Learning Objectives Part 1 CHAPTER 4 1 Explain how changes in activity affect contribution margin and operating income. 2 Prepare and interpret a cost–volume–profit graph. 3 Calculate the contribution margin ratio and the variable expense ratio. Use the contribution margin ratio to compute changes in contribution margin and operating income resulting from changes in sales volume. 4-1 Learning Objectives Part 2 4 Show the effects on contribution margin of changes in variable costs, fixed costs, selling price, and volume. 5 Compute the break-even point in unit sales and sales dollars. 6 Determine the level of sales needed to achieve a desired target profit. 7 Compute the margin of safety and explain its significance. 4-2 Learning Objectives Part 3 8 Explain cost structure, compute the degree of operating leverage at a particular level of sales, and explain how operating leverage can be used to predict changes in operating income. 9 Compute the break-even point for a multiproduct company and explain the effects of changes in the sales mix on the contribution margin and the break-even point.. 4-3 Cost-Volume-Profit Relationship Interactions • Cost-volume-profit (CVP) analysis is a powerful tool that managers use to help them understand the interrelationship among cost, volume and profit in an organization by focusing on interactions among the following five elements: 1.prices of products 2.volume or level of activity 3.per unit variable costs 4.total fixed costs 5.mix of products sold 4-4 Basics of Cost-Volume-Profit Analysis The contribution income statement is helpful to managers in judging the impact on profits of changes in selling price, cost, or volume. The emphasis is on cost behaviour. Example Company Contribution Income Statement For the Month of June Sales (500 units) $ Less: Variable expenses Contribution margin Less: Fixed expenses Net operating income $ 250,000 150,000 100,000 80,000 20,000 Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted. 4-5 Contribution Margin (CM) Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. If an additional unit is sold, $200 additional CM will be generated to cover fixed expenses and profit. Example Company Contribution Income Statement For the Month of June Total Per Unit Sales (500 units) $ 250,000 $ 500 Less: Variable expenses 150,000 300 Contribution margin 100,000 $ 200 Less: Fixed expenses 80,000 Net operating income $ 20,000 % of Sales 100% 60% 40% 4-6 Contribution Margin Ratio The CM ratio is calculated by dividing the total contribution margin by total sales. Example Company Contribution Income Statement For the Month of June Total Per Unit Sales (500 units) $ 250,000 $ 500 Less: Variable expenses 150,000 300 Contribution margin 100,000 $ 200 Less: Fixed expenses 80,000 Net operating income $ 20,000 CM per unit = CM Ratio = SP per unit $200 $500 CM Ratio 100% 60% 40% = 40% 4-7 The Contribution Approach 1 Each month, $80,000 in total CM must be generated to break even. Example Company Contribution Income Statement For the Month of June Total Per Unit Sales (500 units) $ 250,000 $ 500 Less: Variable expenses 150,000 300 Contribution margin 100,000 $ 200 Less: Fixed expenses 80,000 Net operating income $ 20,000 CM Ratio 100% 60% 40% 4-8 The Contribution Approach 2 If 400 units are sold in a month, they will be operating at the break-even point. Example Company Contribution Income Statement For the Month of June Total Per Unit Sales ( 400 units) $ 200,000 $ 500 Less: Variable expenses 120,000 300 Contribution margin 80,000 $ 200 Less: Fixed expenses 80,000 Net operating income $ - CM Ratio 100% 60% 40% 4-9 The Contribution Approach 3 If one more unit is sold (401 units), net operating income will increase by $200. Example Company Contribution Income Statement For the Month of June Total Per Unit Sales ( 401 units) $ 200,500 $ 500 Less: Variable expenses 120,300 300 Contribution margin 80,200 $ 200 Less: Fixed expenses 80,000 Net operating income $ 200 © 2021 McGraw-Hill Limited CM Ratio 100% 60% 40% 4-10 The Contribution Approach 4 • We do not need to prepare an income statement to estimate profits at a particular sales volume. Simply multiply the number of units sold above break-even by the contribution margin per unit. • If 430 units are sold, the net operating income will be $6,000 • 30 units above break-even: 30 x 200 = $6,000 4-11 CVP Relationships in Graphic Form • Relationships among revenue, cost, profit and volume can be expressed graphically by preparing a CVP graph. Below is a contribution margin income statement at 300, 400, and 500 units sold. We will use this information to prepare the CVP graph. Sales Less: variable expenses Contribution margin Less: fixed expenses Net operating income Income 300 units $ 150,000 90,000 $ 60,000 80,000 $ (20,000) Income 400 units $ 200,000 120,000 $ 80,000 80,000 $ - Income 500 units $ 250,000 150,000 $ 100,000 80,000 $ 20,000 4-12 CVP Graph 1 450,000 400,000 350,000 Dollars 300,000 250,000 In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. 200,000 150,000 100,000 50,000 - 100 200 300 400 500 600 700 800 Units 4-13 CVP Graph 2 450,000 400,000 Total Sales 350,000 Dollars 300,000 250,000 Total Expenses 200,000 Fixed Expenses 150,000 100,000 50,000 - 100 200 300 400 500 600 700 800 Units 4-14 CVP Graph 3 450,000 Break-even point (400 units or $200,000 in sales) 400,000 350,000 Dollars 300,000 250,000 200,000 150,000 100,000 50,000 - 100 200 300 400 500 600 700 800 Units 4-15 Contribution Margin Ratio 1 • The contribution margin ratio is: Total CM CM Ratio = Total sales • For Example Company the ratio is: $80,000 = 40% $200,000 • Each $1.00 increase in sales results in a total contribution margin increase of 40¢. 4-16 Contribution Margin Ratio 2 • Or, in terms of units, the contribution margin ratio is: Unit CM CM Ratio = Unit selling price • For Example Company the ratio is: $200 = 40% $500 4-17 Contribution Margin Ratio 3 If sales increase from 400 to 500 units ($50,000), contribution margin will increase by $20,000 ($50,000 × 40%). Here is the proof: Sales Less: variable expenses Contribution margin Less: fixed expenses Net operating income 400 Units $ 200,000 120,000 80,000 80,000 $ - 500 Units $ 250,000 150,000 100,000 80,000 $ 20,000 A $50,000 increase in sales revenue results in a $20,000 increase in CM ($50,000 × 40% = $20,000). 4-18 Contribution Margin Ratio 4 • The effect of a change in sales revenue on the change in CM dollars can be expressed in equation form as follows: Change in CM dollars = CM Ratio x Change in sales revenue 4-19 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch? a. 1.319 b. 0.758 c. 0.242 d. 4.139 4-20 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch? Answer: b. 0.758 4-21 Variable Expense Ratio Variable expense ratio is the ratio of variable expenses to sales: Variable expense ratio = Variable expenses / Sales This leads to a useful equation that relates the CM ratio to the variable expense ratio as follows: CM ratio = CM / Sales CM ratio = (Sales – Variable expenses) / Sales CM ratio = 1 – Variable expense ratio 4-22 Change in Fixed Cost and Sales Volume 1 • What is the profit impact if sales can increase from 500 units to 540 units by increasing the monthly advertising budget by $10,000? 4-23 Change in Fixed Cost and Sales Volume 2 $80,000 + $10,000 advertising = $90,000 Example Company Contribution Income Statement For the Month of June Current Sales (500 units) Sales revenue Projected Sales (540 units) $250,000 $270,000 Less: Variable expenses 150,000 162,000 Contribution Margin 100,000 108,000 Less: Fixed expenses 80,000 90,000 Net Income 20,000 18,000 Sales increased by $20,000, but net operating income decreased by $2,000. 4-24 Change in Fixed Cost and Sales Volume 3 The CM Solution: Increase in CM (40 units x $200) $ 8,000 Increase in advertising expenses (10,000) Decrease in net operating income (2,000) 4-25 Change in Variable Cost and Sales Volume 1 • What is the profit impact if a higher quality of raw materials is used, thus increasing variable costs per unit by $10, to generate an increase in unit sales from 500 to 580? 4-26 Change in Variable Cost and Sales Volume 2 580 units × $310 variable cost/unit = $179,800 Example Company Contribution Income Statement For the Month of June Current Sales (500 units) Sales revenue Projected Sales (580 units) $250,000 $290,000 Less: Variable expenses 150,000 179,800 Contribution Margin 100,000 110,200 Less: Fixed expenses 80,000 80,000 Net Income 20,000 30,200 Sales increase by $40,000, and net operating income increases by $10,200. 4-27 Change in Variable Cost and Sales Volume 3 The CM Solution: Increase in VC of $10 x 500 units $ (5,000) Increase in units sold: 80 units x 190 [200 – 10] 15,200 Decrease in net operating income 10,200 4-28 Change in Fixed Costs, Selling Price and Sales Volume 1 • What is the profit impact if: (1) selling price is cut by $20 per unit, (2) the advertising budget is increased by $15,000 per month, and (3) sales increase from 500 to 650 units per month? 4-29 Change in Fixed Costs, Selling Price and Sales Volume 2 Example Company Contribution Income Statement For the Month of June Current Sales (500 units) Sales revenue Projected Sales (650 units) $250,000 $312,000 Less: Variable expenses 150,000 195,000 Contribution Margin 100,000 117,000 Less: Fixed expenses 80,000 95,000 Net Income 20,000 22,000 Sales increase by $62,000, fixed costs increase by $15,000, and net operating income increases by $2,000. 4-30 Change in Fixed Costs, Selling Price and Sales Volume 3 The CM Solution: Decrease in Selling Price of $20 x 500 units $(10,000) Increase in advertising by $15,000/month (15,000) Increase in sales by 150 units x $180 [200-20] 27,000 Increase in net operating income 2,000 4-31 Change in Variable Cost, Fixed Cost and Sales Volume 1 • What is the profit impact if: (1) instead of paying salespersons flat salaries that currently total $6,000 per month, a $15 sales commission per unit sold is paid, and (2) sales increase from 500 units to 575 units? 4-32 Change in Variable Cost, Fixed Cost and Sales Volume 2 Example Company Contribution Income Statement For the Month of June Current Sales (500 units) Sales revenue Projected Sales (575 units) $250,000 $287,500 Less: Variable expenses 150,000 181,125 Contribution Margin 100,000 106,375 Less: Fixed expenses 80,000 74,000 Net Income 20,000 32,375 Sales increase by $37,500, variable costs increase by $31,125, but fixed expenses decrease by $6,000. Net operating income increased by $12,375. 4-33 Change in Variable Cost, Fixed Cost and Sales Volume 3 The CM Solution: Increase in VC of $15 x 500 units $(7,500) Increase in CM of $185 [200-15] x 75 units 13,875 Decrease (savings) in FC 6,000 Increase in net operating income 12,375 4-34 Break-Even Analysis 1 • Break-even analysis is an aspect of CVP analysis that is designed to answer questions such as how far sales could drop before the company begins to lose money. 4-35 Break-Even Analysis 2 The contribution format income statement can be stated in equation form: Profits = (Sales – Variable expenses) – Fixed expenses OR Profits = [P x Q] – [V x Q] - Fixed expenses Where P = selling price per unit, Q = number of units sold; and VC = variable costs per unit. 4-36 Break-Even Analysis 3 Profits = [P x Q] – [V x Q] - Fixed expenses We can simplify the above formula: Profits = [CM x Q] – Fixed expenses The Break-even point is when profits are zero, therefore the equation becomes: Break-even point in units sold = Fixed expenses Unit CM 4-37 Break-Even Analysis 4 Break-even point in units sold = Fixed expenses Unit CM A variation of the break-even formula using the CM ratio instead of the unit CM is shown below. The result using this formula is the break-even in total sales dollars rather than in total units sold: Break-even point in = Total sales dollars Fixed expenses CM ratio 4-38 Break-Even Analysis 5 • Here is the information from Example Company: Sales (500 units) Less: variable expenses Contribution margin Less: fixed expenses Net operating income Total $ 250,000 150,000 $ 100,000 $ Per Unit $ 500 300 $ 200 Percent 100% 60% 40% 80,000 20,000 4-39 Break-Even Analysis 6 We calculate the break-even point as follows: Break-even point in units sold = Fixed expenses Unit CM = $80,000 / 200 = 400 units Break-even point in total sales dollars = Fixed expenses CM ratio = $80,000 / 40% = $200,000 4-40 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units? a. 872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups 4-41 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units? Answer: d. 1,150 cups 4-42 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in dollars? a. $1,300 b. $1,715 c. $1,788 d. $3,129 4-43 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in dollars? Answer: b. $1,715 4-44 Target Operating Profit Analysis 1 • CVP formulas can also be used to determine • • • the sales volume needed to achieve a target operating profit. The dollar sales needed to achieve a target operating profit. Suppose Example Company wants to know how many units must be sold to earn a profit of $100,000. 4-45 Target Operating Profit Analysis 2 Units sold to attain Fixed expenses + Target operating profit = the target profit Unit contribution margin $80,000 + $100,000 = 900 units $200/unit 4-46 Target Operating Profit Analysis 3 Dollar sales to Fixed expenses + Target operating profit = attain target profit CM Ratio $80,000 + $100,000 = $450,000 40% 4-47 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. How many cups of coffee would have to be sold to attain target profits of $2,500 per month? a. 3,363 cups b. 2,212 cups c. 1,150 cups d. 4,200 cups 4-48 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. How many cups of coffee would have to be sold to attain target profits of $2,500 per month? Answer: a. 3,363 cups 4-49 After-Tax Analysis 1 • For-profit organizations are required to pay corporate income taxes. • In general, operating profit after taxes can be computed as a fixed percentage of income before taxes. 4-50 After-Tax Analysis 2 Profit after taxes = Before-tax profit – Taxes = B – t(B) = B(1-t) Rearranged to calculate before-tax profit (B): B = Profit after taxes / (1-t) 4-51 The Margin of Safety 1 The margin of safety is the excess of budgeted (or actual) sales over the breakeven volume of sales. Margin of safety = Total sales – Break-even sales Margin of safety percentage = Margin of safety in $ Total budgeted (or actual) sales Let’s look at Example Company and determine the margin of safety. 4-52 The Margin of Safety 2 If we assume that actual sales are $250,000, given that we have already determined the breakeven sales to be $200,000, the margin of safety is $50,000 as shown. Sales Less: variable expenses Contribution margin Less: fixed expenses Net operating income Breakeven sales 400 units $ 200,000 120,000 80,000 80,000 $ - Actual sales 500 units $ 250,000 150,000 100,000 80,000 $ 20,000 4-53 The Margin of Safety 3 The margin of safety can be expressed as 20% of sales. ($50,000 ÷ $250,000) Break-even sales 400 units Sales $ 200,000 Less: variable expenses 120,000 Contribution margin 80,000 Less: fixed expenses 80,000 Net operating income $ - Actual sales 500 units $ 250,000 150,000 100,000 80,000 $ 20,000 4-54 The Margin of Safety 4 The margin of safety can be expressed in terms of the number of units sold. The margin of safety is $50,000, and each unit sells for $500. 4-55 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the margin of safety? a. 3,250 cups b. 950 cups c. 1,150 cups d. 2,100 cups 4-56 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the margin of safety? Answer: b. 950 cups 4-57 Cost Structure and Profit Stability 1 • Cost structure refers to the relative proportion of fixed and variable costs in an organization. Managers often have some latitude in determining their organization’s cost structure. 4-58 Cost Structure and Profit Stability 2 There are advantages and disadvantages to high fixed cost (or low variable cost) and low fixed cost (or high variable cost) structures. An advantage of a high fixed cost structure is that income will be higher in good years compared to companies with lower proportion of fixed costs. A disadvantage of a high fixed cost structure is that income will be lower in bad years compared to companies with lower proportion of fixed costs. Companies with low fixed cost structures enjoy greater stability in income across good and bad years. 4-59 Operating Leverage 1 A measure of how sensitive net operating income is to percentage changes in sales. Degree of = operating leverage Contribution margin Operating income % change in = operating income Degree of Op. Leverage x % change in sales 4-60 Operating Leverage 2 Example Company, the degree of operating leverage is 5: Sales Less: variable expenses Contribution margin Less: fixed expenses Net income $100,000 $20,000 Actual sales 500 Units $ 250,000 150,000 100,000 80,000 $ 20,000 = 5 4-61 Operating Leverage 3 With an operating leverage of 5, if sales are increased by 10%, net operating income would increase by 50%. Percent increase in sales Degree of operating leverage Percent increase in profits × 10% 5 50% Here’s the verification! 4-62 Operating Leverage 4 Sales Less variable expenses Contribution margin Less fixed expenses Net operating income Actual sales $ 250,000 150,000 100,000 80,000 $ 20,000 Increased sales (550) $ 275,000 165,000 110,000 80,000 $ 30,000 10% increase in sales from $250,000 to $275,000 . . . . . . results in a 50% increase in income from $20,000 to $30,000. 4-63 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the operating leverage? a. 2.21 b. 0.45 c. 0.34 d. 2.92 4-64 Quick Check Actual sales Coffee Klatch is an espresso stand in a cups 2,100 downtown office building. The average 3,129 selling Sales price of a cupLess: of coffee is $1.49 and the 756 Variable expenses average variable expense per cup is $0.36. Contribution margin 2,373 The average fixed expense per month is Less: Fixed expenses 1,300 $1,300. 2,100 Net cups are sold each month1,073 on operating income average. What is the operating leverage? Answer: a. 2.21 4-65 Quick Check At Coffee Klatch the average selling price of a cup of coffee is $1.49, the average variable expense per cup is $0.36, the average fixed expense per month is $1,300 and an average of 2,100 cups are sold each month. If sales increase by 20%, by how much should net operating income increase? a. 30.0% b. 20.0% c. 22.1% d. 44.2% 4-66 Quick Check At Coffee Klatch the average selling price of a cup of coffee is $1.49, the average variable expense per cup is $0.36, the average fixed expense per month is $1,300 and an average of 2,100 cups are sold each month. If sales increase by 20%, by how much should net operating income increase? Answer: d. 44.2% Percent increase in sales × Degree of operating leverage Percent increase in profit 20.0% 2.21 44.20% 4-67 Verify Increase in Profit Actual sales 2,100 cups Sales $ 3,129 Less: Variable expenses 756 Contribution margin 2,373 Less: Fixed expenses 1,300 Net operating income $ 1,073 % change in sales % change in net operating income Increased sales 2,520 cups $ 3,755 907 2,848 1,300 $ 1,548 20.0% 44.2% 4-68 Sales Mix • • • Sales mix is the relative proportion in which a company’s products are sold. Different products have different selling prices, cost structures, and contribution margins. Let’s assume Example Company sells bikes and carts and that the sales mix between the two products remains the same. 4-69 Sales Mix & Break-Even Analysis 1 Example Co. information: $265,000 = 48.2% (rounded) $550,000 4-70 Sales Mix & Break-Even Analysis 2 4-71 Assumptions of CVP Analysis • Selling price is constant. • Costs are linear and can be accurately divided into variable (constant per unit) and fixed (constant in total) elements. • Variable costs per unit are constant, and fixed costs are constant in total over the entire relevant range. • In multiproduct companies, the sales mix is constant. • In manufacturing companies, inventories do not change (units produced = units sold). 4-72 End of Chapter Summary Part 1 • Cost–volume–profit (CVP) analysis is based on a simple model of how contribution margin (CM) and operating income respond to changes in selling prices, costs, and volume. • A CVP graph depicts the relationships between sales volume in units and fixed expenses, variable expenses, total expenses, total sales, and profits. 4-73 End of Chapter Summary Part 2 • The CM ratio is the ratio of the total CM to total sales. This ratio can be used to estimate the effect of a change in total sales on operating income. • The break-even point is the level of sales (in units or in dollars) at which the company generates zero profits. • The margin of safety is the amount by which the company’s current sales exceed break-even sales. 4-74 End of Chapter Summary Part 3 • The degree of operating leverage measures the effect of a percentage change in sales on the company’s operating income. The higher the degree of operating leverage, the more sensitive operating income will be to a change in sales. • The profits of a multi-product company are affected by its sales mix. 4-75