© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-1 Cost-Volume-Profit Analysis

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-2 Cost-Volume-Profit Analysis Cost-Volume-Profit (CVP) Analysis Cost-Volume-Profit (CVP) Analysis - the study of the interrelationships between costs and volume and how they impact profit. I can’t make a good marketing decision without understanding the CVP relationships.

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-3 osetting prices for products and services. ointroducing a new product or service. oreplacing a piece of equipment. odeciding whether a given product or service should be made within the firm or purchased outside the firm. operforming strategic “what if?” analyses. osetting prices for products and services. ointroducing a new product or service. oreplacing a piece of equipment. odeciding whether a given product or service should be made within the firm or purchased outside the firm. operforming strategic “what if?” analyses. CVP aids management in... Cost-Volume-Profit Analysis

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-4 or Profit = Revenues - Total Costs Revenues = Fixed Costs + Variable Costs + Profits Revenues = Fixed Costs + Variable Costs + Profits (Units sold × Price) = Fixed Cost + (Units sold × Unit Variable Cost) + Profit or Cost-Volume-Profit Analysis

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-5 The CVP Model: (p × Q) = f + (v × Q) + N 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 Q = units sold v = unit variable cost f = total fixed cost p = unit selling price N = operating profit Cost-Volume-Profit Analysis

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-6 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. The Contribution Margin and Contribution Income Statement The total contribution margin is the unit contribution margin multiplied by the number of units sold. p – v = Unit contribution margin

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-7 The Contribution Margin and Contribution Income Statement Fixed cost$5,000$60,000 Desired operating profit$4,000$48,000 Sales$37,500$450,000$75 Variable cost $17,500$210,000$35 Planned production250 units3,000 units Planned Sales250 units3,000 units Fixed cost$5,000$60,000 Desired operating profit$4,000$48,000 Sales$37,500$450,000$75 Variable cost $17,500$210,000$35 Planned production250 units3,000 units Planned Sales250 units3,000 units Per Monthly Annual Unit Household Furnishings, Inc.

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-8 Household Furnishings, Inc. The Contribution Margin and Contribution Income Statement 2,400 units × $75 = $180,000

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-9 The Contribution Margin and Contribution Income Statement Household Furnishings, Inc. $15,000 × 53.33% = $8,000

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-10 Strategic Role of CVP Analysis  What if the expected level of profit at a give sales volume?  What additional amount of sales is needed to achieve a desired level of profit?  What will be the effect on profits of a given increase in sales?  What is the required funding level for a governmental agency, given desired service level?  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?  What if the expected level of profit at a give sales volume?  What additional amount of sales is needed to achieve a desired level of profit?  What will be the effect on profits of a given increase in sales?  What is the required funding level for a governmental agency, given desired service level?  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?

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-11 $75 × Q = $5,000 + ($35 × Q) Selling price per unit The Equation Method: Break-Even in Units CVP Analysis for Breakeven Planning Total fixed cost Variable cost per unit

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-12 $75 × Q = $5,000 + ($35 × Q) The Equation Method: Break-Even in Units CVP Analysis for Breakeven Planning ($75 - $35) × Q = $5,000 Q = $5,000 ÷ $40 Q = 125 units per month

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-13 The Equation Method: Break-Even in Dollars Y = (v ÷ p) × Y + f + N CVP Analysis for Breakeven Planning

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-14 The Equation Method: Break-Even in Dollars Y = (.4667) × Y + f + N CVP Analysis for Breakeven Planning $210,000 ÷ $450,000

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-15 The Equation Method: Break-Even in Dollars Y = (.4667) × Y + f + N CVP Analysis for Breakeven Planning Y =.4467 × Y + $5, Y = $9,375 per month

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-16 Q = f p -v Contribution Margin Method CVP Analysis for Breakeven Planning Q = $5,000 $75 - $35 Q = 125 units per month

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-17 Cost or Revenue Total Revenue Total Cost 0 (5,000) Total Revenue Total Cost Q = 125 Breakeven Point Output Volume The CVP Graph

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-18 Profits 25,000 50,000 75,000 0 Total Cost Q = 125 Output Volume Profits Losses Profit-Volume Graph

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-19 p × Q = f (p - v) ÷ p $5,000 ($75 - $35) ÷ $75 p × Q = p × Q = $9,375 per month CVP Analysis for Breakeven Planning Contribution Margin Method

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-20 Management wants to know the sales volume necessary to achieve $48,000 in annual profit. Revenue Planning units Sales in units = f + N (p – v) dollars Sales in dollars = f + N (p – v) ÷ p

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-21 Management wants to know the sales volume necessary to achieve $48,000 in annual profit. Revenue Planning units Sales in units = f + N (p – v) units Sales in units = $60,000 + $48,000 $75 – $35 units2,700 units per year Sales in units = 2,700 units per year

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-22 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? Trade-offs Between Fixed and Variable Costs Q = 2,700 units p = $75 v = unknown f = ($5,000 + $2,250)×12 = $87,000 N = $48,000

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-23 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? Trade-offs Between Fixed and Variable Costs v = p – (f + N) Q v = $75 – ($87,000 + $48,000) 2,700 $25 = $25

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-24 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? 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)

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-25 Sales Commissions and Salaries f = $5,000 + $450 = $5,450 Fixed costs will increase by $450 per month and variable costs will decrease. Fixed costs will increase by $450 per month and variable costs will decrease. 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? 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

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-26 Sales Commissions and Salaries r × $75 + $27.50 = $75 – r =.0733 $65,400 + $48,000 2,700 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.

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-27 f + p - v Q = N (1 - t ) t = tax rate Including Income Taxes in CVP Analysis If the company is subject to a 20% tax rate. 3,000 units per year Q = 3,000 units per year Q = $60,000 + $48,000/(1 -.2) $75 - $35

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-28 What-if Sensitivity Analysis Sensitivity Analysis of CVP Results Management may look at changes in unit variable cost, total fixed costs or unit selling price on profits. Look at the analysis below:

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-29 Margin of Safety Margin of Safety =Planned Sales - Breakeven Sales Sensitivity Analysis of CVP Results 3,000 units - 1,500 unitsMargin of Safety = 1,500 units

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-30 Cost or Revenue (in millions) 25,000 50,000 75,000 Output in Units 25,000 units = – 25,000 x $10 = – $250,000 Fixed cost/yr.$500,000 Variable cost/ unit$2 Price$12 Contribution margin$10 Total Revenue Total Cost $1.5 $.5 CVP Graph for a Firm with Relatively High Fixed Costs

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-31 Cost or Revenue (in millions) 25,000 50,000 75,000 Output in Units Fixed cost/yr.$500,000 Variable cost/ unit$2 Price$12 Contribution margin$10 Total Revenue Total Cost $1.5 $.5 CVP Graph for a Firm with Relatively High Fixed Costs 75,000 units = 25,000 x $10 = $250,000

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide ,000 50,000 75,000 $1.5 $.5 Fixed cost/yr.$150,000 Variable cost/ unit$9 Price$12 Contribution margin$3 25,000 units = -25,000 x $3 = -$75,000 $1.0 $.l5 CVP Graph of a Firm with Relatively Low Fixed Costs Cost or Revenue (in millions) Output in Units Total Revenue Total Cost

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide ,000 50,000 75,000 $1.5 $.5 Fixed cost/yr.$150,000 Variable cost/ unit$9 Price$12 Contribution margin$3 $1.0 $.l5 CVP Graph of a Firm with Relatively Low Fixed Costs Cost or Revenue (in millions) Output in Units Total Revenue Total Cost 75,000 units = 25,000 x 3 = $75,000

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-34 CVP Analysis with Multiple Products Here is information about two surfboard models manufactured:

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-35 CVP Analysis with Multiple Products Ê Assume a Constant Sales Mix The product mix in units sold is 1.5 Pro : 1 Hang Ten

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-36 CVP Analysis with Multiple Products Hang Ten 1.0 × $62.50 = $62.50 Pro 1.5 × $ = Total contribution $ Ê Assume a Constant Sales Mix = 135 packages (rounded) X = $38, $287.50

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-37 CVP Analysis with Multiple Products X = 135 packages (rounded) Ê Assume a Constant Sales Mix Nose-to-Toes uses a weighted-average product mix to calculate break-even.

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-38 CVP Analysis with Multiple Products Here is the calculation of Nose-to-Toes’ average contribution margin ÷ 2.5 = 40% 40% × $62.50 = $25.00

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-39 CVP Analysis with Multiple Products We find the break-even point as follows... X = $38,750 $38,750 $115 $115 = 337 boards (rounded) = 337 boards (rounded)

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide ,000 20,000 25,000 30,000 $100,000 Output in Units Total Revenue Total Cost Losses Revenues, Total Costs CVP Analysis with Step Cost Behavior

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide ,000 20,000 25,000 30,000 $100,000 Output in Units Total Revenue Losses Revenues, Total Costs CVP Analysis with Step Cost Behavior There is no breakeven below the 10,000 unit level of output.

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-42 Assumptions and Limitations of CVP Analysis  Linearity and the Relevant Range  Identifying Fixed and Variable Cost for CVP Analysis  Linearity and the Relevant Range  Identifying Fixed and Variable Cost for CVP Analysis

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Slide 8-43 End of Chapter 8