetical contribution income statement for Racing Bicycle Company (RBC). Notice:
i. The emphasis on cost behavior. Variable costs are separate from fixed costs.
ii. The contribution margin defined as the amount remaining from sales revenue after variable expenses have been deducted.
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iii. Contribution margin is used first to cover fixed expenses. Any remaining contribution margin contributes to net operating income.
iv. Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. Thus:
1. For each additional unit RBC sells, $200 more in contribution margin will help to cover fixed expenses and provide a profit.
2. Notice, 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).
3. Therefore, if RBC sells 400 units a month, it will be operating at the break-even point.
4. If RBC sells one more bike (401 bikes), net operating income will increase by $200.
v. You 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.
1. For example, if RBC sells 430 bikes, its net operating income will be $6,000.
Helpful Hint: Some students may prefer an algebraic approach to CVP analysis. The basic CVP model can be written as:
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Profit = (p – v)q – F
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orProfit = cm × q – F
Where p is the unit selling price, v is the variable cost per unit, q is the unit sales, F is the fixed cost, and cm is the unit contribution margin.
B. CVP relationships in graphic form
i. The relations among revenue, cost, profit, and volume can be expressed graphically by preparing a cost-volume-profit (CVP) graph. To illustrate, we will use contribution income statements for RBC Company at 300, 400, and 500 units sold.
Helpful Hint: Mention to students that the graphic form of CVP analysis may be preferable to them if they are uncomfortable with algebraic equations.
ii. In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. A CVP graph can be prepared in three steps.
1. Draw a line parallel to the volume axis to represent total fixed expenses.
2. Choose some sales volume (e.g., 500 units) and plot the point representing total expenses (e.g., fixed and variable) at that sales volume. Draw a line through the data point back to where the fixed expenses line intersects the dollar axis.
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3. Choose some sales volume (e.g., 500 units) and plot the point representing total sales
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dollars at the chosen activity level. Draw a line through the data point back to the origin.
iii. Interpreting the CVP graph.
1. The break-even point is where the total revenue and total expenses lines intersect.
2. The profit or loss at any given sales level is measured by the vertical distance between the total revenue and the total expenses lines.
Helpful Hint: As an interesting sidelight, ask students what the CVP graph would look like for a public agency like a county hospital receiving a fixed budget each year and collecting fees less than its variable costs. The graph would look like this:
This is the reverse of the usual situation. If such an organization has volume above the break-even point, it will experience financial difficulties.
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Totalexpenses
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C. Contribution margin ratio (CM ratio)
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i. The CM ratio is calculated by dividing the total contribution margin by total sales.
1. For RBC the CM ratio is 40%. Thus, each $1.00 increase in sales results in a total contribution margin increase of 40¢.
ii. The CM ratio can also be calculated by dividing the contribution margin per unit by the selling price per unit.
1. For RBC the CM ratio is 40%. 2. If RBC increases sales from 400 to 500
bikes, the increase in contribution margin ($20,000) can be calculated by multiplying the increase in sales ($50,000) by the CM ratio (40%).
Quick Check – contribution margin ratio
D. Applications of CVP concepts
Helpful Hint: The five examples that are forthcoming should indicate to students the range of uses of CVP analysis. In addition to assisting management in determining the level of sales that is needed to break-even or generate a certain dollar amount of profit, the examples illustrate how the results of alternative decisions can be quickly determined.
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i. Change in fixed cost and sales volume.
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1. What is the profit impact if RBC can increase unit sales from 500 to 540 by increasing the monthly advertising budget by $10,000?
a. Preparing a contribution income statement reveals a $2,000 decrease in profits.
b. A shortcut solution using incremental analysis also reveals a $2,000 decrease in profits.
ii. Change in variable costs and sales volume.
1. What is the profit impact if RBC 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?
a. A shortcut solution reveals a $10,200 increase in profits.
iii. Change in fixed cost, sales price, and sales volume.
1. What is the profit impact if RBC: (1) cuts its
selling price $20 per unit, (2) increases its advertising budget by $15,000 per month, and (3) increases unit sales from 500 to 650 units per month?
a. A shortcut solution reveals a $2,000 increase in profits.
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iv. Change in variable cost, fixed cost, and sales volume.
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1. What is the profit impact if RBC: (1) pays a
$15 sales commission per bike sold instead of paying salespersons flat salaries that currently total $6,000 per month, and (2) increases unit sales from 500 to 575 bikes?
a. A shortcut solution reveals a $12,375 increase in profits.
v. Change in regular sales price.
1. If RBC has an opportunity to sell 150 bikes to a wholesaler without disturbing sales to other customers or fixed expenses, what price should it quote to the wholesaler if it wants to increase monthly profits by $3,000?
a. The price quote should be $320.
In Business InsightsReal companies regularly manage the CVP levers in an effort to increase profits. For example:
“Playing the CVP Game” (page 250) In 2002, General Motors (GM) gave away almost
$2,600 per vehicle in customer incentives such as price cuts and 0% financing.
GM reported that “The pricing sacrifices have been more than offset by volume gains.” Lehman Brothers analysts estimated that GM would sell an additional 395,000 trucks and SUVs and an extra 75,000 cars in 2002.
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The trucks earn an average contribution margin of $7,000 per vehicle, while the cars earn about $4,000 per vehicle.
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All told, the volume gains were expected to bring in an additional $3 billion in profits for GM.
II. Break-even analysis
A. The breakeven point can be computed using either the equation method or the contribution margin method.
i. The equation method is based on the contribution approach income statement.
2. The equation method can be illustrated using data from RBC.
a. The break-even point in units is
determined by creating the equation as shown, where Q is the number of bikes sold, $500 is the unit selling price, $300 is the unit variable expense, and $80,000 is the total fixed expense.
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b. Solving this equation shows that the break-even point in units is 400 bikes.
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3. The equation can be modified as shown to calculate the break-even point in sales dollars. In this equation, X is total sales dollars, 0.60 is the variable expense as a percentage of sales, and $80,000 is the total fixed expense.
a. Solving this equation shows that the break-even point is sales dollars is $200,000.
ii. The contribution margin method has two key equations:
Break-even point in units sold = Fixed expenses CM per unit
Break-even point in sales dollars = Fixed expenses CM ratio
1. The contribution margin method can be illustrated using data from RBC.
a. The break-even point in unit sales (400 bikes) and sales dollars ($200,000) is the same as shown for the equation method.
Quick Check – break-even calculations
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In Business Insights
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The concept of a breakeven point is critically important to dot.com companies. For example:
“Buying on the GoA Dot.com Tale” (page 240) *CD is a company that allows customers to order
music CDs on their cell phones. Suppose you hear a cut from a CD on your car radio that you would like to own. Pick up your cell phone, punch “*CD,” enter the radio station’s frequency, and the time you heard the song, and the CD will soon be on its way to you.
*CD charges about $17 per CD, including shipping. The company pays its suppliers about $13 per CD.
*CD expects to lose $1.5 million on sales of $1.5 million in its first year of operations. That assumes the company sells 88,000 CDs.
Working backwards, it would appear the company’s fixed costs are about $1,850,000 per year. This means the company would need to sell over 460,000 CDs per year just to break-even!
B. Target profit analysis
i. The equation and contribution margin methods can be used to determine the sales volume needed to achieve a target profit. For example:
1. Suppose RBC wants to know how many bikes must be sold to earn a profit of $100,000.
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a. The equation method can be used to determine that 900 bikes must be sold to earn the desired target profit.
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b. The contribution margin method can also be used to determine that 900 bikes must be sold to earn the target profit.
Quick Check – target profit calculations
C. The margin of safety
i. The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. For example:
1. 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.
2. The margin of safety can be expressed as a percent of sales. For example:
a. RBC’s margin of safety is 20% of sales.
3. The margin of safety can be expressed in terms of the number of units sold. For example:
a. RBC’s margin of safety is 100 bikes.
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Quick Check – margin of safety calculations
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In Business InsightsThe margin of safety concept can be readily applied to real companies. For example:
“Soup Nutsy” (page 243) Pak Melwani and Kumar Hathiramani opened a
soup store in Manhattan after watching a Seinfeld episode featuring the “Soup Nazi.”
The store, called Soup Nutsy, sells soup for $6 per serving while incurring variable costs of $2 per serving. Therefore, their CM ratio is 66.67%.
The owners reported that they netted $210,000 of profit on sales of $700,000.
Given this information it is possible to calculate Soup Nutsy’s total fixed costs ($256,690), break-even sales dollars ($385,000), and margin of safety (45%).
III. CVP considerations in choosing a cost structure
A. Cost structure and profit stability
i. 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.
ii. There are advantages and disadvantages to high fixed cost (or low variable cost) and low fixed cost (or high variable cost) structures.
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1. An advantage of a high fixed cost structure is that income will be higher in good years
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compared to companies with a lower proportion of fixed costs.
2. A disadvantage of a high fixed cost structure is that income will be lower in bad years compared to companies with a lower proportion of fixed costs.
3. Companies with low fixed cost structures enjoy greater stability in income across good and bad years.
In Business InsightsCompanies frequently compete with one another based on their cost structures. For example:
“A Losing Cost Structure” (page 245) Both JetBlue and United Airlines use an Airbus
235 to fly from Dulles International airport near Washington D.C., to Oakland, California. Both planes have a pilot, copilot, and four flight attendants.
Based on 2002 data, the pilot on the United Flight earned $16,350 to $18,000 per month compared to $6,800 per month for the JetBlue pilot.
United’s senior flight attendants earned more than $41,000 per year; whereas the Jet Blue attendants were paid $16,800 to $27,000 per year.
Due to intense fare competition from JetBlue and other low-cost carriers, United was unable to cover its higher operating costs on this and many
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other flights. Consequently, United went into bankruptcy at the end of 2002.
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B. Operating leverage
i. Operating leverage is a measure of how sensitive net operating income is to percentage changes in sales.
ii. The degree of operating leverage is a measure, at any given level of sales, of how a percentage change in sales volume will affect profits. It is computed as follows:
Degree of operating leverage = Contribution margin Net operating income
iii. To illustrate, let’s revisit the contribution income statement for RBC:
1. RBC’s degree of operating leverage is 5 ($100,000/$20,000).
2. With an operating leverage of 5, if RBC increases its sales by 10%, net operating income would increase by 50%.
a. The 50% increase can be verified by preparing a contribution approach income statement.
Quick Check – operating leverage calculations
In Business InsightsOperating leverage is an important concept that managers need to understand. Failure to understand this concept can cause serious problems. For example:
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“Fan Appreciation” (page 247)
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Jerry Colangelo, the managing partner of the Arizona Diamondbacks professional baseball team, spent over $100 million to sign six free agents.
The doubling of the team’s payroll coupled with servicing the debt on the team’s new stadium, raised the D-backs annual operating expenses to about $100 million. Accordingly, the team needed to average 40,000 fans per game to break-even.
In an effort to boost revenue, Colangelo decided, during Fan Appreciation Weekend, to raise ticket prices by 12%. Attendance for the season dropped by 15%, turning what should have been a $20 million profit into a loss of over $10 million.
Note that a drop in attendance of 15% did not cut profits just by 15% – that’s the magic of operating leverage at work.
Helpful Hint: Emphasize that the degree of operating leverage is not a constant like unit variable cost or unit contribution margin that a manager can apply with confidence in a variety of situations. The degree of operating leverage depends on the level of sales and must be recomputed each time the sales level changes. Also, note that operating leverage is greatest at sales levels near the break-even point and it decreases as sales and profits rise.
IV. Structuring sales commissions
A. Companies generally compensate salespeople by paying them either a commission based on sales or a salary plus a sales commission. Commissions based
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on sales dollars can lead to lower profits in a company. Consider the following illustration:
i. Pipeline unlimited produces two types of surfboards, the XR7 and the Turbo. The XR7 sells for $100 and generates a contribution margin per unit of $25. The Turbo sells for $150 and earns a contribution margin per unit of $18.
ii. Salespeople compensated based on sales commission will push hard to sell the Turbo even-though the XR7 earns a higher contribution margin per unit.
iii. To eliminate this type of conflict, commissions can be based on contribution margin rather than on selling price alone.
V. The concept of sales mix
A. The term sales mix refers to the relative proportions in which a company’s products are sold. Since different products have different selling prices, variable costs, and contribution margins, when a company sells more than one product, breakeven analysis become more complex as the following example illustrates:
Helpful Hint: Mention that these calculations typically assume a constant sales mix. The rationale for this assumption can be explained as follows. To use simple break-even and target profit formulas, we must assume the firm has a single product. So we do just that – even for multi-product companies. The trick is to assume the company is really selling baskets of products and each
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basket always contains the various products in the same proportions.
i. Assume the RBC sells bikes and carts. The bikes comprise 45% of the company’s total sales revenue and the carts comprise the remaining 55%. The contribution margin ratio for both products combined is 48.2%.
ii. The break-even point in sales would be $352,697. The bikes would account for 45% of this amount, or $158,714. The carts would account for 55% of the break-even sales, or $193,983.
1. Notice a slight rounding error of $176.
VI. Assumptions of CVP analysis
A. Four key assumptions underlie CVP analysis:
i. Selling price is constant.
ii. Costs are linear and can be accurately divided into variable and fixed elements. The variable element is constant per unit, and the fixed element is constant in total over the entire relevant range.
iii. In multiproduct companies, the sales mix is constant.
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iv. In manufacturing companies, inventories do not change. The number of units produced equals the number of units sold.
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Helpful Hint: Point out that nothing is sacred about these assumptions. When violations of these assumptions are significant, managers can and do modify the basic CVP model. Spreadsheets allow practical models that incorporate more realistic assumptions. For example, nonlinear cost functions with step fixed costs can be modeled using “If…Then” functions.
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TM 6-1
CVP ANALYSIS
Cost-volume-profit (CVP) analysis is concerned with the effects on net operating income of:
• Selling prices.• Sales volume.• Unit variable costs.• Total fixed costs.• The mix of products sold.
AGENDA
1. Review of contribution income statement.2. Effects of changes in sales volume on net operating
A contribution format income statement is very useful in CVP analysis since it highlights cost behavior.EXAMPLE: Last month’s contribution income statement for Nord Corporation, a manufacturer of exercise bicycles, follows:
TotalPer Unit
Percent
Sales (500 bikes)....... $250,000
$500 100%
Less variable expenses.................
150,00 0
300 60
Contribution margin.. 100,000 $200 40 %Less fixed expenses... 80,000 Net operating income $ 20,00
0
CONTRIBUTION MARGIN:• The amount that sales (net of variable expenses) contributes
toward covering fixed expenses and then toward profits.• The unit contribution margin remains constant so long as the
selling price and the unit variable cost do not change.
The CM ratio shows how the contribution margin will be affected by a given change in total sales.EXAMPLE: Assume that Nord Corporation’s sales increase by $150,000 next month. What will be the effect on (1) the contribution margin and (2) net operating income?(1) Effect on contribution margin:
Increase in sales................... $150,000
Multiply by the CM ratio........ × 40% Increase in contribution
margin................................$ 60,000
(2) Effect on net operating income:If fixed expenses do not change, the net operating income for the month will also increase by $60,000.
Present Expected
Change
Sales (in units)............ 500 800 300Sales (in dollars)......... $250,00
The margin of safety is the excess of budgeted (or actual) sales over the break-even sales. The margin of safety can be expressed either in dollar or percentage form. The formulas are:
Company X Company YSales................................ $500,00
The relative proportions in which the products are sold is called the sales mix. If the sales mix changes, the overall contribution margin ratio will change.
Example: Assume that total sales remain unchanged at $400,000. However, the sales mix shifts so that more of Product A is sold than of Product B.
Product A Product B TotalSales.......................... $300,00
1. Selling price is constant. The price does not change as volume changes.
2. Costs are linear and can be accurately split into fixed and variable elements. The total fixed cost is constant and the variable cost per unit is constant.
3. The sales mix is constant in multi-product companies.4. In manufacturing companies, inventories do not change. The
number of units produced equals the number of units sold.
