Chapter 18 Cost Volume Profit Analysis Prof. Baick 1. Cost-Volume Profit Analysis A technique that examines changes in profits in response to changes in sales volumes, costs, and prices 2. Components of Graphing CVP Analysis Relationships $ D C B A units where: F = Total fixed costs P = Price per unit of product (goods or services) Profit = Targeted profit level Q = Quantity of product sold (goods or services) TR = Total revenue TVC = Total variable costs V = Variable cost per unit 1 3.
Assumptions Made in CVP Analysis Number of output units only revenue driver and only cost driver Total costs can be separated into the primary categories of variable costs and fixed costs Total revenues and total costs are linear within the relevant range (and time period) Unit selling price, unit variable costs, and fixed costs known and constant Single product or constant sales mix Time value of money effects ignored 4.
Basic Formula and Terminology Assume that: U = Number of Units Produced and SOLD SP = Selling Price per Unit VC = Variable Cost per Unit FC = Total Fixed Costs
Sales – Variable Costs – Fixed Costs = Profit Breakeven The level of sales whereby total profits are equal to zero.
Contribution margin Sales Revenue – Variable Costs Contribution margin per unit Selling price per unit – Variable cost per unit Contribution margin ratio = Total Sales Revenue – Total Variable Costs Total Sales Revenue OR: Selling price per Unit – Variable costs per Unit Selling price per Unit 2 5. Breakeven Analysis Breakeven sales Breakeven units 6. Target Profit Target sales Target units 7. Margin of Safety 8. Margin of Safety Ratio 9. Product Mix Decisions 10.
Leverage and Cost Structure Definition Increasing sales by a given percent and increasing profits by an increasingly larger proportion. Operating leverage Financial leverage 11. Primacy of Contribution Margin 3 CVP Graphical Analysis 4 IMPORTANT FORMULAS: SP VC FC U = = = = Selling price per unit Variable cost per unit Total Fixed costs Units sold Revenue – Expenses Variable Fixed FC = Net Income SP(U) – VC(U) – = NI BREAK EVEN MEANS REVENUES = EXPENSES OR NET INCOME IS 0 Contribution Margin Ratio = Break-even (Units) = FC __ SP – VC FC____________ Contribution Margin Ratio Break-even (Sales) =
Target Profit (Units) =FC + TP SP – VC Target Profit (Sales) = FC + TP Contribution Margin Ratio = Actual (Expected) Sales – Break-even Sales Margin of Safety Margin of Safety Ratio = Margin of Safety Actual (Expected) Sales Higher is better! Three Ways of Computing Break-Even 1. Mathematical equation SP(U) – VC(U) – FC = NI 2. Contribution Margin Technique (Formulas) 3. Graphs 5 In-Class Problems Example 1. If sales are $80,000, variable costs are $50,000, and fixed costs are $20,000, the contribution margin ratio is: Sales – Variable Costs Sales 80,000 – 50,000 80,000 = . 75 or 37. 5% Example 2. A firm with fixed costs of $61,500 per month sells three products with the following characteristics: Sales Mix Contribution Product Percentage Margin P 25% $48 Q 50% 50 R 25% 52 How many total units must be sold to breakeven? First Compute the Weighted-Average Contribution Margin per Unit = ($48 x . 25) + ($50 x . 50) + ($52 x . 25) = $12 + $25 + $13 = $50 This figure will be used to compute the break-even in total units. Breakeven in Total Units = Total Fixed Costs Weighted-Avg Contribution Margin per Unit $61,500 50 = = 1,230 units in total 6 Example 3.
The Pierson Co. has the following unit and mix data: Do Dah Unit sales price $5. 00 $4. 00 Unit contribution margin 0. 75 1. 20 Sales mix ($) 80% 20% Fixed costs Target profit How many units of Dah must be sold at the breakeven point? = $ 99,000 ($0. 75 x . 80) + ($1. 20 x . 20) = $99,000 $0. 84 = 117,857. 143 -> 117, 858 Total units at breakeven (round up). Total $99,000 24,750 Dah’s Portion of Sales at Breakeven = 117,858 x . 20) = 23,571. 6 -> 23,572 units How many units in total must be sold to earn the target profit? = $99,000 + $24,750 . 84 147,321. 4 or 147,322 units = Example 4. Baldwin’s Bagel Shop had the following activity for December: Total bagels sold Total revenues Total fixed costs Total variable costs 17,000 $595,000 99,000 357,000 What was Baldwin’s margin of safety, in dollars? Contribution Margin Ratio = $595,000 – $357,000 $595,000 Breakeven Sales = $99,000 . 40 Margin of Safety = $595,000 – $247,500 = $347,500 = $247,500 = . 40 What was Baldwin’s margin of safety ratio? = $347,500 $595,000 58. 4% = 8 Example 5. The Nunn Co. produces a single product. Its cost structure is: Fixed Cost $35,000 60,000 Variable Cost Per Unit $15 10
Manufacturing costs Non-manufacturing costs If the firm sells 5,000 units per period, what price should be charged to earn $35,000? SP(U) SP(5,000) SP = $51 – VC(U) 25(5,000) FC 95,000 = = NI 35,0000 Example 6. Smith Co. has a contribution margin ratio of 40% and a breakeven point of $200,000 in sales. If the firm reports net income of $50,000 after taxes of 50%, what were total sales for the year? 0 = Sales – Variable Costs – Fixed Costs 0 = Contribution Margin – Fixed Costs 0 = $200,000(0. 4) – FC FC = $80,000 $50,000 = 0. 5[(. 4 x Sales) – $80,000] Sales = $450,000 Example 7 Sales Variable costs Contribution margin Fixed costs Net income Old $2,000,000 1,400,000 600,000 400,000 200,000 New $2,000,000 600,000 1,400,000 1,200,000 200,000 Note in this example that both Old and New have the same level of Sales and Net income. This means that the total costs for both Old and New are the same. However, the cost structure for each is different. This means that the breakeven point and profitability after breakeven are different for Old and New. In particular, Old and New have different Degrees of Operating Leverage (DOL). 10
Strategic Decision Making Candice Company has decided to introduce a new product, which can be manufactured by either of two methods. The manufacturing method will not affect the quality of the product. The estimated manufacturing costs of the two methods are as follows: Method A $5. 00 $6. 00 $3. 00 $2,440,000 Method B $5. 60 $7. 20 $4. 80 $1,320,000 Direct materials Direct labor Variable overhead Fixed manufacturing cost Candice’s marketing research recommends a selling price of $30 per unit. The fixed selling costs are $500,000 plus $2 per unit sold, regardless of manufacturing method.
A. Calculate the estimated break-even point in annual unit sales of the new product if Candice Company uses: 1) 2) Manufacturing Method A Manufacturing Method B B. Which production technology should the firm use? In particular, discuss the range for the level of output that would make Method A preferable and the range for the level of output that would make Method B preferable. 11 Extra Problem The following information pertains to ABC Company: 2004 $1,020,000 240,000 2005 $960,000 210,000 Sales Net Income Determine the breakeven sales for ABC Company. 12
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