Cost-Volume-Profit Analysis Chapter 3 Cost-Volume-Profit Analysis Prepared by Diane Tanner University of North Florida

Cost-Volume-Profit (CVP) Analysis 2 Cost-Volume-Profit (CVP) Analysis A very powerful management tool Helps explain interactions between Selling prices of products Volume or level of activity Per unit variable costs Total fixed costs Mix of products sold

CVP Terminology Selling price Sales revenue Total cost 3 Selling price The amount for which one unit of product is sold Sales revenue Selling price per unit multiplied by the number of units sold Total cost Total variable costs plus total fixed costs Variable cost (VC) A variable cost per unit of product Total fixed costs (TFC)

Cost and Profit Equations Cost equation Total cost = (VC/unit)(# of units) + Total FC i.e., TC = VCx + TFC Profit equation Sales revenue ‒ Total cost = Profit Or (SP/per unit)(# of units) ‒ Total cost = Profit SPx ‒ VCx ‒ TFC = profit Parallels the components on the variable costing income statement

Assumptions in CVP Analysis Costs can be accurately separated into their variable and fixed components Both unit variable costs and total fixed costs remain constant within the relevant range Inventory levels are zero or do not change Costs are linear Sales mix is constant

CVP Graph Three primary CVP graph lines Total Revenue Total Cost 6 Three primary CVP graph lines Total Revenue Dollars Total Cost Fixed costs Units

Breakeven Point The point where Break-even profit equation Sales revenue equals total cost Contribution margin equals fixed costs Profit is zero Break-even profit equation SPx – VCx – TFC = 0 Activity below the break-even point creates a loss Activity above the break-even point generates a profit

Breakeven Point Total sales revenue = total expenses = VCx + FC 8 Total sales revenue = total expenses = VCx + FC Total Revenue Profit Area Break-even point Dollars Total Cost Loss Area Fixed costs Units

Target Profit Target profit is the level of profit a company desires to achieve CVP can be used to determine the sales volume needed to achieve a target profit ‘Before tax’ target profit equation SPx – VCx – TFC = Target Profit ‘After tax’ target profit equation (SPx – VCx – TFC)(1 – TR) = Target Profit Where TR is the income tax rate

Margin of Safety 10 Margin of safety is…… The amount by which sales (revenue or units) can drop before losses begin to be incurred A cushion available to management before trouble (a loss) occurs Can be measured in Unit sales or Sales dollars Margin of safety = Total sales ‒ Break-even sales

What-If Analysis Using the profit equation, managers can change selected variables to see the effect on profit, units to be sold, or sales revenue. Variables to be changed Selling price Fixed costs Variable costs

Operating Leverage What is cost structure? 12 Operating Leverage What is cost structure? The relative proportion of fixed and variable costs in an company Higher proportions of fixed costs compared to variable costs More sensitive to changes in sales More risk Higher operating leverage Higher proportions of variable costs compared to fixed costs Less sensitive to changes in sales Less risk Lower operating leverage

Degree of Operating Leverage 13 Degree of Operating Leverage A measure of how sensitive net operating income is to percentage changes in sales A risk indicator Contribution Margin Net Operating Income Degree of Operating Leverage = Company A Company B $70,000 $18,000 $49,000 $18,000 = 3.89 = 2.72 Higher degree of operating leverage indicates higher proportion of fixed costs and higher risk.

Pushing Products to Customers 14 Goal is to generate the largest profit Push the product with the higher contribution margin per unit If customers prefer to buy one product and do not care which one they buy Push the product with the higher contribution margin ratio (i.e., the highest profit out of each sales dollar) If customers prefer to spend a fixed sum of money and do not care which products they buy

Sales Mix What is sales mix? 15 What is sales mix? The relative proportion in which a company’s products are sold Based on the premise that different products have different selling prices, cost structures, and contribution margins Two ways to express Unit sales mix 2000 : 8000 1 : 4 Buckets Pails Units 2,000 8,000 Sales $4,000 $6,000 Expenses $1,600 $3,500 Profit $2,400 $2,500 Revenue sales mix 4000 : 6000 2 : 3

Multiproduct Analysis Two approaches Contribution approach Based on the weighted average contribution margin for all products combined Bundle approach Based on the unit contribution margins of each product weighted by the sales mix

Weighted Average Approach Breakeven in Units 17 To determine the breakeven point in units for multiple products Calculate the weighted average CM per unit Total CM / total units Use the CM per unit in the profit equation to calculate breakeven point in units This is the unit breakeven point for all products Calculate the unit sales mix Multiply the sales mix proportion by the unit breakeven point for each product Round up to nearest full unit

Weighted Average Approach Breakeven in Revenue Dollars 18 To determine the breakeven point in sales dollars for multiple products Calculate the weighted average CM ratio Total CM / Total sales revenue Use the CM ratio in the profit equation to calculate breakeven point in sales revenue This is the $ breakeven point for all products Calculate the revenue sales mix Multiply the sales mix proportion by the revenue breakeven point for each product

Bundle Approach Where CM = contribution margin, and SM = sales mix Determine the unit contribution margin for each product Determine the unit sales mix Set up a profit equation that uses these two components as: (CM1)(SM1)x + (CM2)(SM2)x – TFC = 0 Where CM = contribution margin, and SM = sales mix The answer is a ‘per bundle’ amount. Multiply the sales mix for each product separately by the ‘per bundle’ amount. To determine breakeven in sales dollars, multiply the units by the selling price per unit

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