# Chapter 6. Chapter 6-1. Basics of Cost-Volume-Profit Analysis. Basics of Cost-Volume-Profit Analysis. Cost-Volume-Profit Relationships

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1 Chapter 6-1 Chapter 6 Cost-Volume-Profit Relationships McGraw-Hill /Irwin The McGraw-Hill Companies, Inc., 2007 Basics of Cost-Volume-Profit Analysis Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted. 6-2 Basics of Cost-Volume-Profit Analysis CM is used first to cover fixed expenses. Any remaining CM contributes to net operating income. 6-3

2 Chapter 6-2 Learning Objective LO1 To explain how changes in activity affect contribution margin and net operating income. 6-4 The Contribution Approach Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. If Racing sells an additional bicycle, \$200 additional CM will be generated to cover fixed expenses and profit. 6-5 The Contribution Approach Each month, Racing must generate at least \$80,000 in total CM to break even. 6-6

3 Chapter 6-3 The Contribution Approach If Racing sells 400 units in a month, it will be operating at the break-even point. 6-7 The Contribution Approach If Racing sells one more bike (401 bikes), net operating income will increase by \$ The Contribution Approach 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 Racing sells 430 bikes, its net income will be \$6,

4 Chapter 6-4 Learning Objective LO2 To prepare and interpret a cost-volume-profit (CVP) graph CVP Relationships in Graphic Form The relationship among revenue, cost, profit and volume can be expressed graphically by preparing a CVP graph. Racing developed contribution margin income statements at 300, 400, and 500 units sold. We will use this information to prepare the CVP graph. Income 300 units Income 400 units Income 500 units Sales \$ 150,000 \$ 200,000 \$ 250,000 Less: variable expenses 90, , ,000 Contribution margin \$ 60,000 \$ 80,000 \$ 100,000 Less: fixed expenses 80,000 80,000 80,000 Net operating income \$ (20,000) \$ - \$ 20, CVP Graph 450, , , ,000 Dollars 250, , , ,000 50,000 - In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis Units 6-12

5 Chapter 6-5 CVP Graph Dollars 450, , , , , , , ,000 50, Units Fixed Expenses 6-13 CVP Graph 450, , , ,000 Dollars 250, , ,000 Total Expenses Fixed Expenses 100,000 50, Units 6-14 CVP Graph 450,000 Dollars 400, , , , , ,000 Total Expenses Total Sales Fixed Expenses 100,000 50, Units 6-15

6 Chapter 6-6 CVP Graph Dollars 450, , , , , , , ,000 50,000 - Break-even point (400 units or \$200,000 in sales) Loss Area Units Profit Area 6-16 Learning Objective LO3 To use the contribution margin ratio (CM ratio) to compute changes in contribution margin and net operating income resulting from changes in sales volume Contribution Margin Ratio The contribution margin ratio is: CM Ratio = Total CM Total sales For Racing Bicycle Company the ratio is: \$80,000 = 40% \$200,000 Each \$1.00 increase in sales results in a total contribution margin increase of

7 Chapter 6-7 Contribution Margin Ratio Or, in terms of units, the contribution margin ratio is: Unit CM CM Ratio = Unit selling price For Racing Bicycle Company the ratio is: \$200 \$500 = 40% 6-19 Contribution Margin Ratio 400 Bikes 500 Bikes Sales \$ 200,000 \$ 250,000 Less: variable expenses 120, ,000 Contribution margin 80, ,000 Less: fixed expenses 80,000 80,000 Net operating income \$ - \$ 20,000 A \$50,000 increase in sales revenue results in a \$20,000 increase in CM. (\$50,000 40% = \$20,000) 6-20 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. On average, 2,100 cups are sold each month. What is the CM Ratio for Coffee Klatch? a b c d

8 Chapter 6-8 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. On average, 2,100 cups are sold each month. What is the CM Ratio for Coffee Klatch? a b c d Quick Check CM Ratio = Unit contribution margin Unit selling price = (\$1.49-\$0.36) \$1.49 = \$1.13 \$1.49 = LO4 Learning Objective To show the effects on contribution margin of changes in variable costs, fixed costs, selling price, and volume Changes in Fixed Costs and Sales Volume What is the profit impact if Racing can increase unit sales from 500 to 540 by increasing the monthly advertising budget by \$10,000? 6-24

9 Chapter 6-9 Changes in Fixed Costs and Sales Volume \$80,000 + \$10,000 advertising = \$90,000 Sales increased by \$20,000, but net operating income decreased by \$2, Changes in Fixed Costs and Sales Volume The Shortcut Solution Increase in CM (40 units X \$200) \$ 8,000 Increase in advertising expenses 10,000 Decrease in net operating income \$ (2,000) 6-26 Change in Variable Costs and Sales Volume What is the profit impact if Racing can use higher quality raw materials, thus, increasing variable costs per unit by \$10, to generate an increase in unit sales from 500 to 580? 6-27

10 Chapter 6-10 Change in Variable Costs and Sales Volume 580 units \$310 variable cost/unit = \$179,800 Sales increase by \$40,000, and net operating income increases by \$10, Change in Fixed Cost, Sales Price and Volume What is the profit impact if Racing (1) cuts its selling price \$20 per unit, (2) increases its advertising budget by \$15,000 per month, and (3) increases unit sales from 500 to 650 units per month? 6-29 Change in Fixed Cost, Sales Price and Volume Sales increase by \$62,000, fixed costs increase by \$15,000, and net operating income increases by \$2,

11 Chapter 6-11 Change in Variable Cost, Fixed Cost and Sales Volume What is the profit impact if Racing (1) pays a \$15 sales commission per bike sold, instead of paying salespersons flat salaries that currently total \$6,000 per month, and (2) increases unit sales from 500 to 575 bikes? 6-31 Change in Variable Cost, Fixed Cost and Sales Volume Increase in CM (75 units X \$85) \$ 6,375 Reduced fixed costs 6,000 Increase in net operating income \$ 12,375 Sales increase by \$37,500, variable costs increase by \$31,125, but fixed expenses decrease by \$6, Change in Regular Sales Price If Racing has an opportunity to sell 150 bikes to a wholesaler without disturbing sales to other customers or fixed expenses, what price would it quote to the wholesaler if it wants to increase monthly profits by \$3,000? 6-33

12 Chapter 6-12 Change in Regular Sales Price \$ 3, bikes = \$ 20 per bike Variable cost per bike = 300 per bike Selling price required = \$ 320 per bike 150 bikes \$320 per bike = \$ 48,000 Total variable costs = 45,000 Increase in net income = \$ 3, Learning Objective LO5 To compute the breakeven point in unit sales and dollar sales Break-Even Analysis Break-even analysis can be approached in two ways: 1. Equation method 2. Contribution margin method 6-36

13 Chapter 6-13 Equation Method Profits = (Sales Variable expenses) Fixed expenses OR Sales = Variable expenses + Fixed expenses + Profits At the break-even point profits equal zero 6-37 Break-Even Analysis Here is the information from Racing Bicycle Company: Total Per Per Unit Unit Percent Sales (500 (500 bikes) \$ 250,000 \$ % Less: variable expenses 150, % 60% Contribution margin \$ 100,000 \$ % 40% Less: fixed expenses 80,000 Net Net operating income \$ 20, Equation Method We calculate the break-even point as follows: Sales = Variable expenses + Fixed expenses + Profits \$500Q = \$300Q + \$80,000 + \$0 Where: Q = Number of bikes sold \$500 = Unit selling price \$300 = Unit variable expense \$80,000 = Total fixed expense 6-39

14 Chapter 6-14 Equation Method We calculate the break-even point as follows: Sales = Variable expenses + Fixed expenses + Profits \$500Q = \$300Q + \$80,000 + \$0 \$200Q = \$80,000 Q = \$80,000 \$200 per bike Q = 400 bikes 6-40 Equation Method The equation can be modified to calculate the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + \$80,000 + \$0 Where: X = Total sales dollars 0.60 = Variable expenses as a % of sales \$80,000 = Total fixed expenses 6-41 Equation Method The equation can be modified to calculate the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + \$80,000 + \$0 0.40X = \$80,000 X = \$80, X = \$200,

15 Chapter 6-15 Contribution Margin Method The contribution margin method has two key equations. Break-even point in units sold = Fixed expenses Unit contribution margin Break-even point in total sales dollars = Fixed expenses CM ratio 6-43 Contribution Margin Method Let s use the contribution margin method to calculate the break-even point in total sales dollars at Racing. Break-even point in total sales dollars = Fixed expenses CM ratio \$80,000 40% = \$200,000 break-even sales 6-44 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. On average 2,100 cups are sold each month. What is the break-even sales in units? a. 872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups 6-45

16 Chapter 6-16 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 Fixed variable expenses Break-even = expense per cup is \$0.36. The average Unit CM fixed expense per month is \$1,300. On \$1,300 average 2,100 cups are sold each month. = \$1.49/cup What is - \$0.36/cup the break-even sales in units? \$1,300 a. 872 cups = \$1.13/cup b. 3,611 cups = 1,150 cups c. 1,200 cups d. 1,150 cups 6-46 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. On average 2,100 cups are sold each month. What is the break-even sales in dollars? a. \$1,300 b. \$1,715 c. \$1,788 d. \$3, 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. On average 2,100 cups are sold each month. What is the break-even sales in dollars? a. \$1,300 b. \$1,715 c. \$1,788 d. \$3,129 Quick Check Break-even sales Fixed expenses = CM Ratio \$1,300 = = \$1,

17 Chapter 6-17 Learning Objective LO6 To determine the level of sales needed to achieve a desired target profit Target Profit Analysis The equation and contribution margin methods can be used to determine the sales volume needed to achieve a target profit. Suppose Racing Bicycle Company wants to know how many bikes must be sold to earn a profit of \$100, The CVP Equation Method Sales = Variable expenses + Fixed expenses + Profits \$500Q = \$300Q + \$80,000 + \$100,000 \$200Q = \$180,000 Q = 900 bikes 6-51

18 Chapter 6-18 The Contribution Margin Approach The contribution margin method can be used to determine that 900 bikes must be sold to earn the target profit of \$100,000. Unit sales to attain the target profit = Fixed expenses + Target profit Unit contribution margin \$80,000 + \$100,000 \$200/bike = 900 bikes 6-52 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 6-53 Quick Check Unit sales Fixed expenses + Target profit to attain = Coffee Klatch is an espresso stand Unit in a CM target profit downtown office building. The average \$1,300 selling + \$2,500 price of a cup of coffee is \$1.49 and = the \$1.49 average - \$0.36 variable expense per cup is \$0.36. The average fixed expense per month = is \$1,300. \$3,800 How many cups of \$1.13 coffee would have to be sold to attain target profits of \$2,500 per month? = 3,363 cups a. 3,363 cups b. 2,212 cups c. 1,150 cups d. 4,200 cups 6-54

19 Chapter 6-19 Learning Objective LO7 To compute the margin of safety and explain its significance The Margin of Safety The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. Margin of safety = Total sales - Break-even sales Let s look at Racing Bicycle Company and determine the margin of safety The Margin of Safety If we assume that Racing Bicycle Company has actual sales of \$250,000, given that we have already determined the break-even sales to be \$200,000, the margin of safety is \$50,000 as shown Break-even sales 400 units Actual sales 500 units Sales \$ 200,000 \$ 250,000 Less: variable expenses 120, ,000 Contribution margin 80, ,000 Less: fixed expenses 80,000 80,000 Net operating income \$ - \$ 20,

20 Chapter 6-20 The Margin of Safety The margin of safety can be expressed as 20% of sales. (\$50,000 \$250,000) Break-even sales 400 units Actual sales 500 units Sales \$ 200,000 \$ 250,000 Less: variable expenses 120, ,000 Contribution margin 80, ,000 Less: fixed expenses 80,000 80,000 Net operating income \$ - \$ 20, The Margin of Safety The margin of safety can be expressed in terms of the number of units sold. The margin of safety at Racing is \$50,000, and each bike sells for \$500. Margin of Safety in units = \$50,000 \$500 = 100 bikes 6-59 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. On average 2,100 cups are sold each month. What is the margin of safety? a. 3,250 cups b. 950 cups c. 1,150 cups d. 2,100 cups 6-60

21 Chapter 6-21 Quick Check Coffee Klatch is an espresso stand in a downtown Margin office safety building. = Total The sales average Break-even selling sales price of a cup of coffee = 2,100 is \$1.49 cups and 1,150 the cups average variable expense = 950 cups per cup is \$0.36. The average fixed expense or per month is \$1,300. Margin On average of safety 2, cups cups are sold each = month. What is the margin 2,100 of safety? cups = 45% percentage a. 3,250 cups b. 950 cups c. 1,150 cups d. 2,100 cups 6-61 Cost Structure and Profit Stability 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 Cost Structure and Profit Stability 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. 6-63

22 Chapter 6-22 Learning Objective LO8 To compute the degree of operating leverage at a particular level of sales and explain how it can be used to predict changes in net operating income Operating Leverage A measure of how sensitive net operating income is to percentage changes in sales. Degree of operating leverage = Contribution margin Net operating income 6-65 Operating Leverage At Racing, the degree of operating leverage is 5. Actual sales 500 Bikes Sales \$ 250,000 Less: variable expenses 150,000 Contribution margin 100,000 Less: fixed expenses 80,000 Net income \$ 20,000 \$100,000 \$20,000 =

23 Chapter 6-23 Operating Leverage With an operating leverage of 5, if Racing increases its sales by 10%, net operating income would increase by 50%. Percent increase in sales 10% Degree of operating leverage 5 Percent increase in profits 50% Here s the verification! 6-67 Operating Leverage Actual sales (500) Increased sales (550) Sales \$ 250,000 \$ 275,000 Less variable expenses 150, ,000 Contribution margin 100, ,000 Less fixed expenses 80,000 80,000 Net operating income \$ 20,000 \$ 30,000 10% increase in sales from \$250,000 to \$275, results in a 50% increase in income from \$20,000 to \$30, 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. On average 2,100 cups are sold each month on. What is the operating leverage? a b c d

24 Chapter 6-24 Quick Check 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 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. On average2,100 cups are sold each \$ month. What is the operating leverage? a Operating Contribution margin b leverage = Net operating income c \$2,373 d = \$1,073 = 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, and the average fixed expense per month is \$1,300. On average 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% 6-71 At Coffee Klatch the average selling price of a cup of coffee is \$1.49, the average variable expense per cup is \$0.36, and the average fixed expense per month is \$1,300. On average 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% Quick Check Percent increase in sales 20.0% Degree of operating leverage 2.21 Percent increase in profit 44.20% 6-72

25 Chapter 6-25 Verify Increase in Profit Actual sales Increased sales 2,100 cups 2,520 cups Sales \$ 3,129 \$ 3,755 Less: Variable expenses Contribution margin 2,373 2,848 Less: Fixed expenses 1,300 1,300 Net operating income \$ 1,073 \$ 1,548 % change in sales 20.0% % change in net operating income 44.2% 6-73 Structuring Sales Commissions Companies generally compensate salespeople by paying them either a commission based on sales or a salary plus a sales commission. Commissions based on sales dollars can lead to lower profits in a company. Let s look at an example Structuring Sales Commissions Pipeline Unlimited produces two types of surfboards, the XR7 and the Turbo. The XR7 sells for \$100 and generates a contribution margin per unit of \$25. The Turbo sells for \$150 and earns a contribution margin per unit of \$18. The sales force at Pipeline Unlimited is compensated based on sales commissions. 6-75

26 Chapter 6-26 Structuring Sales Commissions If you were on the sales force at Pipeline, you would push hard to sell the Turbo even though the XR7 earns a higher contribution margin per unit. To eliminate this type of conflict, commissions can be based on contribution margin rather than on selling price alone LO9 Learning Objective To compute the break-even point for a multiproduct company and explain the effects of shifts in the sales mix on contribution margin and the break-even point The Concept of 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 Racing Bicycle Company sells bikes and carts and that the sales mix between the two products remains the same. 6-78

27 Chapter 6-27 Multi-product break-even analysis Racing Bicycle Co. provides the following information: \$265,000 \$550,000 = 48.2% (rounded) 6-79 Multi-product break-even analysis Break-even sales Fixed expenses = CM Ratio \$170,000 = 48.2% = \$352, Key Assumptions of CVP Analysis Selling price is constant. Costs are linear. In multi-product companies, the sales mix is constant. In manufacturing companies, inventories do not change (units produced = units sold). 6-81

28 Chapter 6-28 End of Chapter

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