Chapter Four Cost-Volume-Profit Analysis: A Managerial Planning Tool COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Learning Objectives Determine the break-even point in units and sales dollars Determine the number of units that must be sold, and the amount of revenue required to earn a targeted profit Prepare a profit-volume graph and a cost-volume-profit graph and explain the meaning of each Apply cost-volume-profit analysis in a multiple product setting Explain the impact of risk, uncertainty and changing variables on cost-volume-profit analysis COPYRIGHT © 2012 Nelson Education Ltd.

Determine the break-even point in units and sales dollars OBJECTIVE  1 Determine the break-even point in units and sales dollars COPYRIGHT © 2012 Nelson Education Ltd.

Cost-Volume-Profit Analysis A powerful tool for planning and decision making It can be used to calculate: The number of units that must be sold to break-even The impact of an increase in price on profit The impact of a given reduction in fixed costs on the break-even point COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Break-Even Point Total Revenue = Total Cost Or put it another way: Total Revenue Total Costs Zero Profit COPYRIGHT © 2012 Nelson Education Ltd.

Using Operating Income in Cost-Volume-Profit Analysis Contribution Margin Variable Expense Contribution Margin - Sales = Contribution Margin is then used to cover Fixed Costs and Operating Income COPYRIGHT © 2012 Nelson Education Ltd.

Contribution Margin Income Statement Divides costs based on behaviour Costs are divided into variable and fixed components Important subtotal is contribution margin Sales revenue minus variable expenses COPYRIGHT © 2012 Nelson Education Ltd.

Using Operating Income in Cost-Volume-Profit Analysis Contribution Margin Variable Costs - Contribution Margin Sales = Contribution Margin Fixed Costs Operating Income - = Break-even point is when Operating Income = 0 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Cornerstone 4-1 How to Prepare a Contribution Margin Income Statement Information: Whittier Co. plans to sell 1,000 mowers at $400 each in the coming year. Product costs include: Direct materials per mower $180 Direct labour per mower $100 Variable overhead per mower $25 Total fixed factory overhead $15,000 Variable selling expense is a commission of $20 per mower; fixed selling and administrative expense totals $30,000 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Example Required: Calculate the total variable cost per unit Calculate the total fixed expense for the year Prepare a contribution margin income statement for Whittier Co. for the coming year COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Variable Cost Variable Cost Per unit Variable Selling Expense Direct Materials Direct Labour Variable Overhead = + + + Variable Cost Per unit = $180 + $100 + $25 + $20 Variable Cost Per unit = $325 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Fixed Expenses Fixed Selling & Administrative Expense Total Fixed Expenses Fixed Overhead = + Total Fixed Expenses = $15,000 + $30,000 Total Fixed Expenses = $45,000 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Whittier Company Contribution Margin Income Statement For the Coming Year Total Per Unit Sales ($400 × 1,000 mowers) $400,000 $400 Total variable expense ($325 × 1,000) 325,000 325 Total contribution margin $ 75,000 $ 75 Total fixed expense 45,000 Operating income $ 30,000 Each unit contributes $75 to cover fixed costs COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Cornerstone 4-2 How to Solve for the Break-Even Point in Units Information: Whittier Co. plans to sell 1,000 mowers at $400 each in the coming year. Product costs include: Direct materials per mower $180 Direct labour per mower $100 Variable overhead per mower $25 Total fixed factory overhead $15,000 Variable selling expense is a commission of $20 per mower; fixed selling and administrative expense totals $30,000 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Example Required: Calculate the total variable cost per unit Calculate the total fixed expense for the year Calculate the number of mowers that Whittier Co. must sell to break-even Check the answer by preparing a contribution margin income statement based on the break-even point COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Variable & Fixed Costs These were computed in Cornerstone 4-1 Variable Cost Per unit = $180 + $100 + $25 + $20 = $325 Total Fixed Expenses = $15,000 + $30,000 = $45,000 COPYRIGHT © 2012 Nelson Education Ltd.

Break-Even Number of Mowers Formula can be simplified down to: Total Fixed Cost Break-even units = Contribution Margin per unit Selling Price – Variable cost per unit Break-even units $45,000 = ($400 – $325) Break-even units = 600 mowers COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Whittier Company Contribution Margin Income Statement For the Coming Year based on sales of 600 mowers Total Per Unit Sales ($400 × 600 mowers) $240,000 $400 Total Variable Expense ($325 × 600) 195,000 325 Total Contribution Margin $ 45,000 $ 75 Total Fixed Expense 45,000 Operating Income $ 0 Operating income is zero when 600 units are sold. The break-even calculation is correct! COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Cornerstone 4-3 How to Calculate the Variable Cost Ratio and the Contribution Margin Ratio Information: Whittier Co. plans to sell 1,000 mowers at $400 each in the coming year Variable cost per unit is $325 Total fixed cost is $45,000 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Example Required: Calculate the variable cost ratio Calculate the contribution margin ratio using unit figures Prepare a contribution margin income statement based on the budgeted figures for next year In a column next to the income statement, show the percentages based on sales for: Sales Total variable costs Total contribution margin COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Variable Cost Ratio Variable Cost Ratio Variable Cost = Sales Variable Cost Ratio $325 = $400 Variable Cost Ratio = 81.25% COPYRIGHT © 2012 Nelson Education Ltd.

Contribution Margin Ratio Contribution Margin per unit = Sales - Variable Cost Contribution Margin per unit = $75 per unit Contribution Margin Ratio Contribution Margin = Sales $75 Contribution Margin Ratio = = 18.75% $400 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Whittier Company Contribution Margin Income Statement For the Coming Year % of Sales Total Sales ($400 ×1,000 mowers) $400,000 100.00 Total Variable Exp. (0.8125 × $400,000) 325,000 81.25 Total Contribution Margin $ 75,000 18.75 Total Fixed Expense 45,000 Operating Income $ 30,000 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Cornerstone 4-4 How to Solve for the Break-Even Point in Sales Dollars Information: Whittier Co. plans to sell 1,000 mowers at $400 each in the coming year Variable cost per unit is $325 Total fixed cost is $45,000 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Example Required: Calculate the contribution margin ratio Calculate the sales revenue that Whittier Co. must make to break-even by using the break-even point in sales equation Prepare a contribution margin income statement based on the break-even point in sales dollars COPYRIGHT © 2012 Nelson Education Ltd.

Contribution Margin Ratio Contribution Margin per unit = $400 – $325 = $75 per unit Contribution Margin Ratio $75 = = 18.75% $400 These were computed in Cornerstone 4-1 COPYRIGHT © 2012 Nelson Education Ltd.

Break-Even Point in Sales Dollars Break-even sales Total fixed expenses = Contribution margin ratio Break-even sales $45,000 = 0.1875 Break-even sales = $240,000 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Whittier Company Contribution Margin Income Statement For the Coming Year Sales $240,000 Total Variable Exp. (0.8125 × $240,000) 195,000 Total Contribution Margin $ 45,000 Total Fixed Expense 45,000 Operating Income $ 0 Operating Income is zero when sales are $240,000 The break-even calculation is correct! COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. OBJECTIVE  2 Determine the number of units that must be sold and the amount of revenue required to earn a targeted profit COPYRIGHT © 2012 Nelson Education Ltd.

Units to Be Sold to Achieve a Target Income Two Ways: Using Operating Income equation Using the Basic Break-even equation Cornerstone 4-5 will walk us through these computations COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Cornerstone 4-5 How to Solve for the Number of Units to Be Sold to Earn a Target Operating Income Information: Whittier Co. sells mulching mowers at $400 each Variable cost per unit is $325 and total fixed cost is $45,000 Required: Calculate the number of units that Whittier Co. must sell to earn operating income of $37,500 Prepare a contribution margin income statement based on the number of units calculated COPYRIGHT © 2012 Nelson Education Ltd.

Units to Be Sold to Achieve a Target Income Number of units to earn target income Total fixed expense + Target income = Price – Variable cost per unit Number of units to earn target income $45,000 + $37,500 = $400 - $325 Number of units to earn target income = 1,100 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Whittier Company Contribution Margin Income Statement For the Coming Year Sales ($400 ×1,100) $440,000 Total variable expense ($325 × 1,100) 357,500 Total contribution margin $ 82,500 Total fixed expense 45,000 Operating income $ 37,500 The calculation is correct! The operating income is $37,500 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Cornerstone 4-6 How to Solve for the Sales Needed to Earn a Target Operating Income Information: Whittier Co. sells mulching mowers at $400 each Variable cost per unit is $325 and Total fixed cost is $45,000 Required: Calculate the contribution margin ratio Calculate the sales that Whittier Co. must make to earn an operating income of $37,500 Prepare a contribution margin income statement based on the sales dollars calculated COPYRIGHT © 2012 Nelson Education Ltd.

Sales Revenue to Achieve a Target Income Sales dollars to earn target income Fixed Cost + Target Income = Contribution margin ratio Sales dollars to earn target income $45,000 + $37,500 = 0.1875 Contribution margin ratio was computed in Cornerstone 4-3 Sales dollars to earn target income = $440,000 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Whittier Company Contribution Margin Income Statement For the Coming Year Sales $440,000 Total variable exp. (0.8125 × $440,000) 357,500 Total contribution margin $ 82,500 Total fixed expense 45,000 Operating income $ 37,500 The calculation is correct! The operating income is $37,500 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. OBJECTIVE  3 Prepare a profit-volume graph and a cost-volume-profit graph and explain the meaning of each COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Profit-Volume Graph Visually portrays the relationship between profits and units sold Operating Income is the dependent variable Units sold is the independent variable COPYRIGHT © 2012 Nelson Education Ltd.

Cost-Volume-Profit Graph Depicts relationship among cost volume and profits Graph two separate lines: Total revenue Total cost Vertical axis: measured in dollars Horizontal axis: measured in units sold COPYRIGHT © 2012 Nelson Education Ltd.

Assumptions of Cost-Volume-Profit Analysis Revenue and cost functions are linear Price, total fixed costs, and unit variable costs can be identified and remain constant over relevant range All units produced are sold –no changes in inventory levels Sales mix is constant Selling prices and costs are known with certainty COPYRIGHT © 2012 Nelson Education Ltd.

Linear Cost and Revenue Functions Cost-Volume-Profit assumes that cost and revenue functions are linear In other words they are straight lines COPYRIGHT © 2012 Nelson Education Ltd.

Production Equal to Sales Cost-Volume-Profit assumes that what is produced is actually sold Inventory levels do not change over period CVP focuses on current costs by excluding inventory costs of previous periods COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Constant Sales Mix Multiple product break-even analysis requires a constant sales mix Relative combination of products being sold by a firm Sales mix is difficult to predict with certainty COPYRIGHT © 2012 Nelson Education Ltd.

Linear Cost and Revenue Functions Firms seldom know prices, variable costs, and fixed costs with certainty There are formal ways of explicitly building uncertainty into the Cost-Volume-Profit model COPYRIGHT © 2012 Nelson Education Ltd.

OBJECTIVE  4 Apply cost-volume-profit analysis in a multiple-product setting COPYRIGHT © 2012 Nelson Education Ltd.

Multiple-Product Analysis Cost-Volume-Profit analysis becomes more complex with multiple products We need to adapt the single-product formulas COPYRIGHT © 2012 Nelson Education Ltd.

Direct & Common Fixed Expenses Fixed costs that can be traced to each segment and would be avoided if the segment did not exist Fixed costs that are not traceable to the segments and would remain even if one of the segments was eliminated COPYRIGHT © 2012 Nelson Education Ltd.

Multiple-Product Analysis Break-even point in units Key: identify expected sales mix Sales Mix: Measured in units sold Reduced to the smallest possible whole numbers Required in order to determine break-even point in units Sales mix is the relative combination of products being sold by a firm COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Cornerstone 4-7 How to Calculate the Break-Even Units for a Multiple-Product Firm Information: Whittier Co. sells two products: Mulching mowers priced at $400 Riding mowers priced at $800 The variable costs per unit are: $325 per mulching mower $600 per riding mower Total fixed expense is $96,250 Whittier’s expected sales mix is three mulching mowers to two riding mowers COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Example Required: Form a package of mulching and riding mowers, based on the sales mix, and calculate the package contribution margin Calculate the break-even point in units for mulching mowers and for riding mowers Check calculations by preparing a contribution margin income statement COPYRIGHT © 2012 Nelson Education Ltd.

Package Contribution Margin Unit Variable Cost Unit Contrib. Margin Pkg. Unit Contrib. Margin Sales Mix Product Price Mulching $400 $325 $ 75 3 $225 Riding 800 600 200 2 400 Package Total $625 COPYRIGHT © 2012 Nelson Education Ltd.

Break-Even Point in Units Break-even packages Fixed Cost = Package contribution margin Break-even packages $96,250 = $625 Break-even packages = 154 COPYRIGHT © 2012 Nelson Education Ltd.

Break-Even Point in Units 154 Break-even packages Each package contains: 3 mulching mowers, 2 riding mowers Mulching mowers break-even units = 154 × 3 = 462 Riding mowers break-even units = 154 × 2 = 308 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Whittier Company Contribution Margin Income Statement For the Coming Year Mulching Riding Total 462 × $400 Sales $184,800 $246,400 $431,200 Total Variable Expense 150,150 184,800 334,950 Total Contribution Margin $ 34,650 $ 61,600 $ 96,250 Total Fixed Expense $ 96,250 $ 0 Operating Income 462 × $325 308 × $800 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Cornerstone 4-8 How to Calculate the Break-Even Sales Dollars for a Multiple-Product Firm Information: Whittier Co. sells two products that are expected to produce: Total revenue next year of $1,120,000 Total variable costs of $870,000 Total fixed costs are expected to equal $96,250 Required: The break-even point in sales dollars for Whittier Co. Check calculations by preparing a contribution margin income statement COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. CVP Analysis Break-even point in sales dollars Contribution Margin Ratio Expected Contribution Margin = Total Sales Revenue Contribution Margin Ratio $250,000 = $1,120,000 Contribution Margin Ratio = 0.22* *Rounded COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. CVP Analysis Break-even sales Break-Even Sales Fixed Cost = Contribution Margin Ratio Break-Even Sales $96,250 = 0.22 Break-Even Sales $437,500 = COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Whittier Company Contribution Margin Income Statement For the Coming Year Sales $437,500 Total Variable Exp. (0.78 × 437,500) 341,250 Total Contribution Margin $ 96,250 Total Fixed Expense 96,250 Operating Income $ 0 Operating income is zero when sales are $437,500 The break-even calculation is correct! COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. OBJECTIVE  5 Explain the impact of risk, uncertainty, and changing variables on cost-volume-profit analysis COPYRIGHT © 2012 Nelson Education Ltd.

CVP Analysis: Risk and Uncertainty The break-even point can be affected by changes in: Price Unit Contribution Margin Fixed Cost Changes in any of the above will affect the sales mix COPYRIGHT © 2012 Nelson Education Ltd.

Risk and Uncertainty Effects on Managers Must realize the uncertain nature of future prices, costs, and quantities Move from consideration of a break-even point to what might be called a “break-even band” May engage in sensitivity or what-if analysis COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Margin of Safety Units sold or revenue earned above break-even volume Crude measure of risk When there is a downturn in sales, the risk of suffering losses will be less if the firm’s margin of safety is large than if the margin of safety is small COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Cornerstone 4-9 How to Compute the Margin of Safety Information: This year, Whittier Co. plans to sell 1,000 mowers at $400 ea. Variable costs are $325 Fixed costs are $45,000 Break-even units were previously calculated as 600 Required: Calculate the margin of safety for Whittier Co. in units Calculate the margin of safety for Whittier Co. in sales revenue COPYRIGHT © 2012 Nelson Education Ltd.

Margin of Safety in Units Sales in units Break-even units - = Margin of safety in units = 1,000 - 600 Margin of safety in units 400 = COPYRIGHT © 2012 Nelson Education Ltd.

Margin of Safety in Sales Revenue Break-even units = Sales - Margin of safety in sales revenue = $400(1,000) - $400(600) Margin of safety in sales revenue $160,000 = COPYRIGHT © 2012 Nelson Education Ltd.

Degree of operating leverage COPYRIGHT © 2012 Nelson Education Ltd. Relative mix of fixed costs to variable costs Higher proportions of fixed costs to the amount of variable costs create higher operating leverage The greater the degree of operating leverage, the larger the effect on operating income when sales change Degree of operating leverage Contribution margin = Operating income COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Cornerstone 4-10 How to Compute the Degree of Operating Leverage Information: This year, Whittier Co. plans to sell 1,000 mowers at $400 ea. Variable costs are $325 Fixed costs are $45,000 Operating Income at 1,000 units is $30,000 Required: Calculate the degree of operating leverage for Whittier Co. COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Operating Leverage Degree of operating leverage (DOL) can be measured for a given level of sales Degree of operating leverage Contribution Margin = Operating Income Degree of operating leverage ($400 - $325)(1,000 units) = $30,000 Degree of operating leverage = 2.5 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Cornerstone 4-11 How to Compute the Impact of Increased Sales on Operating Income Using the DOL Information: Whittier Co. plans to sell 1,000 mowers and earn operating income equal to $30,000 next year Whittier’s degree of operating leverage is equal to 2.5 Now, the company plans to increase sales by 20 percent next year COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Example Required: Calculate the percent change in operating income expected by Whittier Co. for the next year using the degree of operating leverage Calculate the operating income expected by Whittier Co. next year using the percent change in operating income calculated in the above requirement COPYRIGHT © 2012 Nelson Education Ltd.

Percentage Change in Operating Leverage Percent change in operating leverage Percent change in sales × = DOL Percent change in operating leverage = 2.5 × 20% Percent change in operating leverage = 50% COPYRIGHT © 2012 Nelson Education Ltd.

Expected Operating Income Original operating income = + (percent change × original operating income) Expected operating income = $30,000 + (0.50 × $30,000) Expected operating income = $45,000 COPYRIGHT © 2012 Nelson Education Ltd.