Managerial Accounting Chapter 4 Cost-Volume-Profit Relationships PDF

CHAPTER 4: Cost-Volume- Profit Relationships Prepared by Ruth Ann Strickland, CPA Western...

CHAPTER 4: Cost-Volume- Profit Relationships Prepared by Ruth Ann Strickland, CPA Western University © 2024 McGraw Hill Limited Learning Objectives Part 1 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. Show the effects on contribution margin of changes in variable costs, fixed costs, selling price, and volume. © 2024 McGraw Hill Limited 4-2 Learning Objectives Part 2 5. Compute the break-even point in unit sales and in 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. 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. © 2024 McGraw Hill Limited 4-3 Learning Objectives Part 3 9. Compute the break-even point for a multi- product company and explain the effects of changes in the sales mix on the contribution margin and the break-even point. 10.(Online Appendix 4A) Conduct a cost– volume–profit analysis with uncertainty. © 2024 McGraw Hill Limited 4-4  Cost-Volume-Profit Relationship Interactions Cost-volume-profit (CVP) analysis is a powerful tool that managers use to help them understand the interrelationship between 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 © 2024 McGraw Hill Limited 4-5  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 emphasisExample is on Company cost behaviour. Contribution Income Statement For the Month of June Sales (500 units) $ 250,000 Less: Variable expenses 150,000 Contribution margin 100,000 Less: Fixed expenses 80,000 Net operating income $ 20,000 Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted. © 2024 McGraw Hill Limited 4-6 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 % of Sales Sales (500 units) $250,000 $500 100% Less: Variable expenses 150,000 300 60% Contribution margin $100,000 $200 40% Less: Fixed expenses 80,000 Net operating income $20,000 © 2024 McGraw Hill Limited 4-7 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 % of Sales Sales (500 units) $250,000 $500 100% Less: Variable expenses 150,000 300 60% Contribution margin $100,000 $200 40% Less: Fixed expenses 80,000 Net operating income $20,000 CM per unit $200 CM Ratio = = = 40% SP per unit $500 © 2024 McGraw Hill Limited 4-8 The Contribution Approach 1 in total CM must be Each month, $80,000 generated to break even. Any additional CM become operating income. Per Percen Total Unit t Sales (400 units) $200,000 $500 100% Less: variable expenses 120,000 300 60% Contribution margin $80,000 $200 40% Less: fixed expenses 80,000 Operating income $0 © 2024 McGraw Hill Limited 4-9 The Contribution Approach 2 If 400 units are sold in a month, the company will be operating at the break- even point. Example Company Contribution Income Statement For the Month of June Total Per Unit % of Sales Sales (400 units) $200,000 $500 100% Less: Variable expenses 120,000 300 60% Contribution margin $80,000 $200 40% Less: Fixed expenses 80,000 Net operating income $ - © 2024 McGraw Hill Limited 4-10 The Contribution Approach 3 If one more unit is sold (401 units), net operating income will increase by $200. Percen Total Per Unit t Sales (401 units) $200,500 $500 100% Less: variable expenses 120,300 300 60% Contribution margin $80,200 $200 40% Less: fixed expenses 80,000 Operating income $200 © 2024 McGraw Hill Limited 4-11  The Contribution Approach 4 It is not necessary to prepare an income statement to estimate profits at each different level of sales. 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 © 2024 McGraw Hill Limited 4-12  CVP Relationships in Graphic Form Relationships among revenue, cost, profit and volume can be expressed with a CVP graph. Below is a contribution margin income statement at 300, 400, and 500 units sold. This information will be used to prepare a CVP graph. 300 units 400 units 500 Units Sales $150,000 $200,000 $250,000 Less: variable expenses 90,000 120,000 150,000 Contribution margin $60,000 $80,000 $100,000 Less: fixed expenses 80,000 80,000 80,000 Operating income ($20,000) © 2024 McGraw Hill Limited --- $20,000 4-13  CVP Graph 1 450,000 400,000 350,000 300,000 Dollars 250,000 200,000 In a CVP graph, unit volume is 150,000 usually represented on the horizontal (X) axis and 100,000 dollars on the vertical (Y) 50,000 axis. - - 100 200 300 400 500 600 700 800 Units © 2024 McGraw Hill Limited 4-14  CVP Graph 2 450,000 400,000 350,000 Total Sales 300,000 Total Expenses Dollars 250,000 200,000 150,000 Fixed Expenses 100,000 50,000 - - 100 200 300 400 500 600 700 800 Units © 2024 McGraw Hill Limited 4-15  CVP Graph 3 450,000 400,000 Break-even point (400 units or $200,000 in sales) 350,000 rea fit A 300,000 P ro Dollars 250,000 200,000 150,000 rea 100,000 s A Lo s 50,000 - - 100 200 300 400 500 600 700 800 Units © 2024 McGraw Hill Limited 4-16 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 $0.40 © 2024 McGraw Hill Limited 4-17 Contribution Margin Ratio 2 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 © 2024 McGraw Hill Limited 4-18 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: 400 units 500 units Sales $200,000 $250,000 Less: variable expenses 120,000 150,000 Contribution margin $80,000 $100,000 Less: fixed expenses 80,000 80,000 Operating income --- $20,000 A $50,000 increase in sales revenue results in a $20,000 increase in CM ($50,000 × 40% = $20,000). © 2024 McGraw Hill Limited 4-19 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 © 2024 McGraw Hill Limited 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 $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. 2,100 cups of coffee are sold each month on average. What is the CM Ratio for Coffee Klatch? a. 33% b. 75% c. 25% d. 400% © 2024 McGraw Hill Limited 4-21  Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. 2,100 cups of coffee are sold each month on average. What is the CM Ratio for Coffee Klatch? Answer: b. 75% CM Ratio = Unit Contribution Margin = $4.00 - $1.00 Unit Selling Price $4.00 © 2024 McGraw Hill Limited 4-22  Variable Expense Ratio The 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 © 2024 McGraw Hill Limited 4-23 Change in Fixed Cost and Sales Volume 1 What is the impact on profit if sales increase from 500 units to 540 units due to a $10,000 increase in the monthly advertising budget? © 2024 McGraw Hill Limited 4-24 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 Projected (500 units) Sales (540 units) Sales revenue $250,000 $270,000 Less: Variable 150,000 162,000 expenses Contribution Margin $100,000 $108,000 Less: Fixed expenses 80,000 90,000 Operating Income $ 20,000 $ 18,000 Sales increased by $20,000, but operating income decreased by $2,000. © 2024 McGraw Hill Limited 4-25 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) © 2024 McGraw Hill Limited 4-26 Change in Variable Cost and Sales Volume 1 What is the impact on profit if a higher quality of raw materials is used, thus increasing variable costs per unit by $10. Assume that the increase in quality generates an increase in unit sales from 500 to 580? © 2024 McGraw Hill Limited 4-27 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 Projected Sales (500 Sales (580 units) units) Sales revenue $250,000 $290,000 Less: Variable 150,000 179,800 expenses Contribution Margin $100,000 $110,200 Less: Fixed expenses 80,000 80,000 Operating Income $ 20,000 $ 30,200 Sales increased by $40,000, and operating income increased by $10,200. © 2024 McGraw Hill Limited 4-28 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 Increase in net operating income 10,200 © 2024 McGraw Hill Limited 4-29  Change in Fixed Costs, Selling Price and Sales Volume 1 What is the impact on profit 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? © 2024 McGraw Hill Limited 4-30  Change in Fixed Costs, Selling Price and Sales Volume Example Company 2 Contribution Income Statement For the Month of June Current Projected Sales (500 Sales (650 units) units) Sales revenue $250,000 $312,000 Less: Variable 150,000 195,000 expenses Contribution Margin $100,000 $117,000 Less: Fixed expenses 80,000 95,000 Operating Income $ 20,000 $ 22,000 Sales increased by $62,000, fixed costs increase by $15,000, and net operating income increased by $2,000. © 2024 McGraw Hill Limited 4-31  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) Additional CM on new sales 150 units x $180 [200-20] 27,000 © 2024 McGraw Hill Limited 4-32 Change in Variable Cost, Fixed Cost and Sales Volume 1 What is the impact on profit if: 1. instead of paying fixed salespersons 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? © 2024 McGraw Hill Limited 4-33 Change in Variable Cost, Fixed Cost and Sales Volume Example Company Contribution 2 Income Statement For the Month of June Current Sales Projected (500 units) Sales (575 units) Sales revenue $250,000 $287,500 Less: Variable 150,000 181,125 expenses Contribution Margin 100,000 106,375 Less: Fixed 80,000 74,000 expenses Sales increased by $37,500, variable costs Operating Income 20,000 32,375 increased by $31,125, but fixed expenses decreased by $6,000. Net operating income increased by © 2024 McGraw $12,375. Hill Limited 4-34  Change in Variable Cost, Fixed Cost and Sales Volume 3 The CM Solution: Increase in VC of $15 x 500 units $(7,500) Additional CM on new sales 75 units x $185 [200-15] 13,875 Decrease (savings) in FC 6,000 Increase in net operating income 12,375 © 2024 McGraw Hill Limited 4-35  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. © 2024 McGraw Hill Limited 4-36  Break-Even Analysis 2 The contribution format income statement can be stated in equation form: Profit = (Sales – Variable expenses) – Fixed expenses OR Profit = [P x Q] – [VC x Q] - Fixed expenses Where P = selling price per unit, Q = number of units sold; and VC = variable costs per unit. © 2024 McGraw Hill Limited 4-37  Break-Even Analysis 3 Profit = [P x Q] – [VC x Q] - Fixed expenses We can simplify the above formula: Profit = [CM x Q] – Fixed expenses The break-even point is when profit is zero, therefore the equation becomes: Break-even point in units sold = Fixed expenses Unit CM © 2024 McGraw Hill Limited 4-38  Break-Even Analysis 4 Break-even point in units sold = Fixed expenses A variation of the break-even Unit CM formula using the CM ratio instead of the unit CM is shown below. This formula determines the break-even in total sales dollars rather than in total units sold: Break-even point in = Fixed expenses total sales dollars CM ratio © 2024 McGraw Hill Limited 4-39  Break-Even Analysis 5 Example Company’s current income statement at 500 units shows operating income of $20,000. What is the company’s the break-even in units and in dollars? Total Per Unit Percent Sales $250,000 $500 100% Less: variable expenses 150,000 300 60% Contribution margin $100,000 $200 40% Less: fixed expenses 80,000 Operating income $20,000 © 2024 McGraw Hill Limited 4-40  Break-Even Analysis 6 Calculate Example Company’s break- even point in units and in percent: Break-even point in units sold = Fixed expenses Unit CM = $80,000 / 200 Break-even point in = 400 units total sales dollars = Fixed expenses CM ratio = $80,000 / 40% = $200,000 © 2024 McGraw Hill Limited 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 $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. 2,100 cups of coffee are sold each month on average. What is the break-even sales in units? a. 2,100 cups b. 3,000 cups c. 750 cups d. 1,000 cups © 2024 McGraw Hill Limited 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 $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. 2,100 cups of coffee are sold each month on average. What is the break-even sales in units? Unit 1,000 cups. Sales $4.00 $4,000 Variable expenses $1.00 1,000 Answer: Contribution margin Fixed Expenses $3.00 $3,000 $3,000 Operating Income $0 d. 1,000 cups Break-even = Fixed Expenses =. $3,000. Unit CM $4.00 - $1.00 © 2024 McGraw Hill Limited 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 $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. 2,100 cups of coffee are sold each month on average. What is the break-even sales in dollars? a. $ 4,000 b. $12,000 c. $ 4,400 d. $ 8,400 © 2024 McGraw Hill Limited 4-44  Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. 2,100 cups of coffee are sold each month on average. What is the break-even sales in dollars? 1,000 Unit cups Sales $4.00 $4,000 Variable expenses $1.00 1,000 Answer: Contribution margin Fixed Expenses $3.00 $3,000 $3,000 Operating Income $0 a. $4,000 Break-even = Fixed Expenses = $3,000. CM Ratio 75% ALT: 1,000 units x $4.00 per unit © 2024 McGraw Hill Limited 4-45  Target Operating Profit Analysis 1 CVP formulas can also be used to determine the sales volume needed to achieve a target operating profit. The sales dollars 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. © 2024 McGraw Hill Limited 4-46  Target Operating Profit Analysis 2 Units sold to attain Fixed expenses + Target operating profi = the target profit Unit contribution margin $80,000 + $100,000 = 900 units $200/unit © 2024 McGraw Hill Limited 4-47  Target Operating Profit Analysis 3 Dollar sales to Fixed expenses + Target operating profi = attain target profit CM Ratio $80,000 + $100,000 = $450,000 40% © 2024 McGraw Hill Limited 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 $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. What level of sales dollars will provide a profit of $2,500 per month? a. $ 5,500 b. $ 8,400 c. $ 7,333 d. $22,000 © 2024 McGraw Hill Limited 4-49  Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. What level of sales dollars would provide a profit of $2,500 per month? Unit 1833 Sales $4.00 $7,333 Variable expenses $1.00 1,833 Answer: Contribution margin $3.00 $5,500 Fixed Expenses $3,000 c. $7,333 Operating Income $2,500 Break-even to achieve target profit = Fixed Expenses + Target Profit = $3,000 + $2,500. CM Ratio 75% © 2024 McGraw Hill Limited 4-50  After-Tax Analysis 1 For-profit organizations are required to pay corporate income tax on profits earned. In general, operating profit after tax can be computed as a fixed percentage of income before tax. © 2024 McGraw Hill Limited 4-51  After-Tax Analysis 2 Profit after tax = Before-tax profit – Tax = B – t(B) = B(1-t) Rearranged to calculate before-tax profit (B): B = Profit after tax / (1-t) © 2024 McGraw Hill Limited 4-52  Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. The company pay income tax at a rate of 20%. What level of sales dollars will provide a minimum after-tax profit of $2,500 per month? a. $ 11,781 b. $ 24,500 c. $ 6,125 d. $ 8,167 © 2024 McGraw Hill Limited 4-53  Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. The company pay income tax at a rate of 20%. What level of sales dollars will provide a minimum after-tax profit of $2,500 per month? Answer: d. $8,167 Break-even to achieve target profit = Fixed Expenses + After- Tax Profit CM Ratio = $3,000 + ($2,500/80%) = $3,000 + $3,125 75% 75% ALSO SEE NEXT PAGE … © 2024 McGraw Hill Limited 4-54  Quick Check  2,041.75 Unit cups Sales $4.00 $8,167 Variable expenses $1.00 2,042 Contribution margin $3.00 $6,125 Fixed Expenses $3,000 Operating Income $3,125 20% Income Tax $625 After-Tax Income $2,500 Note that $8,167 is a theoretical answer, as it would not be possible to sell 2,041.75 cups of coffee. Anything over 2,042 will achieve the after-tax profit goal. 4-55 © 2024 McGraw Hill Limited  The Margin of Safety 1 The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. argin of safety = Total sales – Break-even sal Margin of safety percentage = Margin of safety in $ Total sales Determine the margin of safety for Example Company. © 2024 McGraw Hill Limited 4-56  The Margin of Safety 2 If actual sales are $250,000 and break-even sales are $200,000, the margin of safety is $50,000. Break-even sales Actual sales 400 units 500 units Sales $200,000 $250,000 Less: variable expenses 120,000 150,000 Contribution margin $80,000 $100,000 Less: fixed expenses 80,000 80,000 Operating income $0 $20,000 © 2024 McGraw Hill Limited 4-57  The Margin of Safety 3 The margin of safety can be expressed as 20% of sales. ($50,000 ÷ $250,000) Break-even sales Actual sales 400 units 500 units Sales $200,000 $250,000 Less: variable expenses 120,000 150,000 Contribution margin $80,000 $100,000 Less: fixed expenses 80,000 80,000 Operating income $0 $20,000 © 2024 McGraw Hill Limited 4-58  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. Margin of $50,000 100 Safety in units $500 units © 2024 McGraw Hill Limited 4-59  Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. 2,100 cups of coffee are sold each month on average. What is the margin of safety in cups of coffee? a. 1,100 cups b. 2,100 cups c. 825 cups d. 3,300 cups © 2024 McGraw Hill Limited 4-60  Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. 2,100 cups of coffee are sold each month on average. What is the margin of safety in cups of coffee? Answer a. 1,100 cups Margin of safety in units = Total sales – Break-even sales 2,100 cups – 1,000 cups = 1,100 cups © 2024 McGraw Hill Limited 4-61 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 choice in determining their organization’s cost structure. © 2024 McGraw Hill Limited 4-62  Cost Structure and Profit Stability 2 There are advantages and disadvantages to high fixed cost (with low variable cost) and low fixed cost (with high variable cost) structures. An advantage of a high fixedA disadvantage of a high fixed cost structure is that income cost structure is that income will be higher in good years will be lower in bad years compared to companies compared to companies with lower proportion of with lower proportion of fixed costs. fixed costs. A low fixed cost structures generally leads to greater stability in income across good and bad © 2024years. McGraw Hill Limited 4-63  Operating Leverage 1 A measure of how sensitive net operating income is to percentage changes in sales. Degree of Contribution margin = operating leverage Operating income % change in = operating income Degree of Op. Leverage x % change in sales © 2024 McGraw Hill Limited 4-64  Operating Leverage 2 Example Company has a degree of operating leverage of 5: Actual sales 500 units Sales $250,000 Less: variable expenses 150,000 Contribution margin $100,000 Less: fixed expenses 80,000 Operating income $20,000 $100,000 = 5 $20,000 © 2024 McGraw Hill Limited 4-65  Operating Leverage 3 With a degree of operating leverage of 5, if sales increase by 10%, net operating income will increase by 50%. Percent increase in sales 10% Degree of operating leverage x 5 Percent increase in profits 50% Here’s the verification! © 2024 McGraw Hill Limited 4-66  Operating Leverage 4 Increased Actual Sales Sales (550 (500 units) units) Sales $250,000 $275,000 Less: variable expenses 150,000 165,000 Contribution margin $100,000 $110,000 Less: fixed expenses 80,000 80,000 Operating income $20,000 $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 © 2024 McGraw Hill Limited 4-67  Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. 2,100 cups of coffee are sold each month on average. What is the degree of operating leverage? a. 0.392 b. 2.545 c. 1.909 d. 0.909 © 2024 McGraw Hill Limited 4-68  Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. 2,100 cups of coffee are sold each month on average. What is the degree of operating leverage? 2,100 Unit cups Sales $4.00 $8,400 Answer: Variable expenses Contribution margin $1.00 $3.00 2,100 $6,300 c. 1.909 Fixed Expenses Operating Income $3,000 $3,300 Degree of operating leverage = $6,300 / $3,300 = $1.909 © 2024 McGraw Hill Limited 4-69  Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. 2,100 cups of coffee are sold each month on average. If sales increase by 20%, by how much should net operating income increase? a. 20.0% b. 38.2% c. 50.0% d. 0.08% © 2024 McGraw Hill Limited 4-70  Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $4.00 and the average variable expense per cup is $1.00. The average fixed expense per month is $3,000. 2,100 cups of coffee are sold each month on average. If sales increase by 20%, by how much should net operating income increase? Answer: b. 38.2% Degree of operating leverage x % change in sales 1.91 DOL x 20% increase in sales = 38.2% increase in operating income. © 2024 McGraw Hill Limited 4-71 Verify Increase in Profit 20% Actual sales Increase in sales 2,100 cups 2,520 cups Sales $ 8,400 $ 10,080 Less: Variable expenses 2,100 2,520 Contribution margin 6,300 7,560 Less: Fixed expenses 3,000 3,000 Net operating income $ 3,300 $ 4,560 % change in sales 20.0% % change in net operating income 38.2% © 2024 McGraw Hill Limited 4-72  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. Assume that Example Company sells bikes and carts and that the sales mix between the two products remains the same. © 2024 McGraw Hill Limited 4-73  Sales Mix & Break-Even Analysis 1 Example Co. information: Bicycles Carts Total $250,00 $550,00 Sales 0 100% $300,000 100% 0 100.0% Variable expenses 150,000 60% 135,000 45% 285,000 51.8% $100,00 $265,00 Contribution margin 0 40% $165,000 55% 0 48.2% Fixed expenses 170,000 Net operating income $95,000 $250,00 $550,00 Sales mix 0 45% $300,000 55% 0 100.0% $265,000 Weighted Average = 48.2% (rounded) $550,000 CM = © 2024 McGraw Hill Limited 4-74  Sales Mix & Break-Even Break- Analysis Fixed Expenses2= $170,000 = = even $352,697 sales Weighted Average CM Ratio 48.2% Bicycles Carts Total $158,71 $352,69 Sales 4 100% $193,983 100% 7 100.0% Variable expenses 95,228 60% 87,292 45% 182,521 51.8% $ $170,17 Contribution margin 63,486 40% $106,691 55% 6 48.2% Fixed expenses 170,000 Net operating Varianc $ income Rounding e 176 $250,00 $550,00 Sales mix 0 45% $300,000 55% 0 100.0% © 2024 McGraw Hill Limited 4-75  Assumptions of CVP Selling price is Analysis 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). © 2024 McGraw Hill Limited 4-76 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. © 2024 McGraw Hill Limited 4-77  End of Chapter Summary Part The CM ratio is the ratio of 2 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. © 2024 McGraw Hill Limited 4-78 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. © 2024 McGraw Hill Limited 4-79 Cost-Volume-Profit Analysis with Uncertainty Appendix 4A © 2024 McGraw Hill Limited 4-80 Cost-Volume-Profit Analysis with Uncertainty Cost-volume-profit analysis is often used to assess future possibilities under various alternatives. Management can use data for various alternatives to create a decision tree. Subjective probabilities represent what a manager believes will occur and can also be put into the decision tree to determine what the probability is of each alternative. This information can also be used to estimate the expected future profits. © 2024 McGraw Hill Limited 4-81