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## Cost-Volume-Profit Analysis

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**Cost-Volume-Profit Analysis**Chapter 19**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**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**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**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**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**High-Low Method: Steps 1 and 2**• Data • Step 1 • Step 2**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)**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**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**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**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**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**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?**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**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**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**Break Even Example Data**• Unit sale price • Unit variable cost • Fixed costs • Unit contribution margin • $200 • $80 • $12,000 • $120 ($200 - $80)**Income Statement Approach**• Express income in equation form and then break it down into its components:**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**Contribution Margin Approach**• Rearrange the income statement—use the contribution margin to develop a shortcut method • Shortcut equation:**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**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**Contribution Margin Ratio**• Formula: • Example: • Yields the same breakeven as the contribution margin approach earlier Unit CM $120Unit Sale Price $200**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**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**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**3**Use CVP analysis for profit planning, and graph the CVP relations**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**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**S19-6: Computing contribution margin, breakeven point, and**units to achieve operating income Consider the following facts:**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**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**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**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**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**Sensitivity Analysis Summary**• Exhibit 19-6**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**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**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**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**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**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**Step 1**• Calculate the weighted-average contribution margin per unit:**Step 2**• Calculate the breakeven point in units for the “package” of products: