C H A P T E R 2 Analyzing Cost-Volume- Profit Relationships Analyzing Cost-Volume- Profit Relationships

Learning Objective 1 Understand the key factors involved in cost-volume- profit (C-V-P) analysis and why it is such an important tool in management decision making.

CVP - What Questions Does It Answer? 3What happens to profits if we change our selling price? 3What happens to profits if we change the number of units sold? 3How many units do we need to sell to break even? 3How much sales revenue do we need to meet our pretax profit goal? 3What happens to profits if we change our advertising expenses? 3What happens to profits if we discontinue certain products?

CVP Key Variables äRevenues–Price x Quantity äFixed costs– Independent of volume äVariable costs– Dependent upon volume äVolume– Level of activity äProduct mix– Different products äEfficiency & quality of production äCombinations of above

Learning Objective 2 Explain and analyze the basic cost behavior patterns—variable, fixed, mixed, and stepped.

What are Variable Costs? Costs that change in total in direct proportion to changes in activity level. Units Produced Unit Cost: Constant Total Cost: Varies Total Cost

Define Relevant Range and Curvilinear Costs Relevant range: The range of operating level, or volume of activity, over which the relationship between total costs (variable + fixed) and activity level is approximately linear. Curvilinear costs: Variable costs that do not vary in direct proportion to changes in activity level but vary at decreasing or increasing rates due to economies of scale, productivity changes, and so on.

Define Fixed Costs Costs that remain constant in total, regardless of activity level, at least over a certain range of activity. Unit Cost: Varies Total Cost: Constant Total Cost Units Produced

Fixed Costs are Used to Calculate Break-Even l What does break-even mean? l Break-even is the point where revenues equal all costs, neither profit nor loss is incurred. l What is the formula for break-even? Total fixed costs (Sales price per unit - Variable cost per unit)

Define Stepped Costs Production Volume Cost Stepped costs change in total in a stair- step fashion (in large amounts) with changes in volume of activity. Over the relevant range, stepped costs may appear to be fixed. Relevant Range

Define Mixed Costs Mixed costs contain both variable and fixed cost components. Production Volume Cost Variable Fixed For Example: A leased machine might cost $1,000 per month (fixed) plus $20 per hour of usage (variable).

Learning Objective 3 Analyze mixed costs using the scattergraph and high-low methods.

What is the Scattergraph (Visual-Fit) Method? A method of segregating the fixed and variable components of a mixed cost by plotting on a graph total costs at several activity levels and drawing a regression line through the points. Cost Volume of Activity Regression Line

Variable costs per unit are equal to the slope of the regression line. Variable Costs Scattergraph (Visual-Fit) Cost Volume of Activity Fixed costs are represented by the intersection of the regression line and the vertical axis. Fixed Costs

Define the High-Low Method A method of segregating the fixed and variable components of a mixed cost by analyzing the costs at the highest and lowest activity levels within a relevant range.

Cost Volume of Activity Step 1: Identify the highest and lowest activity levels. High-Low Method

Cost Volume of Activity High-Low Method Step 2: Determine the differences between the high and low points.

Step 3: Calculate the variable cost per unit by finding the slope of the regression line between the two points (which reflect total mixed costs). High-Low Method Cost Volume of Activity Rise Run Variable Cost per Unit =

Learning Objective 4 Perform C-V-P analyses, and describe the effects potential changes in C-V-P variables have on company profitability.

Sales revenue –Variable costs =Contribution margin –Fixed costs =Profit Contribution Margin Approach Contribution margin is the portion of sales revenue available to cover fixed costs and provide a profit.

Contribution Margin Approach If a computer sells for $2,000 with variable costs of $800 per computer and fixed costs of $350,000 per year: y What is the total contribution margin on 500 computers? Total Sales revenue$1,000,000 Less variable costs 400,000 Contribution margin$ 600,000

Contribution Margin Approach If a computer sells for $2,000 with variable costs of $800 per computer and fixed costs of $350,000 per year: y What is the total contribution margin on 500 computers? Total Per Unit Sales revenue $1,000,000 $2,000 Less variable costs 400, Contribution margin$ 600,000 $1,200 y What is the contribution margin per unit?

Contribution Margin Approach If a computer sells for $2,000 with variable costs of $800 per computer and fixed costs of $350,000 per year: u What is the total contribution margin on 500 computers? u What is the contribution margin per unit? u What is the contribution margin ratio? Total Per UnitRatio Sales revenue$1,000,000$2, % Less variable costs 400, % Contribution margin$ 600,000$1,200 60%

Contribution Margin Approach If a computer sells for $2,000 with $800 variable costs per computer and $350,000 fixed costs per year: y What is the total contribution margin on 500 computers? y What is the contribution margin per unit? y What is the contribution margin ratio? y What is the total dollar profit after one year? Total Per UnitRatio Sales revenue$1,000,000$2, % Less variable costs 400, % Contribution margin$ 600,000$1,200 60% Less fixed costs 350,000 Profit$ 250,000

The Break-Even Point Example: How many computers will the store have to sell in order to break even if one computer sells for $2,000, costs $800 to make (variable cost), and fixed costs are $350,000? Sales price x units Variable cost x units Independent of units Target Income $2,000(x) - $800(x) - $350,000 = 0 1,200(x) - $350,000 = 0 1,200(x) = 350,000 x = 292 computers

Sales price x units Variable cost x units Costs independent of units Zero for break-even OR OR etc. Multiple Variable Changes

Assume prior year profits of $250,000 for The Store. What if this year the price of our $2,000 computers is reduced by 15 percent due to a decrease in variable costs from $800 to $700 per computer and a decrease in fixed costs from $350,000 to $325,000? What would be the effect on target income (or profit) assuming the production of 500 computers? Target Income= Revenue - variable - fixed X = $1,700(500) - $700(500) - $325,000 X = $850,000 - $350,000 - $325,000 X = $175,000 or a 30% decrease in profit

Learning Objective 5 Visualize C-V-P relationships using graphs.

The Graphic Approach Identify the Break-Even Point, Revenue Line, Total Cost Line, and Fixed Costs Total Cost Line Revenue LineBreak-Even Point Fixed Costs ($350,000) 292 $584,000 Revenue & Cost Number of Computers Sold

Learning Objective 6 Identify the limiting assumptions of C-V-P analysis, and explain the issues of quality and time relative to C-V-P analysis decisions.

What are the Limiting Assumptions of C-V-P Analysis? 1. The behavior of revenues and costs is linear throughout the relevant range. 2. All costs can be categorized as either fixed or variable. 3. Sales mix does not change.

How Do Quality & Time Affect C-V-P Decisions? Change in Quality: - Will it increase cost? - Will it decrease production speed? Change in Production Time: - Will it increase cost? - Will it decrease production speed? If a change in quality or production time either increases cost or decreases production speed, careful consideration should be given to the change.

Expanded Material Learning Objective 7 Analyze mixed costs using the least squares method.

Identify the Parts of the Least Squares Method Equation yAnother method (besides visual-fit and high-low) for separating total mixed costs into variable and fixed portions. yMore precise than visual- fit or high-low methods. yRegression calculations are generally done on a calculator or computer. Total Mixed Costs Fixed Costs (Y-intercept) Variable Cost Rate (Slope) Activity Level

Least Squares Method For Example: Month Computers Produced Total Cost Jan.500 $ 750,000 Feb ,000 Mar ,000 April 1,000 1,100,000 May450420,000 Using least squares regression output: a = Y-intercept= total fixed costs= $49, b = slope= variable cost rate= $ 1, Using least squares regression output: a = Y-intercept= total fixed costs= $49, b = slope= variable cost rate= $ 1,036.45

Expanded Material Learning Objective 8 Explain the effects of sales mix on profitability.

Sales Mix Sales revenue $5,000100%$25,000100% $30,000100% Less variable costs 3,000 60% 20,000 80% 23,000 77% Contribution margin $2,00040%$ 5,00020% $ 7,00023% Sales mix 17% 83% 100% Product Revenue Total Revenue = 5,000 30,000 = 17% Can Openers Microwaves Total Amount % Amount % Amount %

Sales Mix To maximize profit in a company with multiple products, management should emphasize products with the highest contribution margin ratio. Which product should they choose? Can Openers Microwaves Total Amount % Amount % Amount % Sales revenue $5,000100%$25,000100%$30,000100% Less variable costs 3,000 60% 20,000 80% 23,000 77% Contribution margin $2,00040%$ 5,00020%$ 7,00023% Sales mix 17% 83% 100%

Expanded Material Learning Objective 9 Describe how fixed and variable costs differ in manufacturing, service, merchandising, and e- commerce organizations, and illustrate these differences with the operating leverage concept.

Define Operating Leverage lThe extent to which fixed costs are part of a company’s cost structure. lThe higher the proportion of fixed costs to variable costs, the faster income increases or decreases with sales volume. Operating Leverage Contribution Margin Net Income

3 Now what happens to net income if sales are increased by 20 percent? Net income increases 80% Operating Leverage For example: Assume the following data. Total Per UnitRatio Sales revenue$1,000,000$2,000100% Less variable costs 400, % Contribution margin$ 600,000$1,20060% Less fixed costs 450,000 Net income$ 150,000 3What is the operating leverage? 3 What happens to net income if sales are increased by 20 percent? 3Increase fixed costs to $450,000. What is the operating leverage (no sales increase)? Operating leverage = 2.4 Net income increases 48% Operating leverage = 4