Chapter 21

CHAPTER 2

PROFIT PLANNING

OVERVIEW

Managers commonly use an analytical technique called cost-volume-profit (CVP) analysis to predict costs and income at different levels of sales. CVP analysis uses a behavioral classification scheme that identifies a cost as fixed or variable according to whether the cost is relatively constant or changes as volume changes.

Costs that change in total in direct proportion to changes in volume are variable costs. The difference between selling price per unit and variable cost per unit is contribution margin. (In some cases, contribution margin is stated as a percentage of selling price.) Fixed costs remain the same in total regardless of volume. The range of volumes over which the described relationships are expected to hold true is called the relevant range.

The chapter often uses a graphical approach to show the relationships among costs, volume, and profit. The CVP graph shows the break-even point, where revenues equal total costs so that profits are zero. Managers determine the selling price (or sales volume) needed to earn a particular target profit by using a variation of the typical break-even situation. For whatever purpose it is used, CVP analysis must be based on expected, not historical, relationships.

Companies can choose cost structures with relatively high fixed costs and low variable costs, or vice versa. The selection has important implications for risk and return. Appendix 1 shows how income taxes can be incorporated into the various uses of cost-volume-profit analyses described in the chapter. Appendix 2 describes methods for applying CVP analysis to multiproduct firms.

STATEMENTS FOR GUIDED READING

Read the following statements to gain a preview of the chapter, and then use them as an outline for your reading. (Remember that this organized preview and reading guide is not meant to be a substitute for reading the chapter.)

  • Cost-volume-profit (CVP) analysis is a method for analyzing the relationships among sales volume, costs, and profits. Managers use CVP analysis in planning and budgeting.
  • The first step in CVP analysis is to classify costs according to their behavior in relation to changes in activity (volume). Sales volume is commonly used in classifying costs by behavior.
  • A cost is classified as either fixed or variable, according to whether the total amount of the cost changes as sales volume changes.
  • Variable costs change in total in direct proportion to changes in volume.
  • Contribution margin equals selling price per unit minus variable cost. It is sometimes expressed in dollars per unit and sometimes as a percentage of selling price.
  • Fixed costs remain the same in total as volume changes.
  • Total costs are equal to fixed costs plus variable costs multiplied by sales volume.
  • You can predict income by computing expected total contribution margin and then subtracting total fixed costs.
  • Changes in income resulting from changes in sales volume are equal to contribution margin multiplied by the change in sales volume.
  • Because planning relates to the future, the selling price, variable costs and fixed costs that matter are those expected to prevail in the periods being planned for.
  • The format commonly used in an income statement prepared for managerial purposes shows the contribution margin.
  • Using average total cost per unit to predict total costs at any level of volume other than the one on which the average was based is unwise.
  • Income as a percentage of sales (return on sales) differs at different levels of sales.
  • The term relevant range refers to that range of sales volume over which the firm can reasonably expect selling price, variable cost per unit, and total fixed costs to be constant.
  • A CVP graph shows the relationships among revenues, variable costs and fixed costs.
  • A CVP graph also shows the break-even point, that level of sales volume (in units or in dollars) where profit is zero.
  • The break-even point can be computed by using formulas.
  • Companies can set profit targets expressed as absolute dollars or as a percentage, return on sales.
  • With minor revisions, the break-even formulas can be used to determine the sales volume--in units or dollars--necessary to achieve a target profit.
  • Managers use CVP analysis to help determine whether particular changes in plans, such as undertaking a new advertising campaign, are likely to be profitable.
  • A firm that can estimate unit sales can determine the selling price needed to achieve its target profit. The method used depends on whether any of the firm's variable costs are a constant percentage of sales dollars.
  • A firm can couple the concepts of a target profit and a break-even point to develop a target cost for a new product.
  • An important consideration in planning the cost structure of the firm is the attitude of management with regard to risk and reward.
  • The more a company substitutes fixed costs for variable costs, say for automation, the higher the risk of losses, but the higher the potential profits.
  • The margin of safety is the decline in sales from the current level to the break-even point.
  • A company that can use either of two cost structures will often calculate an indifference point, which is the volume level at which total costs are the same under both cost structures.
  • Some managers prefer to study alternative cost structures by using a variation of the CVP graph that plots profit (rather than revenues and costs separately) on the vertical axis.
  • CVP analysis can be used for planning by single-product firms and multi-product firms that have a relatively constant sales mix.
  • In a manufacturing company, the use of CVP analysis assumes that production equals sales.

APPENDIX 1

  • Income taxes are costs and should be considered in planning.
  • To determine the sales necessary to achieve a target after-tax profit, it is necessary to convert the after-tax profit to a pretax profit.

APPENDIX 2

  • Multiproduct firms with relatively constant sales mixes can use CVP analysis.
  • When products have different contribution margins (both per unit and as percentages) and a stable sales mix, CVP analysis uses a weighted- average contribution margin.
  • The sales of complementary products are closely related. Examples are hot dogs and rolls or gasoline and motor oil.
  • Managers accustomed to thinking in dollar terms, such as those in retailing, use a weighted-average contribution margin percentage.
  • A manager considering a change in selling effort that will change the sales mix can forecast the effect of the shift using the weighted-average contribution margin percentage of the projected mix.
  • Managers accustomed to thinking in unit terms, such as those in automobile dealerships, use a weighted-average contribution per unit.

COMPREHENSION CHECK

Directions: For each of the following, circle the letter associated with the best answer.

1.CVP analysis is most commonly used to

a.determine the accuracy of financial accounting statements.

b.predict the anticipated selling price of the firm's stock.

c.predict costs and incomes at differing sales volumes.

d.determine whether a particular cost will be fixed or variable.

2.For CVP analysis, costs are classified according to

a.function.

b.behavior.

c.sales volume.

d.date of payment.

3.Total variable costs change

a.in direct proportion to changes in volume.

b.regardless of changes in volume.

c.in inverse proportion to changes in volume.

d.only when total fixed costs change.

4.Contribution margin is the

a.percentage of income to sales.

b.selling price minus average total cost per unit.

c.selling price minus variable cost per unit.

d.amount of charitable expenditures in the company's plan for the year.

5.An example of a behavioral classification of costs is

a.production, selling, administrative.

b.expired, unexpired.

c.current, noncurrent.

d.fixed, variable.

6.As sales increase, variable cost per unit

a.remains constant.

b.increases.

c.decreases.

d.changes in proportion to the change in sales.

7.Total fixed costs remain the same

a.within the relevant range of volume.

b.unless there are changes in volume.

c.because it is unwise to change them.

d.despite efforts of management to reduce them.

8.Sales minus total variable cost equals

a.net income.

b.gross profit.

c.contribution margin.

d.fixed costs.

9.A company uses target costing

a.when it lacks information about expected sales volume and selling price.

b.to determine the maximum costs that will allow it to meet a profit goal.

c.when it cannot classify its costs by behavior.

d.instead of setting a profit target.

10.Expressing contribution margin as a percentage of sales

a.is particularly useful to multiproduct firms.

b.is not possible if variable cost per unit is constant.

c.prohibits a firm from using CVP analysis.

d.requires the use of calculus.

11.Expressed as per-unit amounts, fixed costs

a.are constant.

b.decrease as volume decreases.

c.increase as volume increases.

d.decrease as volume increases.

12.If you add total fixed costs to the product of variable cost per unit and the number of units sold, you have calculated

a.total costs.

b.contribution margin in total.

c.cost of goods sold.

d.gross operating margin.

13.The total amount by which income will change if sales change is equal to the increase or decrease in the number of units sold multiplied by the

a.fixed cost per unit.

b.variable cost per unit.

c.contribution margin per unit.

d.selling price per unit.

14.If a firm has fixed costs, as volume increases the percentage increase in sales will be

a.less than the percentage increase in income.

b.greater than the percentage increase in income.

c.the same as the percentage increase in income.

d.equal to the historical ratio of income to sales.

15.The relevant range

a.is a stove powered by solar energy.

b.indicates minimum and maximum limits of volume over which CVP relationships are expected to prevail.

c.describes the firm's maximum sales capacity.

d.never changes.

16.The break-even point, in units, equals

a.contribution margin per unit divided by total fixed costs.

b.variable cost per unit divided by total fixed costs.

c.total fixed costs divided by contribution margin per unit.

d.total fixed costs divided by contribution margin percentage.

17.Which of the following is true of a typical CVP graph?

a.The horizontal distance between the revenue line and the total cost line is the amount of profit or loss at any point on the graph.

b.The vertical distance between the revenue line and the total cost line is the amount of profit or loss at any point on the graph.

c.The slopes of the revenue and total cost lines should be the same.

d.The total cost line rises above the revenue line for all volumes greater than the break-even volume.

18.The break-even point stated in sales dollars is equal to

a.selling price divided by contribution margin percentage.

b.variable costs divided by total fixed costs.

c.total fixed costs divided by contribution margin per unit.

d.total fixed costs divided by contribution margin percentage.

19.Average total cost per unit is

a.helpful in predicting income for an anticipated increase in sales.

b.helpful in predicting income for an anticipated decrease in sales.

c.dependent upon the level of volume.

d.the same at every level of volume if a company has no variable costs.

20.The indifference point is the point at which, under two cost structures,

a.fixed costs equal total sales.

b.total costs are equal.

c.revenues are equal.

d.contribution margins are equal.

21.Return on sales is the ratio of

a.fixed costs to sales.

b.contribution margin to sales.

c.variable costs to sales.

d.income to sales.

22.The unit sales volume needed to achieve a dollar target profit is equal to

a.contribution margin per unit divided by the target profit.

b.the sum of fixed costs and target profit, divided by contribution margin per unit.

c.the sum of variable costs and fixed costs, divided by the target profit.

d.the sum of variable costs and target profit, divided by contribution margin per unit.

23.Which of the following is true when the income statement of a retail firm is prepared using the contribution margin format?

a.The only variable cost is cost of goods sold.

b.Sales and income figures are the same as those in an income statement prepared for financial accounting purposes.

c.Costs are classified by object.

d.Volume is overstated in order to ensure a profit margin.

24.Which of the following is true for a manufacturer that uses CVP analysis?

a.Manufacturing costs should be classified as fixed costs.

b.The number of units produced are assumed to equal the number of units sold.

c.Its break-even point will be higher than that of a retailer with the same cost structure.

d.Variable costs must be stated as a percentage of sales rather than as a dollar amount per unit.

25.Which of the following is true?

a.Total sales required to achieve a target profit is higher if the target is stated in dollars than if it is stated as a return on sales.

b.A firm that has only fixed costs has no break-even point.

c.All other things remaining the same, an increase in sales volume lowers the break-even point.

d.All other things remaining the same, a decrease in variable cost per unit lowers the break-even point.

26.What effect do income taxes have on the sales volume a firm needs to achieve its target profit?

a.They raise it.

b.They lower it.

c.They have no effect.

d.Their effect is not determinable without information about costs.

27.What effect do income taxes have on a firm's break-even point?

a.They raise it.

b.They lower it.

c.They have no effect.

d.Their effect is not determinable without information about costs.

28.The margin of safety in dollars is

a.actual sales less expected sales.

b.break-even sales less actual sales.

c.break-even sales less planned sales.

d.actual sales less break-even sales.

29.A weighted-average contribution margin per unit is

a.used by some multiproduct companies.

b.necessary when products have different selling prices.

c.useful only if all of a company's products have the same contribution margin per unit.

d.needed to apply CVP analysis in a single-product company.

30.A weighted-average contribution margin is particularly useful to a company

a.that experiences considerable seasonality in its sales.

b.selling several products with equal selling prices but different variable cost percentages.

c.selling several products with various selling prices but equal variable cost percentages.

d.whose annual fixed costs are not incurred evenly over the year.

Now check your answers with the Answer Key. If you do not understand why an answer you selected is not the most appropriate one, re-read the pertinent section of the text before you continue.

APPLICATIONS

PROBLEM 1

Scottso, Inc. has provided the following data for its one product:

Unit selling price$ 25

Unit variable cost$ 20

Total fixed costs$ 55,000

Unit volume15,000

Required:

(a)Prepare an income statement using the contribution margin format.

(b)The break-even point is ______units or $______dollars.

PROBLEM 2

Genco Enterprises is considering expanding their products in their testing equipment line. Potential sales are 10,000 units at a $350 selling price. Genco would require a 15% return on sales.

Required:

(a)Determine the total costs that Genco can incur and meet the profit objective.

(b)If Genco estimates that fixed costs would be $1,200,000 annually for this product. What is the maximum allowable variable cost per unit?

PROBLEM 3

Albright Videos, a videotape shop, purchases tapes at $8 each and sells them for $14. Variable selling cost is $1 per tape and fixed costs total $24,000 annually.

Required

(a)Contribution margin per tape is $______.

(b)The contribution margin percentage is ______%.

(c)If Albright sells 6,500 tapes, its profit is $______.

(d)The break-even point in units is ______tapes.

(e)To earn a profit of $32,000, Albright must sell ______tapes.

(f)To earn a return on sales of 10%, Albright must sell ______tapes.

(g)If Jolene, Albright's owner, wants a profit of $26,000 and believes sales will be 8,000 tapes, the per-tape selling price must be $______.

(h)If Albright sells 5,000 tapes, its margin of safety in units is and in dollars is $ .

PROBLEM 4

Caddott Company buys and sells decorated beach towels. Caddott purchases towels at $12 each and sells them for $24. Variable selling costs are 25% of sales, and fixed costs are $150,000 annually.

Required

(a)Variable cost per towel sold is $______.

(b)Contribution margin per towel sold is $______.

(c)The contribution margin percentage is ______%.

(d)The break-even point in units is ______.

(e)Break-even sales, in dollars, are $______.

(f)If 32,000 towels are sold, income will be $______.

(g)If Caddott's target profit is $30,000, its sales must be $______or ______towels.

(h)If Caddott desires a profit of $75,000 selling 30,000 towels, it must set its selling price at $______per towel.

(i)If Caddott sets its selling price at $27 and sells 30,000 towels, will it be over or under the target profit of $75,000 and by how much?

______by $______.

(over or under)

(j)Caddott is now selling 30,000 towels at $27 each. If it could spend $5,000 on advertising and be quite sure of selling, as a result of the advertising, an additional 1,000 towels, should it spend the $5,000?

______because it would be $______off.

(yes or no)(better or worse)

(k)If Caddott's profit target is a return on sales (ROS) of 5% on a $24 selling price, the sales it needs to achieve this target are

$______or ______towels.

(l)If Caddott desires a 5% ROS selling 30,000 towels, it must set its selling price per towel at $______. (If need be, round your answer to the nearest penny.)

PROBLEM 5

Danco Company makes several models of GPS (global positioning system) receivers. One component, common to all models, currently costs Danco $3.20 per unit in variable manufacturing cost plus $25,000 per month to rent the machinery needed to produce the component. The machinery is rented on a month-to-month basis.