Chapter 3: Cost-Volume-Profit Analysis (CVP) Identify how changes in volume affect costs: Cost Behavior How costs change in response to changes in a cost driver. Cost driver: any factor whose change makes a difference in a related total cost. In other words, an activity base that can be traced directly to units produced and that serves as a causal factor in the incurrence of overhead costs. Serves as an activity base in an overhead application rate. Volume (units or dollars): most prominent cost driver in cost-volume-profit (CVP) analysis. Managers need to know how a business s costs are affected by changes in its volume of activity. There are three types of costs: 1- change directly in proportion to changes in volume. 2- : remain constant (fixed) for a given time period despite fluctuations in volume. Or costs and expenses that remain unchanged despite changes in the level of the activity base. 3- Mixed costs: Costs that contain both fixed and variable components. Analysis of Mixed Costs: There are many methods of analyzing the mixed costs (semi variable or semi fixed) that include: 1- The Scattergraph method. 2- The High-Low Method. 3- The Regression Method. Using CVP analysis to compute breakeven point Breakeven Point Sales level at which operating income is zero. Sales above breakeven result in a profit. Sales below breakeven result in a loss. CVP Assumptions: CVP analysis assumes that: 1- Expenses can be classified as either variable or fixed. In other words, total costs can be divided into a fixed component and a component that is variable with respect to the level of output. 2- The only factor that affects costs is change in volume. In other words, changes in the level of revenues and costs arise only because of changes in the number of product (or service) units produced and sold. don t change. 3- When graphed, the behavior of total revenues and total costs is linear (straight-line) in relation to output units within the relevant range. 4- The unit selling price, unit variable costs, and fixed costs are known and constant. 5- The analysis either covers a single product or assumes that the sales mix, when multiple products are sold, will remain constant as the level of total units sold changes. 6- All revenues and costs can be added and compared without taking into account the time value of money.
There are several ways to figure the breakeven point, including the: 1- Income statement approach. 2- Contribution approach. 1- The Income Statement Approach: Start by expressing income in equation form: Sales revenue Total costs Operating income Variable cost Fixed cost This income statement classifies expenses according to behavior. Contribution margin is the excess of sales revenue over variable costs that contributes to covering fixed costs and then to providing operating income. To compute breakeven point set the equation equal to zero. 2- Contribution Margin Approach: Contribution margin is sales revenue minus variable costs. It may be expressed as total contribution, contribution per unit or as a percentage of sales. Contribution margin is computed as the difference between total revenues and total variable costs. Contribution margin per unit is the difference between selling price and variable cost per unit. Contribution-margin percentage is the contribution margin per unit divided by selling price. It is called the Contribution margin because the excess of sales revenue over variable costs contributes to covering fixed costs and then providing operating income. We can refer to contribution margin on a total basis or on a per-unit basis, as follows: - Total contribution margin Total sales revenue Total variable costs - Total contribution margin per-unit Total revenue per unit Variable cost per unit The contribution margin statement shows costs by cost behavior variable costs and fixed costs and highlights the contribution margin. The format shows: Sales X - Variable Costs X Contribution Margin X - Fixed Costs X Operating Income X 2
Breakeven Point: Is the sales level at which operating income is zero. At the breakeven point, sales minus variable expenses equals fixed expenses. Total revenues Total costs. Breakeven can be computed by using either the equation method, the contribution margin method, or the graph method. With the equation approach, breakeven sales in units is calculated as follows: Sales revenue Variable cost Operating income. (Unit sales price Units sold) (Variable unit cost Units sold) Operating income. The breakeven is determined by simply dividing the total fixed costs by the contribution margin per unit: Breakeven units sold Using the Contribution Margin ratio to Compute the Breakeven Point in Sales Dollars: Contribution Margin Ratio Contribution margin Sales revenue --- %. Breakeven Sales in Dollars Contribution margin ratio Using CVP to Plan Profits: Target Sales in Dollars Target Sales in units + Operating income Target profit Contribution margin ratio + Target profit An increase in the income tax rate does not affect the breakeven point. Operating income at the breakeven point is zero, and thus no income taxes will be paid at this point. Contribution Margin versus Gross Margin Contribution income statement emphasizes contribution margin. Revenues Variable cost of goods sold Variable operating costs Contribution margin. Contribution margin Fixed operating costs Operating income. Use CVP analysis for profit planning and graph relations: In this method, we plot a line for total revenues and total costs. The breakeven point is the point at which the total revenue line intersects the total cost line. The area between the two lines to the right of the breakeven point is the operating income area. 3
Fixed cost Dollars Variable cost Preparing a CVP Chart Step 1: Choose a sales volume. Plot point for total sales revenue. Draw sales revenue line from origin. Step 2: Draw the fixed cost line. Step 3: Draw the total cost line (fixed plus variable). Step 4: Identify the breakeven point and the areas of operating income and loss. $35,000 $30,000 $28,000 Sales point Step 1: Sales revenue line $20,000 $17,500 Step4: Breakeven sales point Step3: Total expense line $ 7,000 0 0 Step2: Fixed expense line 500 Volume of units 1,000 Example: Happy Feet hiking socks for $6 a pair and sells them for $10. Management budgets monthly fixed costs of for sales volumes between 0 and 12,000 pairs. Requirements: 1- Use both the income statement approach and the shortcut contribution margin approach to compute the company s monthly breakeven sales in units. 2- Use the contribution margin ratio approach to compute the breakeven point sales in dollars. 3- Prepare a graph of Happy Feet s CVP relationships. 4- Compute the monthly sales level (in units) required to earn a target operating income of $6,000. Use either the income statement approach or the shortcut contribution margin approach. 5- Assume that the tax rate is 25%, compute the monthly sales level (in units) required to earn a target net income of $6,000. 4
Dollars Solution: 1- Breakeven sales in units: The income statement approach: Sales revenue Variable cost Operating income. (Unit sales price Units sold) (Variable unit cost Units sold) Operating income. ($10 Units sold) ($6 Units sold) $0 ($10 $6) Units sold Units sold $4 Units sold 2,500 units. Shortcut contribution margin approach: Breakeven units sold Breakeven units sold 2- Breakeven sales in Dollars: Breakeven sales in Dollar Breakeven sales in Dollar * Contribution margin ratio $4 $10 0.4 3- The CVP relationships of Happy Feet: $10 $6 $4 0.40* $25,000 Sales revenue: $25,000 Hiking socks (2,500 units $10) Hiking socks (2,500 units $6) 15,000 Contribution margin Operating income $ 0 $50,000 2,500 units $40,000 Sales revenue line $30,000 Breakeven sales point Total expense line $25,000 $20,000 Fixed expense line 0 0 1,000 2,000 2,500 3,000 4,000 5,000 Units (socks produced) 5
4- The sales level required to earn a target operating income: Income statement equation approach: Sales revenue Variable cost Operating income. (Unit sales price Units sold) (Variable unit cost Units sold) Operating income ($10 Units sold) ($6 Units sold) $6,000 ($10 $6) Units sold + $6,000 Units sold $16,000 $4 Units sold 4,000 units. Shortcut contribution margin approach: + Operating income Target sales in units Target sales in units + $6,000 $16,000 $10 $6 $4 Sales revenue: $40,000 Hiking socks (4,000 units $10) Hiking socks (4,000 units $6) 24,000 Contribution margin $16,000 Operating income $ 6,000 5- The sales level required to earn a target operating income after tax: 4,000 units Target operating income Target net income 1 Tax rate Target operating income $6,000 $6,000 1 25% 0.75 $8,000 Target Sales in $ + $8,000 $18,000 0.40 0.40 Sales revenue: $45,000 Hiking socks (4,500 units $10) Hiking socks (4,500 units $6) 27,000 Contribution margin 18,000 10,000 Operating income 8,000 Income tax ($8,000 25%) 2,000 Net Income $ 6,000 $45,000 6
Operating Leverage: Operating leverage describe the effects that fixed costs have on changes in operating income as change in unit sold and contribution margin. Organizations with a high proportion of fixed costs in their cost structures, have high operating leverage. Degree of operating leverage Contribution Margin Operating Income $18,000 Degree of operating leverage 2,67 $6,000 This result indicate that, when sales are 4,000 units, a percentage change in sales and contribution margin will result in 2.67 times that percentage in operating income. Consider for example, a sales increase of 30% from 4,000 to 5,200 units, the operating income will increase by 2.67 x 30% 80% from $6,000 to $10,800. 7 Sales revenue: $52,000 Hiking socks (5,200 units $10) Hiking socks (5,200 units $6) 31,200 Contribution margin $20,800 Operating income $ 10,800 Using CVP methods to perform sensitivity analysis: Sensitivity Analysis Sensitivity analysis is a "what if" technique that examines how a result will change if the original predicted data are not achieved or if an underlying assumption changes. Changing the Selling Price. Changing Variable costs. Changing. The impact of changes in Selling Price, Variable Cost, and Fixed Costs on the Contribution Margin per Unit and the Breakeven Point: Selling Price per Unit Variable Cost per Unit Total Fixed Cost Cause Effect Result Change Contribution Margin per Unit Breakeven Point Increase Increase Decrease Decrease Decrease Increase Increase Decrease Increase Decrease Increase Decrease Increase Is not affected Increase Decrease Is not affected Decrease Margin of Safety: - Excess of expected sales over breakeven sales. - Drop in sales that the company can absorb before incurring a loss. - Margin of safety Expected sales Breakeven sales. - Managers use the margin of safety to evaluate the risk of both either current operation and their plans for the future.
Calculate the breakeven point for multiple product lines or services: Effect of Sales Mix on CVP Analysis: Multiple Product Break-Even: Use same formulas used earlier, but compute the weighted average contribution margin of all products. Sales mix Combination of products that make up total sales. Multiply each contribution margin per unit times the sales mix and add them together. Divide that number by the total number of units in the sales mix. Step 1: Calculate the contribution margin of the bundle. Step 2: Calculate the number of bundles. Number of bundles contribution margin of the bundle Step 3: Calculate the breakeven point in units for each product line Example: Happy Feet hiking socks for $6 a pair and sells them for $10. Management budgets monthly fixed costs of $12,000 for sales volumes between 0 and 12,000 pairs. Requirements: 1- Calculate the breakeven point in units. 2- Happy Feet reduces its selling price from $10 a pair to $8 a pair. Calculate the new breakeven point in units. 3- Happy Feet finds a new supplier for the socks. Variable costs will decrease by $1 a pair. Calculate the new breakeven point in units. 4- Happy Feet plans to advertise in hiking magazines. The advertising campaign will increase total fixed costs by $2,000 per month. Calculate the new breakeven point in units. 5- In addition to selling hiking socks, Happy feet would like to start selling sports socks. Happy feet expects to sell 1 pair of hiking socks for every 3 pairs of sports socks. Happy feet will buy the sports socks for $4 a pair and sell them for $8 a pair. Total fixed costs will stay at $12,000 per month. Calculate the new breakeven point in units for both hiking socks and sports socks. 6- Suppose Happy Feet expects to sell 3,800 hiking socks. Calculate the margin of safety in units and in Dollars. Solution: 1- Breakeven sales in units: Breakeven units sold 8 Breakeven units sold 2- Changing the Selling Price: Breakeven units sold $12,000 $12,000 $10 $6 $4 3,000 units Breakeven units sold $12,000 $12,000 $8 $6 $2 6,000 units Comment: With the original sale price ($10), Happy Feet s breakeven was 3,000 socks. But with the new lower price of $8 per sock, the breakeven point increases to 6,000 socks. The lower price means that each unit (sock) contributes less toward fixed costs, so Happy Feet must sell 3,000 more socks to break even. Of course, an increase in sale price would have the opposite effect.
3- Changing the Variable Cost: 9 Breakeven units sold Breakeven units sold $12,000 $12,000 $10 $5 $5 2,400 units Comment: With the original variable cost ($6), Happy Feet s breakeven was 3,000 socks. But with the new lower variable cost of $5 per sock, the breakeven point decreases to 2,400 socks. The lower variable cost increases the contribution margin on each sock and hence lower the breakeven point. Of course, an increase in variable cost would have the opposite effect. 4- Changing the Fixed Cost: Breakeven units sold Breakeven units sold $14,000 $14,000 $10 $6 $4 3,500 units Comment: Higher fixed cost increase the total contribution margin required to break even. In the case of Happy Feet, increasing the fixed costs from $12,000 to $14,000 increases the breakeven point from 3,000 socks to 3,500 socks (by 500 socks). Managers usually prefer a lower breakeven point to a higher one. Of course, a decrease in fixed cost would have the opposite effect. 5- Breakeven sales in units (sales mix): Step 1: Calculate the contribution margin of the bundle: Hiking Sports Sales price per unit $ 10 $ 8 Variable cost per unit $ 6 $ 4 $ 4 $ 4 Number of units in each bundle 1 3 Contribution margin of the bundle $ 4 $ 12 $ 16 Step 2: Calculate the number of bundles: The number of bundles Contribution margin of the bundle Breakeven sales in units $12,000 $16 750 bundles Step 3: Calculate the breakeven point in units for each product line Number of hiking socks [750 1] 750 units Number of sport socks [750 4] 2,250 units Hiking Sport Total Sales revenue: Hiking socks (750 units $10) $7,500 Sport socks (2,250 units $8) $18,000 $25,500 Hiking socks (750 units $6) $4,500 Sport socks (2,250 units $4) $9,000 $13,500 Contribution margin $3,000 $9,000 $12,000 $12,000 Operating income $ 0 6- The margin of safety: The margin of safety in units Expected sales in units Breakeven sales in units. The margin of safety in units 3,800 3,000 800 units The margin of safety in Dollars Expected sales in units sale price per unit. The margin of safety in Dollars 800 $10 $8,000 Prepared by Dr. Helal Afify 2013