Cost Behaviourand Cost-Volume Relationships

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Chapter 2

Cost Behaviourand Cost-Volume Relationships

LEARNING OBJECTIVES:

When your students have finished studying this chapter, they should be able to:

1.Explain how cost drivers affect cost behavior.

2.Do a comparison of variable and fixed costs and understand the relevant range in which they are formulated.

3.Calculate break-even sales volume in total dollars and total units and construct a cost-volume profit graph.

4.Construct a cost-volume profit graph.

5.Identify the limiting assumptions that underlie cost-volume-profit analysis.

6.Calculate sales volume in total dollars and total units to reach a target profit.

7.Explain the effects of sales mix on profits.

8.Compute cost-volume-profit relationships on an after-tax basis.

9.Distinguish between contribution margin and gross margin.

CHAPTER 2:OVERVIEW

This chapter examines cost behavior and its impact on company profitability. Note:This IM chapter is delineated according to text sections and is not delineated by LO.

Section One:Discusses cost drivers and their effects on cost behaviour.

Section Two:The behavior of variable and fixed costs is discussed. Variable costs change in proportion to changes in the cost driver, whereas fixed costs in total are unaffected by cost-driver activity.

Section Three:Covers the fundamentals of break-even and cost-volume-profit analysis. The contribution margin and the equation techniques for solving for the break-even point are illustrated.

Section Four: The graphical technique for deriving the break-even point is shown. The break-even point (BEP) is found in terms of units and sales dollars. The assumptions of CVP are stated, changes in fixed expenses and contribution margin are discussed, and solving for a target net profit is explained. At times, an incremental approach is useful to evaluate changes in costs, revenues, and resulting profit. Also, the effects of multiple changes in key factors and the use of computer spreadsheets in evaluating alternatives are discussed.

Section Five:Identifies the limiting assumptions that underlie CVP analysis.

Section Six:Shows how to calculate sales volume in total dollars and total units to reach a target profit.

Section Seven:Shows how a given sales mix affects profits.

Section Eight:Shows how CVP relationships are computed on an after-tax basis.

Section Nine:Explains the difference between the contribution margin and the gross margin.

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CHAPTER 2:OUTLINE

1.Identifying Activities, Costs, and Cost Drivers{LO. 1}

Cost Behaviour – How an organization’s activities affect its costs.

Cost Drivers - Output measures of resources and activities.

Organizations can have many cost drivers. In this chapter, volume-based cost drivers are used in order to examine cost behavior. See EXHIBIT 2-1 for examples of costs and potential cost drivers for value-chain functions.

TEACHING TIP: Cause and Effect Relationships: What may cause a student to perform poorly/well on an examination? An interview? There may be multiple causes.

2.Comparing Variable and Fixed Costs {LO. 2}

Variable and fixed costs refer to how cost behaves with respect to changes in a particular cost driver.

Variable Cost - a cost that changes in direct proportion to changes in the cost driver (i.e., costs per unit do not change, total costs do change). Examples include the costs of materials, merchandise, parts, supplies, commissions, and many types of labor. See EXHIBIT 2-2 for a graph of variable cost behavior within a relevant range.

Fixed Cost - a cost that is not immediately affected by changes in the cost driver (i.e., costs per unit do change, total costs do not change within the relevant range). Examples include real estate taxes, real estate insurance, many executive salaries, and space rentals.

TEACHING TIP: Fixed Costs and Time Period - All costs become variable as the time period is expanded.

A.Relevant Range

Relevant Range - the limits (i.e., time period and/or activity) of cost-driver activity within which a specific relationship between costs and the cost driver is valid. See EXHIBIT 2-3 for a graph of fixed cost behavior within a relevant range.

B.Difficulties in Classifying Costs

Costs may not act in a linear manner with volume-based cost drivers.

Examples: when learning affects the production time, and therefore the labor cost of units of product; some costs may be affected by more than one cost driver; and whether costs are variable or fixed often depends on the decision situation.

3.Cost-Volume-Profit and Breakeven Analysis{LO. 3}

Cost-Volume-Profit (CVP) Analysis - the study of the effects of output volume on revenue (sales), expenses (costs), and net income (net profit). The major simplifying assumption is to classify costs as either variable or fixed with respect to the volume of output activity. A CVP scenario follows.

Break-Even Point: Contribution-Margin and Equation Methods

Break-Even Point (BEP) - the level of sales at which revenues equals expenses and net income is zero. One direct use of the BEP is to assess possible risk. By comparing planned sales with the BEP, managers can determine a Margin of Safety - how far sales can fall below the planned level before losses occur.

Margin of Safety = planned unit sales - break-even unit sales

1.The Contribution-Margin Approach: Contribution Margin (CM) Per Unit - the sales price per unit minus the variable expenses per unit. The BEP is reached when total contribution margin equals total fixed costs. Dividing total fixed costs by the CM per unit gives the BEP in number of units.

CM Percentage or Ratio - the portion of every sales dollar that contributes to covering fixed costs and, hopefully, provides for profit (divide total contribution margin by total sales). Dividing total fixed costs by the CM percentage (total contribution margin / total sales) yields the sales dollars needed to break even. The use of the CM percentage is necessary when a firm produces more than one product.

2.The Income Statement Equation Approach: The basic income statement equation used for CVP analysis is:

sales - variable expenses - fixed expenses = net income

This can be decomposed to:

unit sales price x number of units

- unit variable cost x number of units

- fixed expenses

net income

At the BEP, net income is zero. Let N = the number of units to be sold to break even, put in values for the unit sales price, unit variable cost and fixed expenses, and solve for N.

To compute the sales dollars needed to break even using the equation technique, the variable expenses must be expressed as a proportion of sales, which is called the Variable-Cost Ratio or Percentage. Then, letting S = the sales dollars to break even, solve for S in the equation:

S - (variable-cost ratio x S) - fixed expenses = 0

Alternatively, if you have previously solved for the number of units required to break even, you can multiply that result by the unit-selling price to give the sales dollars needed to break even.

3.Relationship Between the Two Techniques. Both approaches result in the following short-cut formulas:

break-even (units) = (fixed expenses)/(CM per unit)

break-even (dollars) = (fixed expenses)/(CM ratio)

4.Break-Even Point - Graphical Techniques{LO. 4}

The BEP can also be found by graphing the cost and revenue relationships. The process takes the following steps.

Step 1:Draw the axes. The horizontal axis = sales volume, and the vertical axis = dollars of cost and revenue.

Step 2:Plot sales volume. Select a convenient sales volume and plot a point for total sales dollars at that volume. Then draw a line between the origin and the point.

Step 3:Plot the fixed expenses. It should be a horizontal line intersecting the vertical axis at the level of fixed costs.

Step 4:Plot variable expenses. Determine the variable expenses at some volume level. Add this amount to fixed expenses and plot the point. Then draw a line from the intersection of the vertical axis to this point. This line represents total expenses, and the difference between the fixed expense line and this new line represents the variable expenses.

Step 5:Locate the break-even point. The break-even point is where the total expense line crosses the sales line.

See EXHIBIT 2-4 for an illustration of a CVP graph. CVP graphs show profits over a wide volume range easier than numerical exhibits.

Almost all break-even graphs show revenue and cost lines extending back to the vertical axis. This approach misleads because the relationships depicted are only valid within the relevant range. See EXHIBIT 2-5 for the conventional and modified break-even graphs.

5.Assumptions underlying CVP and Breakeven Analysis

{LO. 5}

The assumptions used in constructing the typical cost-volume-profit and break-even graphs include the following:

1.Expenses may be classified into variable and fixed categories.

2.The behavior of revenues and expenses is accurately portrayed and is linear over the relevant range.

3.Efficiency and productivity will be unchanged.

4.Sales Mix (i.e., the relative proportions or combinations of quantities of products that constitute total sales) is constant.

5.The difference in inventory level at the beginning and end of a period is insignificant.

A.Changes in Fixed Expenses

Increases (decreases) in fixed expenses increase (decrease) the BEP.

B.Changes in Contribution Margin per Unit

Increases (decreases) in the CM per unit decrease (increase) the BEP.

6.Calculate the sales volume required to reach a target profit.

{LO. 6}

CVP analysis can be used to determine the target sales, in units and dollars, needed to earn a target profit. Using either the contribution margin or equation techniques results in the following shortcut equations.

target sales volume in units = fixed expenses + target net income

CM per unit

target sales volume in dollars = fixed expenses + target net income

CM ratio

TEACHING TIP: Students should understand that the above formulas are essentially the only ones need to perform any CVP analysis, regardless of the target net income. In a breakeven analysis, the target net income is simply zero!

TEACHING TIP: The instructor may wish to use the “Scope” case as an example to perform CVP analysis.

The Incremental Approach (i.e., the change in total results under a new condition in comparison with some given or known condition) can be used. Divide the target net income by the CM per unit and add the result to the unit BEP to get the target sales volume in units. Likewise, divide the target net income by the CM ratio and add the result to the dollar BEP to get the target sales volume in dollars.

A.Multiple Changes in Key Factors

Multiple factor changes can be demonstrated by constructing income statements reflecting the changes and comparing before change and after change results. Also, an incremental approach can be used to isolate just the effects of the changes and eliminates irrelevant and potentially confusing data.

B.CVP Analysis and Computer-Based Spreadsheets

Numerous combinations of fixed expenses, selling prices, variable expenses, and target income levels can be analyzed quickly using these computerized spreadsheets.

7. Sales-Mix Analysis{LO. 7}

Sales Mix - the relative proportions or combinations of quantities of products that comprise total sales. If the proportions of the mix change, the CVP relationships may also change. Generally speaking, selling a higher (lower) proportion of high CM products than anticipated results in higher (lower) net income. Factors other than CM per unit of product (e.g., CM per unit of time) can be useful in making sales mix decisions (see Chapter 5 for further explanation).

TEACHING TIP: The instructor may wish to use an in-class example whereby the student must calculate the breakeven point in units of each product in a multi-product environment. The instructor should explain the benefits of using a “package contribution margin” approach when computing the breakeven point.

8. Impact of Income Taxes on CVP Analysis {LO.8}

The target sales equation can be altered to the following:

target sales - variable expenses - fixed expenses =target after-tax income/(1 - tax rate)

Letting N = the number of units of sales necessary to achieve the desired after-tax income and substituting values for the selling price per unit, variable expenses per unit, fixed expenses, target after-tax income, and the tax rate into the equation, N can be solved. Alternatively, the following shortcut formula may be used:

change in net income =(change in volume in units) x (CM per unit) x (1 - tax rate)

Each unit beyond the BEP adds to after-tax net profit at the unit CM multiplied by (1 - income tax rate).

When incorporating income taxes in CVP analysis, the BEP does not change because the BEP is the point of zero profits. Therefore, there are no taxes on zero profits.

TEACHING TIP: Students must understand that only PRETAX amounts can be used in the CVP analysis. If a tax rate is given, the student should know how to convert after-tax profits to pre-tax amounts before performing CVP computations. The instructor may wish to perform a simple example whereby students must convert an after-tax profit amount to a pre-tax profit amount.

Uses and Limitations of Cost-Volume Analysis

A.Best Cost Structure

Companies try to find their most desirable combination of fixed- and variable-cost factors. Some choose to increase their CM ratios and fixed costs by automating, while others may choose to lower their fixed costs and lower their CM ratios by putting their sales force on commissions rather than paying salaries.

When the CM percentage of sales is low, great increases in volume are necessary before significant improvements in net profits are possible. As sales exceed the BEP, a high CM percentage increases profits faster than a low CM percentage.

B.Operating Leverage

Operating Leverage - the firm’s ratio of fixed and variable costs. In highly leveraged firms (i.e., those with high fixed costs and low variable costs) small changes in sales volume will result in large changes in net income. Less leveraged firms show smaller changes in net income with changes in sales volume. Above the BEP, net income increases faster for highly leveraged firms. However, below the BEP, losses mount more rapidly. See EXHIBIT 2-6 for a graph comparing high versus low leverage.

9. Distinguish between Contribution Margin and Gross Margin

{LO. 9}

Gross Margin (or Gross Profit) - the excess of sales over the Cost of Goods Sold(i.e., cost of the acquired or manufactured merchandise to be sold). Contribution Margin is the excess of sales over all variable expenses.

Nonprofit Application

Nonprofit organizations, such as government agencies, can use the principles of CVP analysis to determine how many individuals they can serve with limited budgets and to assess the impact of changes in the level of funding and/or costs on their ability to provide services.

CHAPTER 2:Making Managerial Decisions Solutions

Making Managerial Decisions 2.1

Suppose you are analyzing the risks of transporting Mackenzie Delta gas by pipeline or LNG ships through the Bering Strait/Northwest Passage routes. Your company, a Mackenzie Delta gas producer, must commit to one of these options within a year. Explain the risks in terms of (1) operating leverage and (2) the environment. Is there any relationship between these two types of risk?