Chapter 7 CostVolumeProfit Analysis 3 Learning Objectives n

Chapter 7 Cost-Volume-Profit Analysis

3 Learning Objectives n Explain cost-volume-profit (CVP) analysis, the CVP model, and the strategic role of CVP analysis n Apply CVP analysis for breakeven planning n Apply CVP analysis for revenue and cost planning n Apply CVP analysis for activity-based costing Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

4 Learning Objectives n Employ sensitivity analysis to more effectively use CVP analysis when actual sales are uncertain n Adapt CVP analysis for multiple products n Adapt CVP analysis in not-for-profit organizations n Identify the assumptions and limitations of CVP analysis and their effect on the proper interpretation of the results Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

5 Learning Objective One Explain cost-volume-profit (CVP) analysis, the CVP model, and the strategic role of CVP analysis Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

6 Cost-Volume-Profit (CVP) Analysis n Cost-volume-profit (CVP) Analysis is a method for analyzing how various operating decisions and marketing decisions will affect net income I can’t make a good marketing decision without understanding the CVP relationships. Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

7 Cost-Volume-Profit (CVP) Analysis n CVP analysis has many applications, including: setting prices for products and services v introducing a new product or service v replacing a piece of equipment v deciding whether to make or buy a given product or service v performing strategic “what if? ” analyses v Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

8 Cost-Volume-Profit (CVP) Analysis Profit = Revenues - Total Costs or Revenues = Fixed Costs + Variable Costs + Profits or (Units sold × Price) = Fixed Cost + (Units sold × Unit Variable Cost) + Profit Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

9 Cost-Volume-Profit (CVP) Analysis The CVP Model: (p × Q) = f + (v × Q) + N Q = units sold v = unit variable cost f = total fixed cost p = unit selling price N = operating profit Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

The Contribution Margin and Contribution Income Statement The unit contribution margin is the difference between unit sales price and unit variable cost, and is a measure of the increase in profit for a unit increase in sales Mc. Graw-Hill/Irwin 10 The total contribution margin is the unit contribution margin multiplied by the number of units sold p – v = Unit contribution margin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

The Contribution Margin and Contribution Income Statement 11 Insert Exhibit 7. 1 Mc. Graw-Hill/Irwin

The Contribution Margin and Contribution Income Statement 12 n The contribution margin ratio is the ratio of the unit contribution margin to unit sales price (p–v)÷ p n A useful way to show the information developed in CVP analysis is to use the contribution income statement n The contribution income statement focuses on variable costs and fixed costs, in contrast to the conventional income statement, which focuses on product costs and nonproduct costs Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

13 Contribution Income Statement Insert Exhibit 7. 2 (Contribution Income Statement ) Mc. Graw-Hill/Irwin

14 Strategic Role of CVP Analysis n CVP analysis can help a firm execute its strategy by providing an understanding of how changes in its volume of sales affect costs and profits n CVP analysis is important in using both lifecycle costing and target costing n In life-cycle costing, CVP analysis is used in the early stages of the product’s cost life cycle to determine whether the product is likely to achieve the desired profitability Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

15 Strategic Role of CVP Analysis n In addition, CVP analysis can be used at later phases of the life cycle, during manufacturing planning, to determine the most cost-effective manufacturing process n CVP analysis is also used in the final stages of the cost life cycle to help determine the best marketing and distribution systems n Similarly it can help to assess the desirability of a discount program or a promotional plan Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

16 Strategic Role of CVP Analysis What if the expected level of profit at a given sales volume? What additional amount of sales is needed to achieve a desired level of profit? Ž What will be the effect on profit of a given increase in sales? What is the required funding level for a governmental agency, given desired service levels? Is the forecast for sales consistent with forecasted profits? ‘ What additional profit would be obtained from a given percentage of reduction in unit variable costs? Œ Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

17 Learning Objective Two Apply CVP analysis for breakeven planning Mc. Graw-Hill/Irwin © 2005

18 CVP Analysis for Breakeven Planning n The starting point in many business plans is to determine the breakeven point n The breakeven point is the point at which revenues equal total cost and profit is zero Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

19 CVP Analysis for Breakeven Planning The Equation Method: Break-Even in Units $75 × Q = $5, 000 + ($35 × Q) Selling price per unit Mc. Graw-Hill/Irwin Total fixed Variable cost per unit © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

20 CVP Analysis for Breakeven Planning The Equation Method: Break-Even in Units $75 × Q = $5, 000 + ($35 × Q) ($75 - $35) × Q = $5, 000 ÷ $40 Q = 125 units per month Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

21 CVP Analysis for Breakeven Planning It is possible to find the breakeven in sales dollars for all products n Use the equation method in a revised form, where Y is the breakeven point in sales dollars n The Equation Method: Break-Even in Dollars Y = (v ÷ p) × Y + f + N Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

22 CVP Analysis for Breakeven Planning The Equation Method: Break-Even in Dollars Y = (. 4667) × Y + f + N Y =. 4467 × Y + $5, 000 + 0 Y = $9, 375 per month Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

23 Contribution Margin Method Q= Q= f+N p -v $5, 000 $75 - $35

24 The CVP Graph n The CVP graph illustrates how the levels of revenues and total costs change over different levels of output n The profit-volume graph illustrates how the level of profits changes over different levels of output Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

25 The CVP Graph Insert Exhibit 7. 4 Mc. Graw-Hill/Irwin © 2005 The Mc.

26 Learning Objective Three Apply CVP analysis for revenue and cost planning Mc. Graw-Hill/Irwin

CVP Analysis for Revenue and Cost Planning 27 n CVP analysis can be used to determine the level of sales needed to achieve a desired level of profit n The two possible objectives are revenue planning and cost planning n CVP analysis assists managers in revenue planning to determine the revenue required to achieve a desired profit level Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

28 Revenue Planning Management wants to know the sales volume necessary to achieve $48, 000 in annual profit. Sales in units = Sales in dollars= Mc. Graw-Hill/Irwin f+N (p – v) ÷ p © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

29 Revenue Planning Management wants to know the sales volume necessary to achieve $48, 000 in annual profit. Sales in units = f+N (p – v) $60, 000 + $48, 000 $75 – $35 Sales in units = 2, 700 units per year Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

30 Revenue Planning n The solution in sales dollars is: Sales in dollars= p×Q Sales in dollars= $75 × 2, 700 Sales in dollars= $202, 500 per year Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

31 Cost Planning n For cost planning decisions, the manager knows the value of Q and the desired profit but needs to find the value of the required variable cost or fixed cost n To facilitate target costing, CVP analysis is used to determine the most cost-effective trade-off between different types of costs Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

32 Cost Planning Management is considering a new piece of equipment that will reduce variable costs but also increase fixed costs by $2, 250 per month. Annual sales are currently 2, 700 units. How much will unit variable cost have to fall to maintain the current level of profit, assuming sales volume and other factors remain the same? Q p v f N Mc. Graw-Hill/Irwin = = = 2, 700 units $75 unknown ($5, 000 + $2, 250)× 12 = $87, 000 $48, 000 per year © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

33 Cost Planning Management is considering a new piece of equipment that will reduce variable costs but also increase fixed costs by $2, 250 per month. Annual sales are currently 2, 700 units. How much will unit variable cost have to fall to maintain the current level of profit, assuming sales volume and other factors remain the same? (f + N) v = p – Q ($87, 000 + $48, 000) v = $75 – = $25 2, 700 Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

34 Sales Commissions and Salaries Another cost planning use of CVP analysis is to determine the most cost-effective means to manage downstream costs such as selling costs Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

35 Sales Commissions and Salaries Management finds that $1, 000 of the $5, 000 monthly fixed costs is sales salaries, and that $7. 50 of the $35 variable cost is sales commissions. If salaries are increased to $1, 450, how much would sales commission rate need to be decreased to keep profits the same? v = r × $75 + $27. 50 Original $35 - $7. 50 (10% of $75) Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

36 Sales Commissions and Salaries Management finds that $1, 000 of the $5, 000 monthly fixed costs is sales salaries, and that $7. 50 of the $35 variable cost is sales commissions. If salaries are increased to $1, 450, how much would sales commission rate need to be decreased to keep profits the same? v = r × $75 + $27. 50 Fixed costs will increase by $450 per month and variable costs will decrease. f = $5, 000 + $450 = $5, 450 or f = $65, 400 per year Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

37 Sales Commissions and Salaries Managers would have to reduce the commission rate from 10% to 7. 33% to keep profits the same if the salespeople’s salaries are increased by $450. r × $75 + $27. 50 = $75 – $65, 400 + $48, 000 2, 700 r =. 0733 Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Including Income Taxes in CVP Analysis 38 n The manager’s decisions about costs and prices usually must include income taxes because taxes affect the amount of profit for a given level of sales n When taxes are considered, the CVP model is: Q = Mc. Graw-Hill/Irwin N f + (1 - t ) p-v t = tax rate © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Including Income Taxes in CVP Analysis Q = N f + (1 - t ) p-v 39 t = tax rate If the company is subject to a 20% tax rate: Q = $60, 000 + $48, 000/(1 -. 2) $75 - $35 Q = 3, 000 units per year Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

40 Learning Objective Four Apply CVP analysis for activity-based costing Mc. Graw-Hill/Irwin © 2005

CVP Analysis for Activity-based Costing n n n 1. 2. 3. 4. 41 The conventional approach to CVP analysis is to use a volume-based measure An alternative approach is activity-based costing Activity-based costing identifies cost drivers for detailed-level indirect cost activities, such as the following: Machine setup Materials handling Inspection engineering Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

CVP Analysis for Activity-based Costing 42 n In contrast, the volume-based approach combines the costs of these activities and treats them as fixed costs since they do not vary with output volume n Activity-based costing provides a more accurate determination of costs because it separately identifies and traces indirect costs to products rather than combining them in a pool of fixed costs (as the volume-based approach does) Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

CVP Analysis for Activity-based Costing n The 43 CVP model for Activity-based costing is: Q= f VB + N p – v – (v. AB/b) where: f VB = the volume-based fixed costs, the portion of fixed costs that do not vary with the activity cost driver v. AB/b = the cost per unit of product for batch-related costs when the batch is size b Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

44 Learning Objective Five Employ sensitivity analysis to more effectively use CVP analysis when actual sales are uncertain Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

45 Sensitivity Analysis of CVP Results CVP analysis becomes an important strategic tool when mangers use it to determine the sensitivity of profits to possible changes in costs or sales volume n If costs, prices, or volumes can change significantly, the firm’s strategy might also have to change n For example, if there is a risk that sales levels will fall below projected levels, management would be prudent to reduce planned investments in fixed costs n Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

46 Sensitivity Analysis of CVP Results n Sensitivity analysis is the name for a variety of methods used to examine how an amount will change if factors involved in predicting that amount change n Sensitivity analysis is particularly important when a great deal of uncertainty exists about the potential level of future sales volumes, prices, or costs Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

47 Sensitivity Analysis of CVP Results n 1. 2. 3. n n The three most common methods for sensitivity analysis are: what-if analysis margin of safety operating leverage What-if analysis is the calculation of an amount given different levels for a factor that influences that amount What-if analysis is a common approach to sensitivity analysis when uncertainty is present Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

48 Sensitivity Analysis of CVP Results What-if Sensitivity Analysis Management may look at changes in unit variable cost, total fixed costs or unit selling price on profits. Look at the analysis below: Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

49 Margin of Safety n The margin of safety is the amount of sales above the breakeven point n The margin of safety is as follows: Margin of safety = Planned sales – Breakeven sales n The margin of safety ratio is a useful measure for comparing the risk of two alternative products, or for assessing the risk in any given product n The product with a relatively low margin of safety ratio is the riskier of the two products Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

50 Margin of Safety = Planned Sales - Breakeven Sales Margin of Safety = 3, 000 units - 1, 500 units Margin of Safety = 1, 500 units Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

51 Operating Leverage n CVP analysis can play a crucial strategic role because profits are more sensitive to the number of units manufactured and sold n A firm with high fixed costs is riskier because profits are very strongly affected by the level of activity n High profits are earned beyond breakeven, but high losses result from falling below breakeven Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

52 Operating Leverage Insert Exhibit 7. 6 Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill

53 Operating Leverage Insert Exhibit 7. 7 A Mc. Graw-Hill/Irwin © 2005 The Mc.

54 Operating Leverage Insert Exhibit 7. 7 B Mc. Graw-Hill/Irwin © 2005 The Mc.

55 Operating Leverage n CVP analysis is particularly important in planning the use of new manufacturing technologies that have the potential to change the relationship between fixed and variable costs n The potential effect of the risk that sales will fall short of planned levels, as influenced by the relative proportion of fixed to variable manufacturing costs, can be measured by operating leverage n Operating leverage = contribution margin / before tax profit Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

56 Operating Leverage n. A higher value for operating leverage indicates a higher risk in the sense that a given change in sales will have a relatively greater impact on profits n Each firm chooses the level of operating leverage that is consistent with its competitive strategy Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

57 Learning Objective Six Adapt CVP analysis for multiple products Mc. Graw-Hill/Irwin © 2005

58 CVP Analysis for Multiple Products n The adaptation of the CVP model requires one key assumption: the sales of the product will continue at the same sales mix i. e. , the sales of each product will remain at the same proportion of total sales n The weighted-average contribution margin or contribution market rate is used to determine the total sales necessary to attain the desired operating result Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

59 CVP Analysis for Multiple Products Insert Exhibit 7. 8 Mc. Graw-Hill/Irwin © 2005

60 CVP Analysis for Multiple Products n For practicality, this approach is best utilized with a small number of products n With a large number of products, the best approach is to approximate the overall contribution margin ratio and determine the overall breakeven in sales dollars Weighted average contribution margin ratio = 0. 2 x 0. 5 + 0. 25 x 0. 4 + 0. 1 x 0. 1 = 0. 21 n Breakeven sales = $180, 000 / 0. 27 = $800, 000 n Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

61 Learning Objective Seven Adapt CVP analysis in not-for-profit organizations Mc. Graw-Hill/Irwin © 2005

CVP Analysis in Not-for-profit Organizations 62 Not-for-profit organizations and service firms can also use CVP analysis n For example, CVP analysis can help determine how potential budget cuts will affect the level of services that a not-for-profit center provides n To answer this question, management must determine precisely the center’s activity with the associated fixed and variable costs n Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

63 Learning Objective Eight Identify the assumptions and limitations of CVP analysis and their effect on the proper interpretation of the results Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Assumptions and Limitations of CVP Analysis 64 § Linearity and the Relevant Range § Identifying Fixed and Variable Cost for CVP Analysis § The ending inventory level is constant § The sales mix is constant Mc. Graw-Hill/Irwin © 2005 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.