Overview managerial accounting chapter 06

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.. CVP a

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

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 4, 10, 11, 12, 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:

Sales = Variable expenses + Fixed expenses + Profits

a The above equation can be expressed in terms of unit sales as follows:

Price × Unit sales = Unit variable cost × Unit sales + Fixed expenses + Profits

⇓ Unit contribution margin × Unit sales = Fixed expenses + Profits

⇓ Unit sales = Fixed expenses +Profits

Unit contribution margin

b The basic equation can also be expressed in terms of sales dollars using the variable expense ratio:

Sales = Variable expense ratio × Sales + Fixed expenses + Profits

⇓

(1 − Variable expense ratio) × Sales = Fixed expenses + Profits

⇓ Contribution margin ratio* × Sales = Fixed expenses + Profits

⇓ Sales = Fixed expenses +Profits

Contribution margin ratio

* 1 − Variable expense ratio = 1−Variable expenses

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 = Fixed expenses +$0

Unit contribution margin =

Fixed expenses Unit contribution margin

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 = Fixed expenses +$0

Contribution margin ratio =

Fixed expensesContribution margin ratio

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 = Fixed expenses +Target profits

Unit contribution margin

Dollar sales to attain target profits = Fixed expenses +Target profits

Contribution margin ratioNote 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 = Margin of safety in dollars

Total sales

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:

Contribution marginDegree of operating leverage =

Net operating income

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:

Degree of operating Percentage change

leverage × in sales = Contribution margin New sales-Sales

Net operating income Sales

= Contribution margin New sales-SalesSales Net operating income

= CM ratio New sales-Sales

Net operating income

= CM ratio New sales-CM ratio Sales

Net operating income

New contribution margin-Contribution margin

Net operating income

Net operating income

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?

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 = Total contribution margin

Total sales

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 = Fixed expenses

Overall CM ratio

Sales to achieve target profits = Fixed expenses +Target profits

Overall CM ratioNote 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

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

Assignment Materials

Assignment Topic

Level of Difficulty

Suggested Time

Exercise 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

ratio Basic 30 min Exercise 6-16 Operating leverage Basic 15 min Exercise 6-17 Multi-product break-even analysis Basic 30 min Problem 6-18 Basic CVP analysis; graphing Basic 60 min Problem 6-19 Basics of CVP analysis; cost structure Basic 60 min Problem 6-20 Basics of CVP analysis Basic 60 min Problem 6-21 Sales mix; multi-product break-even analysis Basic 30 min Problem 6-22 Break-even analysis; pricing Medium 45 min Problem 6-23 Interpretive questions on the CVP graph Medium 30 min Problem 6-24 Various CVP questions; break-even point; cost structure;

target sales Medium 75 min Problem 6-25 Graphing; incremental analysis; operating leverage Medium 60 min Problem 6-26 Changes in fixed and variable costs; break-even and target

profit analysis Medium 30 min Problem 6-27 Break-even and target profit analysis Medium 30 min Problem 6-28 Changes in cost structure; break-even analysis; operating

leverage; margin of safety Medium 60 min Problem 6-29 Sales mix; break-even analysis; margin of safety Medium 45 min Problem 6-30 Sales mix; multi-product break-even analysis Medium 60 min Case 6-31 Detailed income statement; CVP analysis Difficult 60 min Case 6-32 Missing data; break-even analysis; target profit; margin of

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

Essential Problems: Problem 18 or Problem 25, Problem 19 or Problem 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 6 Lecture 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

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Profit = (p – v)q – F

or Profit = 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 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

Total expenses

Total revenue

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C Contribution margin ratio (CM ratio)

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

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

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

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

“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

• 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

1 The equation can be stated in one of two ways:

Profits = (Sales – Variable expenses) – Fixed Expenses

$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

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

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In Business Insights

The concept of a breakeven point is critically important

to dot.com companies For example:

“Buying on the Go − A 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

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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

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 even volume of sales For example:

break-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