High low method questions and answers pdf

6 Cost Estimation and Cost-Volume-Profit Relationships

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Learning Objectives

After studying Chapter 6, you will be able to:

• Understand the significance of cost behavior to decision making and control.

• Identify the interacting elements of cost-volume-profit analysis.

• Explain the break-even equation and its underlying assumptions.

• Calculate the effect on profits of changes in selling prices, variable costs, or fixed costs.

• Calculate operating leverage, determine its effects on changes in profit, and understand how margin of safety relates to operating leverage.

• Find break-even points and volumes that attain desired profit levels when multiple products are sold in combination.

• Obtain cost functions by account analysis, the engineering approach, the scattergraph approach, and the high-low method.

• Estimate cost functions using regression analysis, construct control limits, and apply multiple regression.

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Chapter Outline

6.1 Significance of Cost Behavior to Decision Making and Control Decision Making Planning and Control Trends in Fixed Costs

6.2 Cost-Volume-Profit (CVP) Analysis Basics of CVP Analysis A Desired Pretax Profit A Desired Aftertax Profit

6.3 Graphical Analysis The Break-Even Chart Curvature of Revenue and Cost Lines The Profit-Volume Graph

6.4 Analysis of Changes in CVP Variables Sales Volume Variable Costs Price Policy Fixed Costs Ethical Considerations When Changing CVP Variables

6.5 Measures of Relationship Between Operating Levels and Break- Even Points Operating Leverage Margin of Safety

6.6 The Sales Mix

6.7 Cost Estimation Account Analysis Engineering Approach Scattergraph and Visual Fit High-Low Method Ethical Considerations in Estimating Costs Other Issues for Cost Estimation

6.8 Regression and Correlation Analyses Linear Regression Control Limits Multiple Regression

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Section 6.1 Significance of Cost Behavior to Decision Making and Control

“Can You Lose a Little on Each One, but Make It Up on Volume?”

David Scott, owner of Baker Cruise Lines, began his cruise business 15 years ago. During that time, he has enjoyed a number of upswings and weathered several downturns in the economy. Generally, the business has had profitable years and has provided a high standard of living for David and his family.

But times are changing. Personnel costs continue to rise, particularly fringe benefits like medical insurance premiums. Other costs of operating the cruise ships continue to rise as well. At the same time, because of increased competition from new competitors, prices of cruises have fallen dramatically. David has begun to slash operating costs, but he still faces shrinking profit margins.

Because of high profitability in the past, David never analyzed how his costs change in relation to changes in activity levels, nor did he analyze the relationships among revenues, costs, and passenger volume to see how they relate to profit levels. Now, David is wondering how far revenues can drop before he sees the red ink in losses. With that information, he hopes to identify what changes will keep operations profitable. David sees many other businesses closing their doors and is fearful he will have to follow suit someday. He just doesn’t know what factors will influence his future costs and revenues.

Managers like David Scott of Baker Cruise Lines need to understand cost behavior and cost estimation to be in a better position to plan, make decisions, and control costs. As we dis- cussed in Chapter 1, cost behavior describes the relationship between costs and an activity as the level of activity increases or decreases. Determining cost behavior is important to management’s understanding of overhead costs, marketing costs, and general and admin- istrative expenses and for proper implementation of budgets and budgetary controls. With knowledge of cost behavior, managers can also estimate how costs are affected as future activity levels change, which can lead to better decisions. In addition, knowledge of cost behavior can assist managers in analyzing the interactions among revenues, costs, and vol- ume for profit-planning purposes. These interactions are covered later in this chapter.

6.1 Significance of Cost Behavior to Decision Making and Control

To understand more fully the significance of a manager’s analysis of cost behavior, we look at three areas: decision making, planning and control, and trends in fixed costs.

Decision Making Cost behavior affects the decisions management makes. Variable costs are the incremental or differential costs in most decisions. Fixed costs change only if the specific decision includes a change in the capacity requirement, such as more floor space or adding another salaried employee.

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Section 6.1 Significance of Cost Behavior to Decision Making and Control

Cost-based pricing requires a good understanding of cost behavior because fixed costs pose conceptual problems when converted to per-unit amounts. Fixed costs per unit assume a given volume. If the volume turns out to be different from what was used in determining the cost-based price, the fixed cost component of the total cost yields a misleading price. For instance, if fixed costs total $2,000 and currently 2,000 units are being produced, then the fixed cost per unit is $1. However, if production is cut in half, then the fixed cost per unit increases to $2 ($2,000 / 1,000). Managers must know which costs are fixed, as well as antici- pated volume, to make good pricing decisions.

Planning and Control A company plans and controls variable costs differently than it plans and controls fixed costs. Variable costs are planned in terms of input/output relationships. For example, for each unit produced, the materials cost consists of a price per unit of materials times the number of units of materials; the labor cost consists of the labor rate times the number of labor hours. Once operations are underway, levels of activities may change. The input/output relation- ships identify changes in resources necessary to respond to the change in activity. If activity levels increase, this signals that more resources (materials, labor, or variable overhead) are needed. If activity levels decrease, the resources are not needed, and procedures can be trig- gered to stop purchases and reassign or lay off workers. In cases where more materials or labor time are used than are necessary in the input/output relationship, inefficiencies and waste are in excess of the levels anticipated, and managers must investigate causes and elimi- nate or reduce the financial impact of the unfavorable variances.

Fixed costs, on the other hand, are planned on an annual basis, if not longer. Control of fixed costs is exercised at two points in time. The first time is when the decision is made to incur a fixed cost. Management evaluates the necessity of the cost and makes the decision to move forward or reject the proposal. Once fixed costs are incurred, another point of control enters, that being the daily decision of how best to use the capacity provided by the cost. For example, a university makes a decision to build a new classroom and faculty office building. That deci- sion is the first point of control. After construction, control is implemented in using the build- ing to its maximum capacity. This will occur if classes are scheduled throughout the day and evening.

Another difference in the planning and control of variable and fixed costs is the level at which costs are controllable. Variable costs can be controlled at the lowest supervisory level. Fixed costs are often controllable only at higher managerial levels.

Trends in Fixed Costs Organizations are finding that an increasing portion of their total costs are fixed costs. The following are a few of the more critical changes taking place.

Implementation of more automated equipment is replacing variable labor costs and a major share of the variable overhead costs. Many companies have laid off hourly employees, which is a variable cost, and replaced them with machinery that creates depreciation and other fixed costs. Thus, fixed costs are becoming a more significant part of total costs. Costs associated

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Section 6.2 Cost-Volume-Profit (CVP) Analysis

with the additional automated equipment such as depreciation, taxes, insurance, and fixed maintenance charges are substantially higher. Some industries, like steel and automobile, are becoming essentially fixed cost industries, with variable costs playing a less important role than was once the case.

Another factor that has helped to increase fixed costs significantly is the movement in some industries toward a guaranteed annual wage for production workers. Employees who were once hourly wage earners are now becoming salaried. With the use of more automated equip- ment, the workers of a company may not represent “touch labor,” that is, work directly on the product. Instead, the production worker may merely observe that the equipment is operating as it should and is properly supplied with materials or may monitor production by means of a television screen. The production line employee is handling more of the functions normally associated with indirect labor, and the cost is a fixed cost.

Contemporary Practice 6.1: Separating Variable and Fixed Costs

A survey of 148 German companies and 130 U.S. companies found that 46% of U.S. companies separate variable and fixed costs for each cost center, as compared to 36% of German companies.

Source: Krumwiede, K., & Suessmair, A. (2007, June). Getting down to specifics on RCA. Strategic Finance, 51–55.

6.2 Cost-Volume-Profit (CVP) Analysis The separation of fixed costs from variable costs contributes to an understanding of how revenues, costs, and volume interact to generate profits. With this understanding, managers can perform any number of analyses that fit into a broad category called cost-volume-profit (CVP) analysis or, more commonly, break-even analysis. Examples of such analyses include finding the:

1. Number of unit sales required to break even (i.e., total revenues equal total costs) 2. Dollars of sales needed to achieve a specified profit level 3. Effect on profits if selling prices and variable costs increase or decrease by a specific

amount per unit 4. Increase in selling price needed to cover a projected fixed cost increase

CVP analysis, as its name implies, examines the interaction of factors that influence the level of profits. Although the name gives the impression that only cost and volume determine profits, several important factors exist that determine whether we have profits or losses and whether profits increase or decrease over time. The key factors appear in the basic CVP equation:

(Unit selling price)(Sales volume) – (Unit variable cost)(Sales volume) – Total fixed cost =

Pretax profit

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Section 6.2 Cost-Volume-Profit (CVP) Analysis

The basic CVP equation is merely a condensed income statement, in equation form, where total variable costs (Unit variable cost × Sales volume in units) and total fixed costs are deducted from total sales revenues (Unit selling price × Sales volume in units) to arrive at pretax profit. This equation, as well as other variations that will be discussed later, appears as Equation 1 in Figure 6.1.

Figure 6.1: Equations for CVP analysis

1. Basic CVP equation:

2. CVP equation taxes:

3. Break-even point in units:

4. Break-even point in dollars:

5. Target pretax profit, in dollars:

6. Target pretax profit, in units

7. Target aftertax profit, in units:

8. Target aftertax profit, in dollars:

(p – v)x – FC = PP

[(p – v)x – FC](1 – t) = AP

FC (p – v)

FC CM%

FC + PP p – v

FC + PP CM%

FC + (1 – t) p – v

AP FC + PP p – v

=

FC +

(1 – t) CM%

AP FC + PP CM%

=

= Fixed cost dollars

= Selling price per unit

= Variable cost per unit

= Contribution margin ratio (p – v) / p

= Aftertax profit

= Pretax profit

= Income tax rate

= Sales volume in units

FC

p

v

CM%

AP

PP

t

x

Where:

The excess of total sales revenue over total variable cost is called the contribution margin or, more precisely, variable contribution margin. From the basic CVP equation, we see that the contribution margin contributes to covering fixed costs as well as generating operating income. The contribution margin, as well as the contribution margin ratio, often plays an important role in CVP analysis. The latter measure is the ratio of the contribution margin to total sales revenue (or, equivalently, the ratio of the contribution margin per unit to the selling price).

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Section 6.2 Cost-Volume-Profit (CVP) Analysis

Before proceeding, several fundamental assumptions are made to strengthen CVP analysis:

1. Relevant range—CVP analysis is limited to the company’s relevant range of activity (i.e., the normal range of expected activity).

2. Cost behavior identification—fixed and variable costs can be identified separately. 3. Linearity—the selling price and variable cost per unit are constant across all sales

levels within the company’s relevant range of activity. 4. Equality of production and sales—all units are produced and sold and inventory

changes are ignored. 5. Activity measure—the primary cost driver is volume of units. 6. Constant sales mix—the sales of each product in a multiproduct firm is a constant

percentage.

Assumptions 1, 2, and 3 are straightforward. Assumption 4 is required because if sales and production are not equal, some amount of variable and fixed costs are treated as assets (inventories) rather than expenses. As long as inventories remain fairly stable between adja- cent time periods, this assumption does not seriously limit the applicability of CVP analysis. Regarding assumption 5, factors other than volume may drive costs, as we have discussed earlier in this chapter, and as we will discuss further in later chapters. Costs that vary with cost drivers other than volume can be added to the fixed-cost component. Assumption 6 is discussed in detail later in this chapter. In many cases, these assumptions are and must be violated in real-world situations, but the basic logic and analysis adds value. While our discus- sion may appear to presume that CVP analysis is applicable only to companies that sell physi- cal products, these techniques are just as applicable to service organizations.

Basics of CVP Analysis CVP analysis is often called break-even analysis because of the significance of the break-even point, which is the volume where total revenue equals total costs. It indicates how many units of product must be sold or how much revenue is needed to at least cover all costs. All break-even analysis can be approached by using Equation 1 and by creating its derivations, as shown in Figure 6.1.

Each unit of product sold is expected to yield revenue in excess of its variable cost and thus contribute to the recovery of fixed costs and provide a profit. The point at which profit is zero indicates that the contribution margin is equal to the fixed costs. Sales volume must increase beyond the break-even point for a company to realize a profit.

Let’s look at CVP relationships in the context of Felsen Electronics, a wholesale distributor of calculators. Assume that price and costs for its calculators are as follows:

Dollars per Unit Percentage of Selling Price

Selling price $25 100%

Variable cost 15  60%

Contribution margin $10  40%

Total fixed cost $100,000

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Section 6.2 Cost-Volume-Profit (CVP) Analysis

Each calculator sold contributes $10 to covering fixed costs and the creation of a profit. Hence, the company must sell 10,000 calculators to break even. The 10,000 calculators sold will result in a total contribution margin of $100,000, equaling total fixed cost.

The break-even point can be calculated by using the basic CVP equations that appear as Equa- tions 3 and 4 in Figure 6.1. For Felsen Electronics, the break-even point is determined as follows:

Break-even point in units = Total fixed cost / Contribution margin per unit

= $100,000 / $10 per unit

= 10,000 units

A break-even point measured in sales dollars can be computed by directly using Equation 4 of Figure 6.1, as follows:

Total fixed cost / Contribution margin ratio = Break-even point in sales dollars

$100,000 / 0.40 = $250,000

A Desired Pretax Profit In business, only breaking even is not satisfactory, but the break-even relationships do serve as a base for profit planning. If we have a target profit level, we can insert that number into the basic CVP equation. This yields the following equations, which appear as Equations 5 and 6 in Figure 6.1:

(Total fixed cost + Pretax profit) / Contribution margin ratio = Sales dollars required

(Total fixed cost + Pretax profit) / Contribution margin per unit = Unit sales required

Continuing with the Felsen Electronics illustration, suppose that Enoch Goodfriend, the Presi- dent, had set a profit objective of $200,000 before taxes. The units and revenues required to attain this objective are determined as follows:

($100,000 + $200,000) / $10 = 30,000 calculators

or

($100,000 + $200,000) / 0.40 = $750,000

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Section 6.3 Graphical Analysis

A Desired Aftertax Profit The profit objective may be stated as a net income after income taxes. Rather than changing with volume of units, income taxes vary with profits after the break-even point. When income taxes are to be considered, the basic CVP equation is altered using Equations 2, 7, and 8 in Figure 6.1. Equation 7 works as follows:

Target aftertax profit in units =

(Fixed costs + (Aftertax profit / (1 – Tax rate))) / Contribution margin per unit

Equation 8 yields the sales dollars needed to earn the desired aftertax profit.

Suppose Enoch Goodfriend had budgeted a $105,000 aftertax profit and that the income tax rate was 30%. We use the above equations to obtain the following volume and sales:

($100,000 + ($105,000 / (1 – 0.30))) / $10 = 25,000 calculators

or

($100,000 + ($105,000 / (1 – 0.30))) / 0.40 = $625,000

Contemporary Practice 6.2: Break-Even Attendance per Game for Hockey Team

“The Wheeling Nailers announced on Thursday the team again will play 10 of its home dates in Johnstown next season . . . Going over the lease, the ticket prices, our travel and our expenses we came out with 2,500 (attendance) to break even” (Mastovich, 2011).

6.3 Graphical Analysis Total sales dollars and total costs at different sales volumes can be estimated and plotted on a graph. The information shown on the graph can also be given in conventional reports, but it is often easier to grasp the fundamental facts when they are presented in graphic or pictorial form. Let’s look at two common forms of graphical analysis—the break-even chart and the profit-volume graph.

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Section 6.3 Graphical Analysis

The Break-Even Chart Dollars are shown on the vertical scale of the break-even chart, and the units of product to be sold are shown on the horizontal scale. The total costs are plotted for the various quanti- ties to be sold and are connected by a line. This line is merely a combination of the fixed and variable cost diagrams from Chapter 1. Total sales at various levels are similarly entered on the chart.

The break-even point lies at the intersection of the total revenue and total cost lines. Losses are measured to the left of the break-even point; the amount of the loss at any point is equal to the dollar difference between the total cost line and the total revenue line. Profit is measured to the right of the break-even point, and, at any point, is equal to the dollar difference between the total revenue line and the total cost line. This dollar difference equals the contribution margin per unit multiplied by the volume in excess of the break-even point.

In Figure 6.2, a break-even chart has been prepared for Felsen Electronics using the following data associated with sales levels between 5,000 and 30,000 calculators.

Number of Calculators Produced and Sold

5,000 10,000 15,000 20,000 25,000 30,000

Total revenue $125,000 $250,000 $375,000 $500,000 $625,000 $750,000

Cost:

Variable $ 75,000 $150,000 $225,000 $300,000 $375,000 $450,000

Fixed 100,000 100,000 100,000 100,000 100,000 100,000

Total cost $175,000 $250,000 $325,000 $400,000 $475,000 $550,000

Profit (loss) ($50,000) 0 $ 50,000 $100,000 $150,000 $200,000

Curvature of Revenue and Cost Lines In some cases, revenues and costs cannot be represented by straight lines. If more units are to be sold, management may have to reduce selling prices. Under these conditions, the revenue function is a curve instead of a straight line. Costs may also be nonlinear depending on what changes take place as volume increases. The cost curve may rise slowly at the start, then more steeply as volume is expanded. This occurs if the variable cost per unit becomes higher as more units are manufactured. Also, fixed costs might change as volume increases. For exam- ple, volume increases might cause a jump in supervision, equipment, and space costs. There- fore, it may be possible to have two break-even points, as shown in Figure 6.3.

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Section 6.3 Graphical Analysis

Figure 6.2: Break-even chart

Number of Calculators (in Thousands)

Variable cost

Fixed cost

5 10 15 20 25 30

100

200

300

400

500

600

700

$800

D ol

la rs

( in

T ho

us an

ds )

Loss area

Break-even point

Profit area

Total revenue line

Total cost line

Units of Product Sold

D ol

la rs

Break-even point

Break-even point

Tot al c

os t li

ne

To tal

re ve

nu e li

ne

Figure 6.3: Break-even chart with two break-even points

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Section 6.3 Graphical Analysis

The Profit-Volume Graph A profit-volume (P/V) graph is sometimes used in place of, or along with, a break-even chart. Data used in the earlier illustration of a break-even chart in Figure 6.2 have also been used in preparing the P/V graph shown in Figure 6.4. In general, profits and losses appear on the vertical scale; units of product, sales revenue, and/or percentages of capacity appear on the horizontal scale. A horizontal line is drawn on the graph to separate profits from losses. The profit or loss at each of various sales levels is plotted. These points are then connected to form a profit line. The slope of the profit line is the contribution margin per unit if the hori- zontal line is stated as units of product and is the contribution margin ratio if the horizontal line is stated as sales revenue.

The break-even point is the point where the profit line intersects the horizontal line. Dollars of profit are measured on the vertical scale above the line, and dollars of loss are measured below the line. The P/V graph may be preferred to the break-even chart because profit or loss at any point is shown specifically on the vertical scale. However, the P/V graph does not clearly show how cost varies with activity. Break-even charts and P/V graphs are often used together, thus obtaining the advantages of both.

Number of Calculators (in Thousands)

Revenue

(Thousands of Dollars)

$125 $250 $375 $500 $625 $750

Lo ss

es

P

ro fit

s

(T ho

us an

ds o

f D ol

la rs

)

Break-even point

Profit line

5 10 15 20 25 30

100

100

$200

200

0

Figure 6.4: Profit-volume graph

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Section 6.4 Analysis of Changes in CVP Variables

6.4 Analysis of Changes in CVP Variables Break-even charts and P/V graphs are convenient devices to show how profit is affected by changes in the factors that impact profit. For example, if unit selling price, unit variable cost, and total fixed cost remain constant, how many more units must be sold to realize a greater profit? Or, if the unit variable cost can be reduced, what additional profit can be expected at any given volume of sales? The effects of changes in sales volume, unit variable cost, unit sell- ing price, and total fixed cost are discussed in the following paragraphs. In all these cases, the starting point for analysis is the CVP equations in Figure 6.1.

Sales Volume For some companies, substantial profits depend on high sales volume. For example, if each unit of product is sold at a relatively low contribution margin, high profits are a function of selling in large quantities. This is more significant when the fixed cost is high.

For an illustration, consider Adrian Grant & Company, which handles a product with a selling price of $1 per unit. Assume a variable cost of $0.70 per unit and a fixed cost of $180,000 per year. The contribution margin, therefore, is $0.30 per unit ($1 – $0.70). Before any profit is realized, the company must sell enough units for the total contribution margin to recover the fixed cost. Therefore, 600,000 units must be sold just to break even: