Cost-Volume-Profit Analysis: A Managerial Planning Tool Management Accounting: The Cornerstone for Business Decisions Copyright ©2006 by South-Western, a division of Thomson Learning. All rights reserved.

Learning Objectives 1.Determine the break-even point in number of units and in total sales dollars. 2.Determine the number of units that must be sold and the amount of revenue required, to earn a targeted profit. 3.Prepare a profit-volume graph and a cost-volume-profit graph and explain the meaning of each.

Learning Objectives 4.Apply cost-volume-profit analysis in a multiple-product setting 5.Explain the impact of risk, uncertainty, and changing variables on cost-volume- profit analysis.

Define Contribution Margin ◙ Sales less variable costs ◙ What’s left from sales after subtracting all variable costs, manufacturing, selling and administrative variable costs ◙ Contribution margin is used to cover fixed costs then accumulates as operating income

Describe the layout of the Contribution Margin Income Statement Sales Less: Total Variable Costs Contribution Margin Less: Total Fixed Costs Operating Profit $ XXX (XXX) $ XXX (XXX) $ XXX

How to prepare a contribution margin income statement. Whittier Company plans to sell 1,100 mowers in the next year at $440 each. Direct materials per mower$ 185 Direct labor per mower 105 Variable overhead per mower 28 Total fixed factory overhead17,000 Variable selling expense is a commission of $22 per mower; fixed selling and administrative expense totals $ 33,

REQUIRED: ◙ Calculate the total variable cost per unit. ◙ Calculated the total fixed expense for the year. ◙ Prepare a contribution margin income statement. Calculation: 1.The variable cost per unit = direct materials + direct labor + variable overhead + variable selling expense = $185 + $105 + $28 + $22 = $340 2.Total fixed costs = $17,000 + $33,000 = $50,000 How to prepare a contribution margin income statement. 4-1

How to prepare a contribution margin income statement. 4-1 Sales($440 x 1,100 mowers) Total Variable Expenses($340 x 1,100) Contribution Margin Total Fixed Expenses Operating Profit $ 484, ,000 $ 110,000 50,000 $ 60,000 $ $ 100

What is the formula for break-even? Fixed Costs Price – Variable costs per unit Fixed Costs Contribution margin per unit or

The Break-Even Concept

How to solve for the break- even point in units. Whittier Company plans to sell 1,100 mowers in the next year at $440 each. Direct materials per mower$ 185 Direct labor per mower 105 Variable overhead per mower 28 Total fixed factory overhead17,000 Variable selling expense is a commission of $22 per mower; fixed selling and administrative expense totals $ 33,

REQUIRED: 1.Calculate the total variable cost per unit. 2.Calculated the total fixed expense for the year. 3.Calculate the number of mowers that Whittier Company must sell to break even. 4.Check your answer by preparing a contribution margin income statement based on the break-even point. How to prepare a contribution margin income statement. 4-2

Calculation: 1.The variable cost per unit = direct materials + direct labor + variable overhead + variable selling expense = $185 + $105 + $28 + $22 = $340 2.Total fixed costs = $17,000 + $33,000 = $50,000 3.Break-even number of mowers = $50,000 / ($440 - $340) = 500 mowers How to solve for the break- even point in units. 4-2

Sales($440 x 500 mowers) Total Variable Expenses ($340 x 500) Contribution Margin Total Fixed Expenses Operating Profit $ 220, ,000 $ 50,000 50,000 $ 0 How to solve for the break- even point in units. 4-2

Whittier Company plans to sell 1,100 mowers at $440 each in the coming year. Variable cost per unit is $340. Total fixed cost is $50,000 REQUIRED: 1.Calculate the variable cost ratio. 2.Calculate the contribution margin ratio using unit figures. 3.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, and total contribution margin. How to calculate the variable cost ratio and the contribution margin ratio. 4-3

Calculation: 1.Variable cost ratio = $340 / $440 =.7727 or 77.27% 2.Contribution margin per unit = $440 - $340 = $100 Contribution margin ratio = $100 / $440 =.2273 or 22.73% 3. Contribution margin income statement based on budget figures is on the following slide. How to calculate the variable cost ratio and the contribution margin ratio. 4-3

How to calculate the variable cost ratio and the contribution margin ratio. 4-3 Sales($440 x 1,100 mowers) Total Variable Expenses ($340 x 1,100) Contribution Margin Total Fixed Expenses Operating Profit $ 484, ,000 $ 110,000 50,000 $ 60,000

Discuss the Relationship of the Size of Fixed Costs and Contribution Margin

Whittier Company 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 REQUIRED: 1.Calculate the contribution margin ratio. 2.Calculate the sales revenue that Whittier Company must make to break-even by using the break-even point in sales equation. 3.Check your answer by preparing a contribution margin income statement based on the break-even point in sales dollars. How to solve for the break- even point in sales dollars. 4-4

1.Contribution margin per unit = $400 - $325 = $75 Contribution margin ratio = contribution margin per unit / Price = $75 / $400 = r 18.75% [Hint: The contribution margin ratio comes out cleanly to four decimal places. Don’t round it, and our break- even point in sales dollars will yield an operating income of $0 (rather than being off a few dollars for rounding).] Notice that the variable cost ratio equals.8125, or the difference between and the contribution margin ratio. 2. Calculate the break-even point in sales dollars. Break-even sales dollars = $45,000 /.1875 = $240,000 How to solve for the break- even point in sales dollars. 4-4

3.Contribution margin income statement based on sales of $240,000: How to solve for the break- even point in sales dollars. 4-4 Sales Total Variable Expenses (.8125 x $240,000) Contribution Margin Total Fixed Expenses Operating Profit $ 240, ,000 $ 45,000 45,000 $ 0

Whittier Company sells mulching mowers at $400 each in the coming year. Variable cost per unit is $325. Total fixed cost is $45,000. REQUIRED: 1.Calculate the number of units Whittier Company must sell to earn an operating profit of $60, Check your answer by preparing a contribution margin income statement based on the number of units calculated. How to solve for the number of units to be sold to earn a target operating income. 4-5

Calculation: 1.Number of units = ($45,000 + $60,000) / $75 = 1,400 units 2.Contribution margin income statement based on sales of 1,400 units How to solve for the number of units to be sold to earn a target operating income. 4-5

How to solve for the number of units to be sold to earn a target operating income. 4-5 Sales ($400 x 1,400) Total Variable Expenses ($325 x 1,400) Contribution Margin Total Fixed Expenses Operating Profit $ 560, ,000 $ 105,000 45,000 $ 60,000

How to solve for the sales needed to earn a target operating income. 4-6 Whittier Company sells mulching mowers at $400 each in the coming year. Variable cost per unit is $325. Total fixed cost is $45,000. REQUIRED: 1.Calculate the contribution margin ratio. 2.Calculate the number of units Whittier Company must sell to earn an operating profit of $75, Check your answer by preparing a contribution margin income statement based on the number of units calculated.

Calculation: 1.Contribution margin ratio = ($400 -$325) / $400 = Sales Dollars = ($45,000 + $75,000) / = $640,000 3.Contribution margin income statement based on sales revenue of $640,000 is on the following slide. How to solve for the sales needed to earn a target operating income. 4-6

How to solve for the sales needed to earn a target operating income. 4-6 Sales Total Variable Expenses ($640,000 x.8125) Contribution Margin Total Fixed Expenses Operating Profit $ 640, ,000 $ 120,000 45,000 $ 75,000

The Profit-Volume Graph

The Cost-Volume-Profit Graph Fixed Expense Units Sold $ Revenue Total Cost Break-Even Point Variable Expense Loss Profit

List 5 C-V-P Assumptions 1.Revenue and cost functions are linear. 2.You can accurately identify sales, prior total fixed costs, unit variable costs and they remain constant in the relevant range. 3.You sell all you produce. 4.Sales mix is known in multi-product situations. 5.Selling price and cost is known with certainty.

Define Sales Mix ◙ The combination of products being sold by the firm. What is the package contribution margin? It is made up of the contribution margin of the individual products in the sales mix summed together. Whittier has a sales mix of 3 : 2. Mulching mower CM is $75 x 3 = $225 Riding mower CM is $200 x 2 = $400 Summed = Package CM $625

Recall that Whittier Company sells two products: mulching mowers priced at $400 and riding mowers priced at $800. The variable costs per unit are $325 per mulching mower and $600 per riding mower. Total fixed expense is $96,250. Whittier’s expected sales mix is three mulching mowers to two riding mowers. REQUIRED: 1.Form a package of mulching and riding mowers based on the sales mix and calculate the package contribution margin. 2.Calculate the break-even point in units for mulching and riding mowers. 3.Check you answers by preparing a contribution margin income statement. How to calculate the break-even units for a multiple product firm. 4-7

How to calculate the break-even units for a multiple product firm. Calculation: 1.Each package consists of three mulching and two riding mowers. 4-7 ProductPrice Variable Cost Unit CM Sales Mix Package Unit CM Mulching $ 400 $ 325 $ 75 3 $ 225 Riding Package total $ 625

2.Break-even packages = fixed costs / package contribution margin = $96,250 / $625 = 154 packages Mulching mowers break-even units = 154 x 3 = 462 Riding mowers break-even units = 154 x 2 = 308 How to calculate the break-even units for a multiple product firm. 4-7

How to calculate the break-even units for a multiple product firm. 3.Income statement – break-even solution: 4-7 Mulching Mower Riding MowerTotal Sales $184,800 $246,400 $431,200 Less: Variable expenses 150, , ,950 Contribution margin $ 34,650 $ 61,600 $ 96,250 Less: Total fixed expenses 96,250 Operating income $ -

Recall that the Whittier Company sells two products that are expected to produce total revenue of $1,120,000 and total variable costs of $870,000. Total fixed costs are expected to equal $96,250. REQUIRED: 1.Calculate the break-even point in dollars for the Whittier Company. 2.Check your answer by preparing a contribution margin income statement. How to calculate the break-even dollars for a multiple product firm. 4-8

1.The contribution margin ratio = $250,000 / $1,120,000 = 0.22 Break-even sales = fixed costs contribution margin ratio = $96,250 / 0.22 =$437, Income statement – break-even solution How to calculate the break-even dollars for a multiple product firm. 4-8 Sales Total Variable Expenses (0.78 x $437,500) Contribution Margin Total Fixed Expenses Operating Profit $ 437, ,250 $ 96,250 96,250 $ 0

List Ways C-V-P Can Be Used 1.To forecast changes in sales, when fixed costs change 2.To forecast changes in volume when sales prices change 3.To forecast changes in profit when costs or prices change 4.To combine any of the above

Differentiate Between Risk and Uncertainty

Define: Margin of Safety

Margin of Safety

How to compute margin of safety. Whittier Company plans to sell 1,050 mowers at $420 each in the next year. Whittier has a variable cost of $335 and fixed cost of $48,875. The break-even was calculated as 575 units. REQUIRED: 1.Calculate the margin of safety for Whittier Company in number of units. 2.Calculate the margin of safety for Whittier Company in sales revenue. 4-9

How to compute margin of safety. Calculation: 1.Margin of safety in units = = 1,050 – 575 = Margin of safety in sales revenue = = $420(1,050) - $420(575) = $199,

Define Operating Leverage and Degree of Operating Leverage (DOL) ◙ The use of Fixed Costs to Extract Higher Percentage of Changes in Profits as Sales Activity Changes ◙ DOL = CM / Operating Income

How to compute the degree of operating leverage. Recall that Whittier Company plans to sell 1,050 mowers at $420 each in the next year. Whittier has a variable cost of $335 and fixed cost of $48,875. Operating income on Cornerstone 4-9 was computed as $40,375. REQUIRED: Calculate the degree of operating leverage for Whittier Company. Calculation: Degree of operating leverage= CM / Operating Income = ($420 - $335) x 1,050/ $40,375 =

How to compute the impact of increased sales on operating income using the degree of operating leverage. Recall that Whittier Company had expected to sell 1,050 mowers and earn operating income equal to $40,375. Whittier’s degree of operating leverage is equal to The company plans to increase sales by 20% next year. REQUIRED: 1.Calculate the percent change in operating income expected by Whittier Company for next year using the degree of operating leverage. 2.Calculate the operating income expected by Whittier Company next year using the percent change in operating income calculated in Requirement

Calculation: 1.Percent change in operating income = = DOL x % Change in sales = 2.21 x 20% = 44.2% 2.Expected operating income = $40,375 + (0.442 x $40,375) = $58,221 How to compute the impact of increased sales on operating income using the degree of operating leverage 4-11

What is sensitivity analysis?