Determine the breakeven point and output level needed to achieve a target operating income using theequation, contribution margin, and graph methods 4.. Definition of CVP analysis: exami
Trang 1CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS
LEARNING OBJECTIVES
1 Understand the assumptions underlying cost-volume-profit (CVP) analysis
2 Explain the features of CVP analysis
3 Determine the breakeven point and output level needed to achieve a target operating income using theequation, contribution margin, and graph methods
4 Understand how income taxes affect CVP analysis
5 Explain CVP analysis in decision making and how sensitivity analysis helps managers cope with uncertainty
6 Use CVP analysis to plan fixed and variable costs
7 Apply CVP analysis to a company producing different products
8 Adapt CVP analysis to situations in which a product has more than one cost driver
9 Distinguish between contribution margin and gross margin
CHAPTER OVERVIEW
Chapter 3 presents the cost-volume-profit (CVP) analysis model Much “what-if” knowledge may be derived from the use of a model, certainly the case with CVP analysis Models are developed from known relationships and used for forecasting CVP uses one cost driver, volume of units produced and sold, and uses the behavior of costs, variable or fixed, in relation to that cost driver As with all models, acomplex situation is simplified The assumptions of CVP analysis identify the simplifications made Throughout the chapter, reference is made to changes in the CVP model to allow for more complexity The complexities do not render the model useless, they generally require additional factors be considered for producing better predictions
Relevant information for strategic and planning decisions can be made readily available The text focuses
on accountants providing value for decision makers CVP analysis is a useful tool for providing
cost/beneficial information on a timely basis The basic CVP model deserves careful study The last section of the appendix is noteworthy With the emphasis on decision making in the text, the point made about distinguishing between a good decision and a good outcome and/or a good decision and a bad outcome seems especially relevant
TEACHING TIP: An excellent article on the value of models is “Going Forward in Reverse” by Einhorn
& Hogarth, Harvard Business Review, Jan./Feb 1987, pp 66-70.
Trang 2I Basic Cost-Volume-Profit (CVP) model
I
A Definition of CVP analysis: examines the behavior of total revenues, total costs, and operating
income as changes occur in output level, selling price, variable cost per unit, and/or fixed costs
Learning Objective 1:
Understand the assumptions underlying cost-volume-profit (CVP) analysis
B Assumptions
1 Simplifications of complex relationships
a Number of output units only revenue driver and only cost driver
b Total costs can be separated into the primary categories of variable costs and fixed costs
c Total revenues and total costs are linear within the relevant range (and time period)
d Unit selling price, unit variable costs, and fixed costs known and constant
e Single product or constant sales mix
f Time value of money effects ignored
2 Complexities noted in chapter that affect basic model
a Multiple revenue and multiple cost drivers
b Lack of linearity
Do multiple choice 1 Assign Exercise 3-16.
Learning Objective 2:
Explain the features of CVP analysis
C Features and terminology
1 Income model: Revenues – Expenses = Income
2 Contribution margin: Total revenues – Total variable costs
a Calculated per unit: Selling price/unit – Variable cost/unit [Exhibit 3-1]
b Calculated as a percent of sales or ratio: Contribution Margin/Sales
c Calculated as a total: Sales (Revenues) – Variable costs
3 Multiple-step-type income statement: Rev – VC = CM – FC = OI
4 Operating income versus Net income
Trang 3a OI + Nonoperating Rev – Nonoperating Costs – Income Tax = NI
b Chapter 3 assumes zero for nonoperating revenues and expenses
Do multiple choice 2 Assign Exercises 3-17 and 3-20.
II Breakeven concept
A Definition of breakeven point: quantity of output sold at which total revenues equal total costs
Learning Objective 3:
Determine the breakeven point and output level needed to achieve a target operating income using the equation, contribution margin, and graph methods
B Contribution margin approach to calculation
1 Equation method: (USP x Q) – (UVC x Q) – FC = OI
2 Contribution margin method
a Per unit approach that calculates breakeven in units of output [Use algebraic equation UCM x Q = FC + OI —>UCM x Q = Total CM to calculate Q , units, as FC + OI = CM]
b Ratio or percentage approach that calculates breakeven in dollars of revenue [Use
equation CM% x Revenues = FC + OI—>CM% x Revenues = Total CM to calculate Revenues by dividing both sides by CM%: CM% = CM/Revenues]
3 Graph method: x-axis output units, y-axis dollars; total revenue and total cost lines intersect at breakeven output quantity [Exhibits 3-2 and 3-3]
Do multiple choice 3 Assign Exercises 3-21 and 3-23 and Problem 3-34.
TEACHING TIP: Exercise 3-23 is a good example to use before studying sales mix This exercise uses
an average revenue amount for the calculations When studying sales mix, referencing an “average sales check per customer” provides an illustration of differing products, from a cup of coffee to a full dinner More sales checks for cups of coffee than for full dinners would change the “average” downward
C Useful for target income
1 Operating income: FC + Target OI can be divided by UCM for units of output or divided by CM% for dollars of revenue (sales)
Learning Objective 4:
Understand how income taxes affect CVP analysis
2 Net income: Target OI must be adjusted by incorporating income tax
Target net income/(1 – Tax rate) = Target operating income
TEACHING TIP: The use of the income statement format may be helpful to some students,
Trang 4Tax (Tax Rate x TOI) 35% -35%TOI {.35x40,000 14,000}
Target Net Income 65%TOI = $26,000 —> TOI = $26,000 / 0.65 = $40,000
3 Any of the three approaches for calculating breakeven may be used for target income
TEACHING TIP: A caution for students when calculating target income, especially if using total rather
than unit costs: variable costs in total are variable with respect to volume and will change if output units
change or are expected to change Use of an equation with contribution margin is helpful To calculate revenues use the equation, CM% x Revenues = CM in total dollars, or to calculate output units, UCM x Q
= CM in total dollars [CM in total dollars in equal to FC + target OI.]
Do multiple choice 4 Assign Problem 3-36
D Effect of income taxes: BEP unaffected by income taxes because no tax is no operating income
Do multiple choice 5 Assign Problem 3-39.
Learning Objective 5:
Explain CVP analysis in decision making and how sensitivity analysis helps managers cope with
uncertainty
E Useful for decision making
1 Can incorporate changes in total fixed costs, selling price per unit (changes CM per unit), unitvariable cost, and units sold
2 Helps managers by estimating long-term profitability of choices
3 Evaluates risk to operating income if original predicted data not achieved
III Sensitivity analysis [Exhibit 3-4]
A Definitions
1 Sensitivity analysis: “what-if” technique managers use to examine how a result will change
if original predicted data not achieved or if an underlying assumption changes
2 Uncertainty: possibility that an actual amount will deviate from an expected amount
B Used before committing costs
1 Analysis of changes in operating income for changes underlying assumptions
2 Systematic and efficient approach
3 Allows for calculation of margin of safety: amount of budgeted revenues over and above
breakeven revenues
4 [Appendix] Probability and expected value incorporated
Trang 5Do multiple choice 6 Assign Problems 3-38, 3-40 and 3-41.
Learning Objective 6:
Use CVP analysis to plan fixed and variable costs
II C Highlights risks and returns
1 Highlights risks and returns as fixed costs are substituted for variable costs in cost structure
TEACHING TIP: A section in the chapter appendix references a manager’s attitude toward risk (each
decision has its own attitude as well as each manager has such an attitude) Following are descriptive
phrases for discussing risk attitudes: (1) risk neutral: decision maker weighs each dollar as a full dollar,
no more, no less; (2) risk averse: decision maker weighs loss of dollar as greater than gain of dollar; (3) risk seeking: decision maker weighs gain of dollar as greater than loss of dollar.
2 Demand for product or service is variable [Exhibit 3-5]
3 Use of operating leverage: effect fixed costs have on changes in operating income as changes occur in units sold (contribution margin)—degree of operating leverage equals
contribution margin divided by operating income [Concepts in Action]
Do multiple choice 7 Assign Exercise 3-26.
TEACHING TIP: Operating leverage is obviously named for the “lever” effect that comes from the use
of fixed costs to generate more profit Costs are incurred to generate revenues If the choice exists to incur fixed or variable cost, and fixed is chosen, then variable cost would be less, yielding a larger
contribution margin and the possibility of larger profit Once the fixed costs are recovered, the
contribution margin is profit This effect can be seen on a breakeven graph The intersecting revenue andtotal cost lines create equal and opposite angles at the intersection point One can note that the risk (downside) is equal to the reward (upside) The larger the fixed cost, the wider the intersection angles usually: the greater the opportunity for reward, the greater the possibility of loss
4 Cost labels as fixed or variable
a Time frame affects costs: shorter the time frame, more costs fixed
b Relevant range assumes limits for constancy of total fixed costs or unit variable costs
c Specific question/decision affects relevancy of cost classification
IV Products and CVP: A complexity
Learning Objective 7:
Apply CVP analysis to company producing different products
A Sales mix: CVP assumption for one product or a constant mix of different products
1 No unique breakeven point when selling a mix of multiple products: each new mix, a new BEP
Trang 62 Profit varies even though same total quantity of units sold: Mix with more units of larger dollar amount of contribution margin per unit yields greater profit{affects BEP}
3 Profit varies even though same total dollars of revenue: Mix with more units of larger contribution margin ratio sold yields greater profit
Do multiple choice 8 Assign Exercise 3-28 and Problems 3-44 and 3-46.
B Service as a product
1 Define “product” or output unit for measurement
2 Use CVP model for relationship between revenues, variable costs and fixed costs
3 Use CVP analysis for prediction and consideration for adjusting operations
Learning Objective 8:
Adapt CVP analysis to situations in which a product has more than one cost driver
C Multiple cost drivers
1 No unique breakeven point
2 CVP model can be adapted by changes to the variable cost for situation but simple formula cannot be used
Do multiple choice 9 Assign Exercise 3-30 and Problem 3-43.
Learning Objective 9:
Distinguish between contribution margin and gross margin
D CVP uses contribution margin as opposed to gross margin* on financial accounting income statements
1 Service-sector companies
a Costs primarily classified as either variable or fixed for calculating contribution margin
b Do not have cost of goods sold so cannot use gross margin emphasis
Trang 73 Manufacturing-sector companies
a Costs primarily classified as variable or fixed for calculating contribution margin
b Costs primarily classified as manufacturing or nonmanufacturing in calculating gross margin
c Variable nonmanufacturing costs above the “margin line” for contribution margin calculation but below for gross margin
d Fixed manufacturing costs above the “margin line” for gross margin calculation but below for contribution margin
e Fixed manufacturing costs used as per unit cost for cost of goods sold (gross margin) but
as total cost for contribution margin
4 For statement comparison purposes costs should be classified with both classifications
a Variable manufacturing and variable nonmanufacturing
b Fixed manufacturing and fixed nonmanufacturing
* Gross margin can be expressed as a total, as an amount per unit, or as a percentage If gross margin is expressed
as a percentage the basis could be revenue or cost of goods sold Conversion is simple from one base to the other, but the base must be noted for one to know to convert See TEACHING TIP for conversion
TEACHING TIP: Quick conversion calculation for GM as a percentage of CGS or revenue:
Conversion: Divide GM (as a percentage of CGS) by revenue (when CGS is 100%) to convert GM to a
percentage of revenue: 25%/125% = 20%; a markup of 25% with a margin of 20% or for GM as a percentage of CGS when originally given as percentage of revenue: 33.3%/66.7% = 50%; a margin of
33.3% with a markup of 50%
Do multiple choice 10 Assign Exercise 3-31.
V Appendix: Decision models and uncertainty [Exhibit 3-6]
A Use of a decision model
B Identify events (differentiated from actions)
C Consider past experience to project probabilities
D Incorporate risk attitude
E Distinguish between good decision and good outcome
CHAPTER QUIZ SOLUTIONS: 1.a 2.c 3.b 4.a 5.c 6.d 7.b 8.c 9.b 10.d
Trang 8CHAPTER QUIZ
1 Which of the following is not an assumption of cost-volume-profit analysis?
a The time value of money is incorporated in the analysis
b Costs can be classified into variable and fixed components
c The behavior of revenues and expenses is accurately portrayed as linear over the relevant range
d The number of output units is the only driver
2 Contribution margin is calculated as
a total revenue – total fixed costs
b total revenue – total manufacturing costs (CGS)
c total revenue – total variable costs
d operating income + total variable costs
Questions 3–5 are based on the following data:
Tee Times, Inc., produces and sells the finest quality golf clubs in all of Clay County The company expects the following revenues and costs in 2003 for its Elite Quality golf club sets:
Revenues (400 sets sold @ $600 per set) $240,000
6 One way for managers to cope with uncertainty in profit planning is to
a use CVP analysis because it assumes certainty
b recommend management hire a futurist whose work it is to predict business trends
c wait to see what does happen and prepare a report based on actual amounts
d use sensitivity analysis to explore various what-if scenarios in order to analyze changes in revenues or costs or quantities
Trang 97 The Beta Mu Omega Chi (BMOC) fraternity is looking to contract with a local band to perform at its annual mixer If BMOC expects to sell 250 tickets to the mixer at $10 each, which of the following arrangements with the band will be in the best interest of the fraternity?
a $2500 fixed fee
b $1000 fixed fee plus $5 per person attending
c $10 per person attending
d $25 per couple attending
8 Twin Products Company produces and sells two products Product M sells for $12 and has variable costs of $6 Product W sells for $15 and has variable costs of $10 Twin predicted sales of 25,000 units of M and 20,000 of W Fixed costs are $60,000 per month Assume that Twin achieved its sales goal of $600,000 for September, but fell short of its expected operating income of $190,000 Which of the following descriptions best describes the actual results reported of revenue of $600,000 and operating income of less than $190,000?
a Twin sold 50,000 of M and no product W
b Twin sold more of both products M and W than expected
c Twin sold more of product W and less of product M than expected
d Twin sold more of product M and less of product W than expected
9 In the situation of multiple cost drivers, CVP analysis can be
a modified so that the various simple formulas can be used by applying them separately to each cost driver
b used with the same formulas as used with a single cost driver
c changed by incorporating all of the cost drivers into the breakeven formula to calculate the unique point of output at which the company would break even
d adapted by incorporating the cost drivers into the calculation of the variable costs
10 Which of the following statements is true?
a “Gross margin” can be used only in financial accounting income statements
b “Gross margin” implies a different cost classification usage than the term “contribution margin” when used in income statements
c “Contribution margin” can be used in place of “gross margin” if management prefers that terminology in their financial statements
d Only manufacturing-sector companies use the term “gross margin” in their income statements
Trang 10WRITING/DISCUSSION EXERCISES
1 Understand the assumptions underlying cost-volume-profit (CVP) analysis
How helpful is a model, such as CVP analysis, if the assumptions on which it is based seem too simplistic? Even the simplest models can be helpful Models describe known relationships and their use can prevent errors of omission by focusing on basic concepts and interactions as well as enable learning From a simple checklist to the most sophisticated artificial intelligence program, models force one to take certain steps and combine factors in particular ways Airline pilots, even the most experienced, use a checklist before take-off to insure that they did not forget a key item Models or simulations are also helpful in teaching a person to perform a task
The CVP analysis model is a cost-effective tool that managers can use for gathering relevant information
in the process of making decisions The simple CVP relationships are helpful in strategic and long-range planning decisions, for example Knowing the assumptions of the basic model, one can incorporate changes to refine or particularize for a given situation The need for a more complex model is recognized after using the basic ideas of the CVP analysis The choice of incurring additional costs is supported for
gaining significant benefit of improved decisions with a more complicated and expensive approach
2 Explain the features of CVP analysis
Why is contribution margin such an important element in CVP analysis? Contribution
margin is an effective summary of the reasons that operating income changes as the number of units sold changes Variable costs increase in total as volume of output units sold increase, the same behavior as revenue Contribution margin is the net or “summary” of those two elements, revenues and variable costs
If revenues increase due to volume increases, the contribution margin increases A change in the selling price will change the contribution margin as will a change in variable cost per unit Understanding contribution margin can enable one to quickly note that an increase in selling price without a
corresponding change in variable cost will increase the “contribution” to fixed cost and income Or a decrease in variable cost without a corresponding decrease in selling price will “contribute” more to income and/or the coverage of fixed costs Using revenues and variable costs as per unit measures, the
“contribution” per unit of product sold can provide a shortcut to breakeven calculations or “what-if” questions Each unit of product sold contributes that amount as it “walks out the door.”
Contribution margin is the connecting link between the behavior of variable cost and fixed cost It is the amount that “contributes” to covering total fixed costs and providing income In the calculation of number of output units or total revenues to achieve targeted operating income, contribution margin is the pivot point The total amount of contribution margin, fixed costs in total added to targeted operating income as a total, is equal to an amount of contribution margin per unit multiplied by the number of units needed to be sold to achieve that desired amount of income Contribution margin converts total dollars tounits
Trang 113 Determine the breakeven point and output level needed to achieve target operating income using the equation, contribution margin, and graph methods
How can a company have more than one breakeven point? CVP analysis suggests only one breakeven point because of its assumptions The authors of the text note that there is no unique breakevenpoint in the case of multiple products and multiple cost drivers Likewise a curved, rather than a straight line depicting the time value with the compounding of interest allows for more than one breakeven point The CVP analysis assumptions preclude the use of these characteristics
Economists note at least two breakeven points in graphing revenues and costs The revenue line is depicted as an upward arcing curve to the right intersecting the straight diagonal line of costs, forming a type of bow (as in archery—the bow frame as revenue and the cost line as its cord) The first or lowest point of intersection is the CVP analysis breakeven point The second or upper point of intersection is determined by the relationship in demand, quantity, and price To keep or increase demand for the product, the economic assumption is that the price must be reduced accordingly Reducing the price will tend to lower total revenue even though output quantity (supply) is increasing, which concurrently causes increasing costs CVP analysis recognizes these assumptions by imposing the relevant range and time period constraints
The question may be how can a company calculate only one breakeven point when realistically the point
at which loss becomes profit, or vice versa, can exist at many turns The value of examining the
relationships between revenues and costs enables managers to avoid pitfalls A simple or basic
calculation is a good starting point to understanding the complex interactions
4 Understand how income taxes affect CVP analysis
What changes to CVP analysis would have to be made if a company did have
nonoperating revenues and expenses? The presence of nonoperating revenues and expenses would not change CVP analysis CVP analysis is an operations concept and accordingly uses operating income Tax effects on operating decisions are important information for managers and can be
incorporated by using net income The text assumes the nonoperating items to be zero for ease of
computation Most nonoperating items are noted net of tax, causing no change to the income tax on operations The use of the subtotal “Income before income taxes” is used to compute the amount of income taxes in arriving at net income “Income before income taxes” would be defined as target
operating income + nonoperating revenues – nonoperating expenses
Target net income = (Income before income taxes) – [(Income before income taxes) x (Tax rate)]
+Nonoperating revenue 80,000
Income before income tax $500,000 100%
Income tax expense (30%) 150,000 30%
Net income (targeted) $350,000 70%