CHAPTER 2 Analyzing CostVolume Profit Relationships Learning Objective

CHAPTER 2 Analyzing Cost-Volume. Profit Relationships

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

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

CVP Key Variables ä ä ä ä Revenues – Price x Quantity Fixed costs – Independent of volume Variable costs – Dependent upon volume Volume – Level of activity Product mix – Different products Efficiency & quality of production Combinations 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. Total Cost Units Produced Unit Cost: Constant Total Cost: Varies

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

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

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

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

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 Regression Line Volume of Activity

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

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.

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

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

High-Low Method 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). Cost Rise Run Volume of Activity = 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.

Contribution Margin Approach Contribution margin is the portion of sales revenue available to cover fixed costs and provide a profit. – = Sales revenue Variable costs Contribution margin Fixed costs 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? Sales revenue Less variable costs Contribution margin Total $1, 000 400, 000 $ 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? y What is the contribution margin per unit? Sales revenue Less variable costs Contribution margin Total $1, 000 400, 000 $ 600, 000 Per Unit $2, 000 800 $1, 200

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? Sales revenue Less variable costs Contribution margin Total $1, 000 400, 000 $ 600, 000 Per Unit $2, 000 800 $1, 200 Ratio 100% 40% 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? Sales revenue Less variable costs Contribution margin Less fixed costs Profit Total $1, 000 400, 000 $ 600, 000 350, 000 $ 250, 000 Per Unit $2, 000 800 $1, 200 Ratio 100% 40% 60%

The Break-Even Point Sales price x units Variable cost x units Independent of units Target Income 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? $2, 000(x) - $800(x) - $350, 000 = 0 1, 200(x) = 350, 000 x = 292 computers

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

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 X X X = Revenue - variable - fixed = $1, 700(500) - $325, 000 = $850, 000 - $325, 000 = $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 Revenue & Cost Break-Even Point $584, 000 Revenue Line Total Cost Line Fixed Costs ($350, 000) 292 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 Total Mixed Costs Fixed Costs (Y-intercept) y Another method (besides visual-fit and high-low) for separating total mixed costs into variable and fixed portions. y More precise than visualfit or high-low methods. Variable Cost Rate (Slope) Activity Level y Regression calculations are generally done on a calculator or computer.

Least Squares Method For Example: Month Jan. Feb. Mar. April May Computers Produced 500 800 650 1, 000 450 Total Cost $ 750, 000 900, 000 600, 000 1, 100, 000 420, 000 Using least squares regression output: a = Y-intercept b = slope = total fixed costs = variable cost rate = $49, 211. 82 = $ 1, 036. 45

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

Sales Mix Can Openers Amount % Sales revenue $5, 000 100% Less variable costs 3, 000 60% Contribution margin $2, 000 40% Sales mix Microwaves Amount % $25, 000 100% 20, 000 80% $ 5, 000 20% 17% Product Revenue Total Revenue 83% = 5, 000 30, 000 Total Amount % $30, 000 100% 23, 000 77% $ 7, 000 23% 100% = 17%

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 Amount % Sales revenue $5, 000 100% Less variable costs 3, 000 60% Contribution margin $2, 000 40% Sales mix 17% Microwaves Amount % $25, 000 100% 20, 000 80% $ 5, 000 20% 83% Total Amount % $30, 000 23, 000 $ 7, 000 100% 77% 23% 100%

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

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

Operating Leverage For example: Assume the following data. Total Per Unit Sales revenue $1, 000 $2, 000 Less variable costs 400, 000 800 Contribution margin $ 600, 000 $1, 200 Less fixed costs 450, 000 Net income $ 150, 000 3 What is the operating leverage? 3 What happens to net income if sales are increased by 20 percent? Ratio 100% 40% 60% Operating leverage = 2. 4 Net income increases 48% 3 Increase fixed costs to $450, 000. What is the operating leverage (no Operating leverage = 4 sales increase)? 3 Now what happens to net income if Net income increases 80% sales are increased by 20 percent?