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  1. Cost-Volume-Profit Analysis Chapter 19

  2. Types of Costs • The effect of volume of activity on costs • Variable costs • Increase or decrease in total in direct proportion to changes in the volume of activity • Fixed costs • Do not change over wide ranges of volume • Mixed costs • Have both variable and fixed components

  3. Variable Costs • Total variable costs change in direct proportion to changes in the volume of activity • If activity increases, so does the cost • Unit variable cost remains constant • Volume can be measured in many different ways: • Number of units sold • Number of units produced • Number of miles driven by a delivery vehicle • Number of phone calls placed

  4. Total Variable Costs

  5. Fixed Costs • Tend to remain the same in amount, regardless of variations in level of activity • Examples: • Straight-line depreciation • Salaries • Total fixed costs do not change, but the fixed cost per event depends on the number of events • The more activity, the less the fixed cost per unit

  6. Total Fixed Costs and Fixed Costs per Unit

  7. Mixed Costs • Have both a fixed and variable component • Example: • Utilities that charge a set fee per month, plus a charge for usage • Your cell phoneprovider

  8. Mixed Costs

  9. High-Low Method • Method to separate mixed costs into variable and fixed components • Identify the highest and lowest levels of activity over a period of time • STEP 1: Calculate variable cost per unit • STEP 2: Calculate total fixed cost • STEP 3: Create and use equation to show the behavior of a mixed cost Variable cost per unit = Change in total cost ÷ Change in activity volume Total fixed cost = Total mixed cost – Total variable cost Total mixed cost = (Variable cost per unit X number of units) + Total fixed costs

  10. High-Low Method: Steps 1 and 2 • Data • Step 1 • Step 2

  11. Step 3 ($2 x 400 event-playing hours) + $1,000 = $1,800 Now check your formula against the original data ($2 x 480 + $1000 = $1960) or($2 x 240 + $1,000 = $1480)

  12. Relevant Range • Range of volume: • Where total fixed costs remain constant and variable cost per unit remains constant • Outside the relevant range, costs can differ

  13. S19-1: Variable, fixed, and mixed costs • Philadelphia Acoustics builds innovative speakers for music and home theater systems. Consider the following costs. Identify the costs as variable (V), fixed (F), or mixed (M). V V F M V

  14. S19-1: Variable, fixed, and mixed costs • Philadelphia Acoustics builds innovative speakers for music and home theater systems. Consider the following costs. Identify the costs as variable (V), fixed (F), or mixed (M). F V M V F

  15. S19-3: Mixed costs—high-low method Martin owns a machine shop. In reviewing his utility bill for the last 12 months, he found that his highest bill of $2,800 occurred in August when his machines worked 1,400 machine hours. His lowest utility bill of $2,600 occurred in December when his machines worked 900 machine hours. • Calculate (a) the variable rate per machine hour and (b) Martin’s total fixed utility cost. Variable cost per unit = Change in total cost ÷ Change in activity volume a. Variable cost per unit = ($2,800 - $2,600) ÷ (1,400 – 900) Variable cost per unit = $200 ÷ 500 = 0.40 per machine hour b. Total fixed cost = Total mixed cost – Total variable cost Total fixed cost = $2,800 – (0.40 X 1,400) Total fixed cost = $2,800 - $560 Total fixed cost = $2,240

  16. S19-3: Mixed costs—high-low method Martin owns a machine shop. In reviewing his utility bill for the last 12 months, he found that his highest bill of $2,800 occurred in August when his machines worked 1,400 machine hours. His lowest utility bill of $2,600 occurred in December when his machines worked 900 machine hours. 2. Show the equation for determining the total utility cost for Martin’s. $ 0.40 per machine hour + $2,240 3. If Martin’s anticipates using 1,200 machine hours in January, predict his total utility bill using the equation from Requirement 2. ($ 0.40 per machine hour x 1,200 machine hours) + $2,240 $480 +$2,240 = $2,720

  17. Basic CVP Analysis • Expresses the relationships among costs, volume, and profit or loss • Answers: • How many products or services must the company sell to break even? • What will profits be if sales double? • How will changes in selling price, variable costs, or fixed costs affect profits?

  18. Basic CVP Analysis • Assumptions: • Managers can classify each cost as either variable or fixed • Only factor that affects total costs is change in volume, which increases variable and mixed costs • Fixed costs do not change

  19. Breakeven Point • Sales level at which operating income is zero: • Total revenues equal total costs (expenses) • Sales above breakeven result in a profit • Sales below breakeven result in a loss

  20. Breakeven Point • Two methods to compute breakeven point: • Income statement approach • Sales revenue − Total costs = Operating income • Contribution margin approach • Sales revenue – Variable costs = Contribution margin – Fixed costs = Operating income

  21. Break Even Example Data • Unit sale price • Unit variable cost • Fixed costs • Unit contribution margin • $200 • $80 • $12,000 • $120 ($200 - $80)

  22. Income Statement Approach • Express income in equation form and then break it down into its components:

  23. Contribution Margin Approach • Shortcut method • The contribution margin is sales revenue minus variable costs (expenses) • Called contribution margin because the excess of sales revenue over variable costs contributes to covering fixed costs

  24. Contribution Margin Approach • Rearrange the income statement—use the contribution margin to develop a shortcut method • Shortcut equation:

  25. Contribution Margin Approach • Given fixed costs total $12,000. The contribution margin per event is $120 ($200 sale price – $80 variable cost) • Check your answer

  26. Contribution Margin Ratio • Ratio of contribution margin to sales revenue • Used to compute the breakeven point in terms of sales dollars • Contribution margin is equal to: • Sales price – variable cost • Contribution margin divided by sales revenue yields a percentage • Percentage of each dollar of sales revenue that contributes toward fixed costs and profit

  27. Contribution Margin Ratio • Formula: • Example: • Yields the same breakeven as the contribution margin approach earlier Unit CM $120Unit Sale Price $200

  28. S19-4: Computing breakeven point in sales units Story Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month. 1. Compute the number of tickets Story must sell to break even. Perform a numerical proof to show that your answer is correct. Units sold = ($240,000 + 0) ÷ ($50 - $10) Units sold = $240,000 ÷ $40 = 6,000 units to breakeven

  29. S19-4: Computing breakeven point in sales units Story Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month. 1. Compute the number of tickets Story must sell to break even. Perform a numerical proof to show that your answer is correct. • Total sales revenue $300,000 (6,000 x 50) • Variable cost 60,000 (6,000 x 10) • Contribution margin $240,000 • - Fixed cost 240,000 • Operating income $ 0

  30. S19-5: Computing breakeven point in sales dollars Story Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month. 1. Compute Story Park’s contribution margin ratio. Carry your computation to two decimal places. $50 - $10 = $40 $40 ÷ $50 = 0.80 or 80% 2. Use the contribution margin ratio CVP formula to determine the sales revenue Story Park needs to break even. $240,000 ÷ 0.80 = $300,000

  31. 3 Use CVP analysis for profit planning, and graph the CVP relations

  32. Using CVP to Plan Profits • Managers more interested in: • Sales level needed to earn a target profit • Profits they can expect to earn • How many products or service events must be sold to earn a specific operating profit • Use either method (equation or CM) • Set operating profit equal to desired profit

  33. Using CVP to Plan Profits

  34. Graphing Cost-Volume-Profit Relations • Graph provides a picture that shows how changes in the levels of sales will affect profits • Four steps: • Choose a sales volume and plot the point for total sales revenue at that volume • Draw the fixed cost line • Draw the total cost line (total costs are the sum of variable costs plus fixed costs) • Identify the breakeven point and the areas of operating income and loss

  35. Preparing a CVP Chart 35

  36. S19-6: Computing contribution margin, breakeven point, and units to achieve operating income Consider the following facts:

  37. S19-6: Computing contribution margin, breakeven point, and units to achieve operating income Consider the following facts: $72,000/$60 ($72,000 + $180,000)/$60

  38. Sensitivity Analysis • Predict how changes in sale prices, cost, or volume affect profits • “What-if?” analysis • Allows managers to see how various business strategies affect profits • Changing selling price • Changing variable Costs • Changing fixed Costs

  39. Sensitivity Analysis: Example • How will the lower sale price affect the breakeven point? • Lower price yields higher unit sales to breakeven • Higher prices yields lower unit sales to breakeven

  40. Sensitivity Analysis: Example • How will increased costs affect the breakeven point? • Higher cost yields higher unit sales to breakeven • Lower cost yields lower unit sales to breakeven

  41. Sensitivity Analysis: Example • How will the increased fixed costs affect the breakeven point? • Higher fixed costs yields higher unit sales to breakeven • Lower fixed costs yields lower unit sales to breakeven

  42. Sensitivity Analysis Summary • Exhibit 19-6

  43. Margin of Safety • Excess of expected sales over breakeven sales • Cushion, drop in sales, a company can absorb without incurring a loss • Margin of safety in units • Margin of safety in dollars

  44. S19-7: Sensitivity analysis of changing sale price and variable costs on breakeven point Story Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month. 1. Suppose Story Park cuts its ticket price from $50 to $40 to increase the number of tickets sold. Compute the new breakeven point in tickets and in sales dollars. Units sold = ($240,000 + 0) ÷ ($40 - $10) Units sold = $240,000 ÷ $30 = 8,000 units to breakeven $320,000 sales dollars to breakeven Old Breakeven 6,000 units, $300,000

  45. S19-7: Sensitivity analysis of changing sale price and variable costs on breakeven point Story Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month. 2. Ignore the information in Requirement 1. Instead, assume that Story Park increases the variable cost from $10 to $20 per ticket. Compute the new breakeven point in tickets and in sales dollars. Units sold = ($240,000 + 0) ÷ ($50 - $20) Units sold = $240,000 ÷ $30 = 8,000 units to breakeven = $400,000 in sales dollars

  46. S19-9: Computing margin of safety Story Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month. 1. If Story Park expects to sell 6,200 tickets, compute the margin of safety in tickets and in sales dollars. Expected sales - Breakeven sales = Margin of safety in units 6,200 – 6,000 = 200 in units Margin of safety in units x Sales price = Margin of safety in dollars 200 units x $50 = $10,000

  47. Breakeven Point Multiple Product Lines • Selling prices and variable costs differ for each product • Different contribution to profits • Weighted-average contribution margin computed • Sales mix provides weights to make up total product sales • Weights equal 100% of total product sales

  48. Steps for Computing Breakeven Point with Multiple Product Lines • To compute breakeven sales in units for multiple products, complete the following three steps: • STEP 1: Calculate the weighted-average contribution margin per unit • STEP 2: Calculate the breakeven point in units for the “package” of products • STEP 3: Calculate the breakeven point in units for each product and then multiply the “package” breakeven point in units by each product’s proportion of the sales mix

  49. Step 1 • Calculate the weighted-average contribution margin per unit:

  50. Step 2 • Calculate the breakeven point in units for the “package” of products: