CHAPTER 5 COST - VOLUME - PROFIT Managerial Accounting, Fourth Edition Study Objectives Distinguish between variable and fixed costs. Explain the significance of the relevant range. Explain the concept of mixed costs. List the five components of cost-volume-profit analysis. Indicate what contribution margin is and how it can be expressed. Study Objectives Identify the three ways to determine the break-even point. Give the formulas for determining sales required to earn target net income. Define margin of safety, and give the formulas for computing it. Preview of Chapter To manage any business, you must understand: How costs respond to changes in sales volume and The effect of costs and revenues on profit To understand cost-volume-profit (CVP), you must know how costs behave Cost-Volume-Profit Cost Behavior Analysis Cost-Volume-Profit Analysis Variable costs Fixed costs Relevant range Mixed costs Identifying variable and fixed costs Basic components CVP income statement Break-even analysis Target net income Margin of safety Cost Behavior Analysis Cost Behavior Analysis is the study of how specific costs respond to changes in the level of business activity. Some costs change; others remain the same A knowledge of cost behavior helps management plan operations and decide between alternative courses of action Cost behavior analysis applies to all types of entities LO 1: Distinguish between variable and fixed costs. Cost Behavior Analysis - Continued Starting point in cost behavior analysis is measuring key business activities Activity levels may be expressed in terms of: Sales dollars (in a retail company) Miles driven (in a trucking company) Room occupancy (in a hotel) Dance classes taught (by a dance studio) Many companies use more than one measurement base LO 1: Distinguish between variable and fixed costs. Cost Behavior Analysis - Continued For an activity level to be useful: Changes in the level or volume of activity should be correlated with changes in costs The activity level selected is called the activity or volume index The activity index: Identifies the activity that causes changes in the behavior of costs Allows costs to be classified according to their response to changes in activity as either: Variable Costs Fixed Costs Mixed Costs LO 1: Distinguish between variable and fixed costs. Variable Costs Variable costs are costs that vary in total directly and proportionately with changes in the activity level Example: If the activity level increases 10 percent, total variable costs will increase 10 percent Example: If the activity level decreases by 25 percent, total variable costs will decrease by 25 percent Variable costs remain the same per unit at every level of activity. LO 1: Distinguish between variable and fixed costs. Variable Costs – Example Damon Company manufactures radios that contain a $10 digital clock The activity index is the number of radios produced For each radio produced, the total cost of the clocks increases by $10: If 2,000 radios are produced, the total cost of the clocks is $20,000 (2,000 X $10) If 10,000 radios are produced, the total cost of the clocks is $100,000 (10,000 X $10) LO 1: Distinguish between variable and fixed costs. Variable Costs – Graphs LO 1: Distinguish between variable and fixed costs. Fixed Costs Fixed costs are costs that remain the same in total regardless of changes in the activity level. Fixed costs per unit cost vary inversely with activity: As volume increases, unit cost declines, and vice versa Examples include: Depreciation on buildings and equipment Property taxes Insurance Rent LO 1: Distinguish between variable and fixed costs. Fixed Costs - Example Damon Company leases its productive facilities at a cost of $10,000 per month Total fixed costs of the facilities remain constant at every level of activity - $10,000 per month Fixed costs on a per unit basis vary inversely with activity - as activity increases, unit cost declines and vice versa. At 2,000 radios, the unit cost is $5 ($10,000 ÷ 2,000 units) At 10,000 radios, the unit cost is $1 ($10,000 ÷ 10,000 units) LO 1: Distinguish between variable and fixed costs. Fixed Costs - Graphs LO 1: Distinguish between variable and fixed costs. Let’s Review Variable costs are costs that: a. Vary in total directly and proportionately with changes in the activity level. b. Remain the same per unit at every activity level. c. Neither of the above. d. Both (a) and (b) above. LO 1: Distinguish between variable and fixed costs. Relevant Range Throughout the range of possible levels of activity, a straight-line relationship usually does not exist for either variable costs or fixed costs The relationship between variable costs and changes in activity level is often curvilinear For fixed costs, the relationship is also nonlinear – some fixed costs will not change over the entire range of activities while other fixed costs may change LO 2: Explain the significance of the relevant range. Relevant Range - Graphs LO 2: Explain the significance of the relevant range. Relevant Range Defined as the range of activity over which a company expects to operate during a year Within this range, a straight-line relationship usually exists for both variable and fixed costs LO 2: Explain the significance of the relevant range. Let’s Review The relevant range is: a. The range of activity in which variable costs will be curvilinear. b. The range of activity in which fixed costs will be curvilinear. c. The range over which the company expects to operate during a year. d. Usually from zero to 100% of operating capacity. LO 2: Explain the significance of the relevant range. Mixed Costs Costs that have both a variable cost element and a fixed cost element Sometimes called semivariable cost Change in total but not proportionately with changes in activity level LO 3: Explain the concept of mixed costs. Mixed Costs: High–Low Method For purposes of CVP analysis, mixed costs must be classified into their fixed and variable elements One approach to separate the costs is called the high-low method Uses the total costs incurred at the high and low levels of activity to classify mixed costs into fixed and variable components The difference in costs between the high and low levels represents variable costs, since only variable costs change as activity levels change LO 3: Explain the concept of mixed costs. Mixed Costs: Steps in High–Low-Method STEP 1: Determine variable cost per unit using the following formula: STEP 2: Determine the fixed cost by subtracting the total variable cost at either the high or the low activity level from the total cost at that level LO 3: Explain the concept of mixed costs. Mixed Costs: High–Low Method Example High Level of Activity: April $63,000 50,000 miles Low Level of Activity: January 30,000 20,000 miles Difference $33,000 30,000 miles Step 1: Using the formula, variable costs per unit are $33,000 30,000 = $1.10 variable cost per mile Data for Metro Transit Company for 4 month period: LO 3: Explain the concept of mixed costs. Mixed Costs: High–Low-Method Example Step 2: Determine the fixed costs by subtracting total variable costs at either the high or low activity level from the total cost at that same level LO 3: Explain the concept of mixed costs. Mixed Costs: High–Low-Method Example Maintenance costs: $8,000 per month plus $1.10 per mile To determine maintenance costs at a particular activity level: 1. multiply the activity level times the variable cost per unit 2. then add that total to the fixed cost EXAMPLE: If the activity level is 45,000 miles, the estimated maintenance costs would be $8,000 fixed costs and $49,500 variable ($1.10 X 45,000 miles) for a total of $57,500. LO 3: Explain the concept of mixed costs. Let’s Review Mixed costs consist of a: a. Variable cost element and a fixed cost element. b. Fixed cost element and a controllable cost element. c. Relevant cost element and a controllable cost element. d. Variable cost element and a relevant cost element. LO 3: Explain the concept of mixed costs. Cost-Volume-Profit Analysis CVP Analysis - the study of the effects of changes in costs and volume on a company’s profits Important in profit planning A critical factor in setting selling prices, determining product mix, and maximizing use of production facilities LO 4: List the five components of cost-volume-profit analysis. Cost-Volume-Profit Analysis CVP analysis considers the interrelationships among five basic components: LO 4: List the five components of cost-volume-profit analysis. Assumptions Underlying CVP Analysis Behavior of both costs and revenues is linear throughout the relevant range of the activity index Costs can be classified accurately as either variable or fixed Changes in activity are the only factors that affect costs All units produced are sold When more than one type of product is sold, the sales mix will remain constant LO 4: List the five components of cost-volume-profit analysis. Let’s Review One of the following is NOT involved in CVP analysis. That factor is: a. Sales mix. b. Unit selling prices. c. Fixed costs per unit. d. Volume or level of activity. LO 4: List the five components of cost-volume-profit analysis. CVP Income Statement Classifies costs and expenses as fixed or variable Reports contribution margin in the body of the statement. Contribution margin – amount of revenue remaining after deducting all variable costs Reports the same net income as a traditional income statement A statement for internal use only LO 5: Indicate what contribution margin is and how it can be expressed. CVP Income Statement - Example Vargo Video Company produces a DVD player/recorder. Relevant data for June 2008: LO 5: Indicate what contribution margin is and how it can be expressed. Contribution Margin Per Unit Contribution margin is the amount available to cover fixed costs and to contribute to income The formula for contribution margin per unit and the computation of the contribution margin per unit for Vargo Video are: Thus, for every DVD player sold, Vargo Company has $200 to cover fixed costs and contribute to net income LO 5: Indicate what contribution margin is and how it can be expressed. CVP Income Statement – Contribution Margin Effect Since Vargo Company has fixed costs of $200,000, it must sell 1,000 DVD players ($200,000 ÷ $200) before it can earn any net income Vargo’s CVP income statement, assuming a zero net income is: LO 5: Indicate what contribution margin is and how it can be expressed. CVP Income Statement – Contribution Margin Effect For every DVD player that Vargo sells above 1,000 units, net income increases by the amount of the contribution margin, $200 Vargo’s CVP income statement, assuming 1001 units sold is: LO 5: Indicate what contribution margin is and how it can be expressed. Contribution Margin Ratio Shows the percentage of each sales dollar available to apply toward fixed costs and profits The contribution margin ratio is the contribution margin per unit divided by the unit selling price. For Vargo Company, the computation is: In this case, the contribution margin ratio of 40% means that $ .40 of each sales dollar is available to apply to fixed costs and contribute to net income LO 5: Indicate what contribution margin is and how it can be expressed. Contribution Margin Ratio As shown below, the contribution margin ratio helps to determine the effect of changes in sales on net income LO 5: Indicate what contribution margin is and how it can be expressed. Let’s Review Contribution margin: a. Is revenue remaining after deducting variable costs. b. May be expressed as contribution margin per unit. c. Is selling price less cost of goods sold. d. Both (a) and (b) above. LO 5: Indicate what contribution margin is and how it can be expressed. Break-Even Analysis A key relationship in CVP analysis is the level of activity at which total revenue equals total costs (both fixed and variable) This level of activity is called the break-even point At this volume of sales, the company will realize no income, but will also suffer no loss Can be computed or derived: from a mathematical equation, by using contribution margin, or from a cost-volume profit (CVP) graph The break-even point can be expressed either in sales units or in sales dollars LO 6: Identify the three ways to determine the break-even point. Break-Even Analysis: Mathematical Equation Break-even occurs where total sales equal variable costs plus fixed costs; i.e., net income is zero. The formula for the break-even point in units and the computation for Vargo Video are: To find sales dollars required to break-even: 1,000 units X $500 = $500,000 (break-even sales dollars) LO 6: Identify the three ways to determine the break-even point. Break-Even Analysis: Contribution Margin Technique At the break-even point, contribution margin must equal total fixed costs (Contribution Margin = total revenues – variable costs) The break-even point (BEP) can be computed using either contribution margin per unit or contribution margin ratio. LO 6: Identify the three ways to determine the break-even point. Contribution Margin Technique When the contribution margin per unit is used, the formula to compute the BEP in units for Vargo Video is: When the BEP in dollars is desired, contribution margin ratio is used in the following formula for Vargo Video: LO 6: Identify the three ways to determine the break-even point. Break-Even Analysis: Graphic Presentation A cost-volume profit (CVP) graph shows the relationships between costs, volume and profits. To construct a CVP graph: Plot the total-sales line starting at the zero activity level Plot the total fixed cost using a horizontal line Plot the total-cost line (starts at the fixed-cost line at zero activity) Determine the break-even point from the intersection of the total-cost line and the total-sales line LO 6: Identify the three ways to determine the break-even point. Break-Even Analysis: Graphic Presentation LO 6: Identify the three ways to determine the break-even point. Let’s Review Gossen Company is planning to sell 200,000 pliers for $4 per unit. The contribution margin ratio is 25%. If Gossen will break even at this level of sales, what are the fixed costs? a. $100,000. b. $160,000. c. $200,000. d. $300,000. LO 6: Identify the three ways to determine the break-even point. Break-Even Analysis: Target Net Income Rather than just breaking even, management usually sets an income objective called “target net income” Indicates sales or units necessary to achieve this specified level of income Can be determined from each of the approaches used to determine break-even sales/units: from a mathematical equation, by using contribution margin, or from a cost-volume profit (CVP) graph Expressed either in sales units or in sales dollars LO 7: Give the formulas for determining sales required to earn target net income. Break-Even Analysis: Target Net Income Mathematical Equation Using the basic formula for the break-even point, simply include the desired net income as a factor. The computation for Vargo Video is as follows: LO 7: Give the formulas for determining sales required to earn target net income. Break-Even Analysis: Target Net Income Contribution Margin Technique To determine the required sales in units for Vargo Video: To determine the required sales in dollars for Vargo Video: LO 7: Give the formulas for determining sales required to earn target net income. Let’s Review The mathematical equation for computing required sales to obtain target net income is: Required sales = ? a. Variable costs + Target net income. b. Variable costs + Fixed costs + Target net income. c. Fixed costs + Target net income. d. No correct answer is given. LO 7: Give the formulas for determining sales required to earn target net income. Break-Even Analysis: Margin of Safety Difference between actual or expected sales and sales at the break-even point Measures the “cushion” that management has, allowing it to break-even even if expected sales fail to materialize May be expressed in dollars or as a ratio To determine the margin of safety in dollars for Vargo Video assuming that actual/expected sales are $750,000: LO 8: Define margin of safety, and give the formulas for computing it. Break-Even Analysis: Margin of Safety Margin of Safety Ratio Computed by dividing the margin of safety in dollars by the actual or expected sales To determine the margin of safety ratio for Vargo Video assuming that actual/expected sales are $750,000: The higher the dollars or the percentage, the greater the margin of safety LO 8: Define margin of safety, and give the formulas for computing it. Let’s Review Marshall Company had actual sales of $600,000 when break-even sales were $420,000. What is the margin of safety ratio? a. 25%. b. 30%. c. 33 1/3%. d. 45%. LO 8: Define margin of safety, and give the formulas for computing it. All About You A Hybrid Dilemma Hybrid vehicles typically cost $3,000 to $5,000 more than conventional vehicles The most fuel efficient hybrids can save about $660 per year in fuel costs Each gallon of gas not burned reduces carbon dioxide emissions by 19 pounds All About You A Hybrid Dilemma What do you think? Do you think that making the investment in a hybrid car will slow the cash outflow from your wallet due to high gas prices and save your feet? Because of the premium charged for hybrid cars, would you ever break-even on your investment? Chapter Review - Brief Exercise 5-4 Deines Company accumulates the following data concerning a mixed cost, using miles as the activity level. Miles Total Miles Total Driven Cost Driven Cost January 8,000 $14,150 March 8,500 $15,000 February 7,500 $13,600 April 8,200 $14,490 Compute the variable and fixed cost elements using the high-low method. Chapter Review - Brief Exercise 5-4 High Level of Activity: March $15,000 8,500 miles Low Level of Activity: February 13,600 7,500 miles Difference $ 1,400 1,000 miles Step 1: Variable Cost per Unit = $1,400 ÷ 1,000 miles = $1.40 variable cost per mile Step 2: High Low Total Cost: $15,000 $13,600 Variable Cost: 8,500 X $1.40 11,900 7,500 X $1.40 10,500 Total Fixed Costs $ 3,100 $ 3,100 Copyright Copyright © 2008 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express written permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. 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