Unformatted text preview: CHAPTER 6
COST VOLUME PROFIT RELATIONSHIPS CostVolumeProfit Relationships Major Topics Contribution Margin Contribution Margin Ratio Cost Volume Profit Concepts (i.e. CVP)
– Breakeven Analysis Sales Mix – Target Profit Analysis The equation method; The contribution margin method; and The graphical method. Review from Chapter #5 In Chapter #5 we learned the concept of the Contribution Income Statement. The following Contribution Income Statement for the Racing Bicycle Company will be used for several of the concepts being introduced in this Chapter: Racing Bicycle Company – Contribution Income Statement – For the Month of September Sales (500 Bicycles) Less Variable Costs Contribution margin Less: Fixed Expenses Net income $ 250,000 <150,000> 100,000 < 80,000> $ 20,000 Notes Contribution Margin (i.e. CM) is the amount remaining from sales revenues after variable expenses have been deducted. Contribution margin is used first to cover fixed expenses. Any remaining CM contributes to net operating income. We will see later in this Chapter that when the company is able to cover its Fixed Expenses of $80,000 from it’s contribution margin the company will have reached it’s breakeven point (i.e. BEP) CM can be expressed on a per unit basis Under the contribution approach, sales, variable expenses and CM can be expressed on a per unit basis. We have restated the financial above: Racing Bicycle Company Contribution Income Statement For the Month of September Total Per Unit $ 500 <300> $ 200 Sales (500 Bicycles) Less Variable Costs Contribution margin Less: Fixed Expenses Net income $ 250,000 <150,000> 100,000 < 80,000> $ 20,000 What does this additional information give us? We have learned that each additional bicycle that is sold provides an additional $200 of contribution margin will be generated to cover fixed expenses and hopefully generate some profits for the company after reaching its BEP. Again the company’s breakeven point is $80,000 (i.e. company’s fixed costs). It will need to sell 400 bicycles (i.e. 400 x $500/bike) each month in order to reach its breakeven point. Illustration: If we know that our BEP is 400 bikes, what will be our profit if we sell 430 bikes? Sales in units 430 BEP in Units <400> Sales over BEP 30 x CM/unit x 200 Profit $6,000 Contribution Margin The contribution margin is the difference between total sales and total variable expenses and can be stated as follows: Sales (500 Bicycles) $ 250,000 Variable Costs <150,000> Contribution margin $100,000 Unit Contribution Margin The unit contribution margin is the difference between the unit selling price and the unit variable expenses and can be stated as follows: Sales (500 Bicycles) Less Variable Costs Contribution margin Per Unit $ 500 <300> $ 200 What does this additional information give us? We have learned that each additional bicycle that is sold provides an additional $200 of contribution margin will be generated to cover fixed expenses and hopefully generate some profits for the company after reaching its BEP. Again the company’s breakeven point is $80,000 (i.e. company’s fixed costs). It will need to sell 400 bicycles (i.e. 400 x $500/bike) each month in order to reach its breakeven point. Illustration: If we know that our BEP is 400 bikes, what will be our profit if we sell 430 bikes? Sales in units BEP in Units Sales over BEP x CM/unit Profit 430 <400> 30 x 200 $6,000 Net income is equal to the contribution margin less fixed expenses: Sales (500 Bicycles) $ 250,000 Less Variable Costs <150,000> Contribution margin 100,000 Less: Fixed Expenses < 80,000> Net income $ 20,000 Contribution Margin Ratio: The contribution margin ratio is computed by dividing the total contribution margin by total sales revenue. The CM ratio can be used to estimate the change in contribution margin that would result from changes in sales revenue. CM Ratio = Contribution Margin Sales CM RATIO continued Single Product:
CM Ratio = Unit Contribution margin Unit Selling Price For example, a CM ratio of 0.40 indicates that a dollar increase in sales revenue will result in a 40 cents increase in contribution margin and in net operating income. Illustration If Company B has lower variable costs than Company A, it has a higher contribution margin ratio. Consequently, Company B’s contribution margin (and net operating income) will increase more rapidly than Company A’s as sales increase. Illustration: Racing Bicycle Co. Total Sales (400 Bicycles) Less Variable Costs Contribution margin Less: Fixed Expenses Net income Per Unit $ 200,000 $ 500 <120,000> <300> 80,000 $ 200 < 80,000> $ 0 Solution CM Ratio = Contribution Margin Sales CM Ratio = CM Ratio = $80,000 $200,000 40% Alternative Solution (in terms of units) CM Ratio = CM Ratio = CM Ratio = Unit CM Unit selling price $200 $500 40% Illustration #2 – Shortcut Solution What is the impact on profits if unit sales increase to 540 due to increasing the monthly advertising budget by $10,000? Racing Bicycle Company Contribution Income Statement For the Month of September 500 540 Sales Less Variable Costs Contribution margin Less: Fixed Expenses Net income $ 250,000 $ 270,000 <150,000> <162,000> 100,000 108,000 < 80,000> < 90,000> $ 20,000 $ 18,000 Note: Net sales increase of $20,000, but net operating income decreased by $2,000. THE SHORTCUT SOLUTION Increase in CM (40 units x $200) $ 8,000 Increase in advertising expenses 10,000 Decrease in net operating income $ <2000> Breakeven Point The breakeven point is the level of sales at which profit is zero. Three approaches to breakeven analysis are (a) the equation method, (b) the contribution margin method, and (c) the graphical method. Breakeven Point Equation method, the equation Profits = (Sales – Variable expenses) – Fixed expenses is solved to determine the breakeven point in units or dollar sales. Profits = (Sales – Variable expenses) Fixed expenses Or Sales = Variable Expenses + Fixed Expenses + Profits Note: At BEP profits are always zero. Illustration: BEP Equation (in units)
Racing Bicycle Company Contribution Income Statement For the Month of September Total Sales (500 Bicycles) Less Variable Costs Contribution margin Less: Fixed Expenses Net income Per Unit % $ 250,000 $ 500 100 % <150,000> <300> <60> 100,000 $ 200 40 % < 80,000> $ 20,000 Illustration continued Sales = Variable Expenses + Fixed Expenses + Profits $500Q $200Q Q Q = $300Q + $80,000 + 0 = $80,000 = $80,000/$200 per bike = 400 bikes = = Where: Q $500 $300 $80,000 Number or bikes sold = Unit selling price = Unit variable expense Total fixed expenses BEP Contribution margin method Contribution margin method, total fixed expenses are divided by the contribution margin per unit to obtain the breakeven point in units. Alternatively, total fixed expenses can be divided by the contribution margin ratio to obtain the breakeven point in sales dollars. BEP in Units Sold BEP in Total Sales $ = Fixed Expenses Unit Contribution Margin = Fixed Expenses CM Ratio Illustration: Racing Example
Racing Bicycle Company Contribution Income Statement For the Month of September Total Sales (500 Bicycles) Less Variable Costs Contribution margin Less: Fixed Expenses Net income Per Unit % $ 250,000 $ 500 100 % <150,000> <300> <60> 100,000 $ 200 40 % < 80,000> $ 20,000 Solution BEP in Total Sales $ BEP = = = Fixed Expenses CM Ratio $80,000 40% $200,000 BEP Alternative BEP in Units Sold: BEP in Units Sold = Fixed Expenses Unit Contribution Margin = = $80,000 $200/unit BEP BEP 400 bikes BEP Graphical method Graphical method, total cost and total revenue data are plotted on a graph. The intersection of the total cost and the total revenue lines indicates the breakeven point. (a) If the selling price decreases, the total revenue line will be less steep and the breakeven point will occur at a higher volume. (b) If the fixed cost increases, then both the fixed cost line and the total cost line will shift upward and the breakeven point will occur at a higher volume. (c) If the variable cost per unit increases, then the total cost line will be steeper and the breakeven point will occur at a higher volume. NICE TO KNOW BUT WE WON’T BE USING GRAPHICAL METHOD BUT (A), (B) & (C) MAYBE A MULTLIPLE CHOICE QUESTION CostVolumeProfit (CVP): Incremental Analysis: An incremental analysis focuses on the changes in revenue, cost, and volume that will result from a particular action. Types of CVP Analysis: 1. Target profit analysis used to determine how much the company would have to sell to attain a specific target profit. Profits = (Sales – Variable Expenses) Fixed expenses Can be rewritten as follows: Sales = Variable expenses + Fixed expenses + Profits Illustration Racing Example using CVP Equation Method Company wants to know how many bikes it must sell to earn a profit of $100,000. Sales = Variable expenses + Fixed expenses + Profits $ 500Q = $ 300Q + $80,000 + $100,000 $200Q = $180,000 900 bikes Q = Alternative Method (The Contribution Margin Approach)
Unit sales to attain = Fixed expenses + Target Profit Target Profit Unit Contribution Margin Racing Bicycle Company Contribution Income Statement For the Month of September Total Per Unit % Sales (500 Bicycles) Less Variable Costs Contribution margin Less: Fixed Expenses Net income $ 250,000 <150,000> 100,000 <80,000> $ 20,000 $ 500 100 % <300> <60> $ 200 40 % Solution Unit sales to attain = Fixed expenses + Target Profit the Target Profit Unit contribution margin X X = = $ 80,000 + $ 100,000 $ 200/bike 900 Bikes Margin of Safety The margin of safety is the excess of budgeted (or actual) sales over the breakeven volume of sales. It is the amount by which sales can drop before losses begin to be incurred. Margin of Safety = Total sales BEP Sales Illustration: Bike Company If Racing has actual sales of $250,000, what is the margin of safety? Margin of safety = $ 250,000 $ 200,000 = $ 50,000 Alternative Solution Or as a % of Sales
Margin of Safety = $ 50,000 $ 250,000 = 100 bikes Degree of Operating Leverage The degree of operating leverage is computed by dividing the contribution margin by the net operating income at a given level of sales. It can be used to estimate the impact on net operating income of a given percentage change in sales. Degree of Operating Leverage = Contribution Margin Net operating income Illustration If Racing has actual sales of $250,000, a contribution margin of $100,000 and a net operating income of $20,000 the degree of operating leverage would be as follows: Racing Bicycle Company Contribution Income Statement For the Month of September Actual Sales Sales (500 Bicycles) Less Variable Costs Contribution margin Less: Fixed Expenses Net income $ 250,000 <150,000> 100,000 < 80,000> $ 20,000 Illustration continued
DOL = $ 100,000 $ 20,000 = 5 Observation Note: With an operating leverage of 5, if Racing increases its sales by 10%, net operating income would increase by 50% Percent increase in sales Degree of operating leverage x Percentage increase in profits 5 50 % 10 % Proof
Racing Bicycle Company Contribution Income Statement For the Month of September Actual Sales 500 Increased Sales 550 Sales (500 Bicycles) $ 250,000 $ 275,000 Less Variable Costs <150,000> <165,000> Contribution margin 100,000 110,000 Less: Fixed Expenses < 80,000> <80,000> Net income $ 20,000 $ 30,000 OBSERVATION #2 A 10% INCREASE IN SALES FROM $250,000 TO $275,000 RESULTS IN A 50% INCREASE IN INCOME $20,000 TO $30,000. Sales Mix The sales mix is the relative proportions in which a company’s products are sold. The usual assumption in costvolumeprofit analysis is that the sales mix is constant. Different products have different selling prices, cost structures, and contribution margins. If the sales mix shifts from high contribution margin products to low contribution margin products, the company will have a lower average contribution margin ratio. Unless sales increase, this would result in less total contribution margin and lower net operating income. With a lower contribution margin ratio, the formula for the breakeven point shows that the breakeven point would be higher. See Problem #3. Key Assumptions of CVP Analysis Selling price is constant. Costs are linear. In multiproduct companies, the sales mix is constant. In manufacturing companies, inventories do not change (units produced = units sold). Problem #1 Hardee Company sells a single product. The selling price is $30 per unit and the variable expenses are $18 per unit. The company’s most recent annual contribution format income statement is given below: Sales Less variable expenses Contribution margin Less fixed expenses Net operating income $ 135,000 81,000 54,000 48,000 $ 6,000 Required Compute the contribution margin per unit. Compute the CM ratio. Compute the breakeven point in sales dollars. Compute the breakeven point in units sold. How many units must be sold next year to double the company’s profits. Compute the company’s degree of operating leverage. Sales for next year (in units) are expected to increase by 5%. Using the degree of operating leverage, compute the expected percentage increase in net operating income. Verify your answer to part g above by preparing a contribution format income statement showing 5% increase in sales. Solutions a & b a. Selling price Less: variable expenses Unit contribution margin Per Unit $ 30 18 $ 12 % 100 % 60 40 % b. CM ratio = Contribution Margin Sales = $ 54,000 $ 135,000 Solution c Sales = Variable Expenses + Fixed Exp. + Profits C. X = 0.60X + $48,000 + $0 0.40X = $48,000 X = $48,000/0.40 X = $ 120,000 Alternative Solution c Alternative solution: BEP = Fixed expenses In Total Sales CM Ratio = $ 48,000 0.40 = $ 120,000 Solution d d. Sales = Variable expenses + Fixed Expenses + Profits $30Q = $18Q + $48,000 + $0 $12Q = $48,000 Q = $48,000/$12 per unit Q = 4,000 units Solution d Alternative solution: Breakeven Point = Fixed Expenses in units sold CM Ratio = $48,000 0.40 = 4,000 units Solution e e. Sales = Variable expenses + Fixed Expenses + Profits $30Q = $18Q + $48,000 + 12,000 $12Q = $60,000 Q = $60,000/$12 per unit Q = 5,000 units Alternative Solution e Alternative solution: Units sold to = Fixed Exp. + Target Profit Attain Target Profit Unit Contribution Margin = $46,000 + $12,000 $12 per unit = 5,000 units Solution f Degree of operating = Contribution margin leverage Net Income = $ 54,000 $ 6,000 = 9.0 f. Solution g Percentage change in dollar sales 5 % Degree of operating leverage x 9.0 Percentage change in net operating income 45 % g. Solution h h. New sales volume: $4,500 units x 105% = 4,725 units $ 141,750 <85,050> 56,700 <48,000> $ 8,700 $ 6,000 2,700 $ 8,700 Sales (4,725 units @ $30 per unit) Less: variable expenses (4,725 units @ $18/unit) Contribution margin Less: fixed expenses Net operating income Present net operating income Expected increase: ($6,000 x 45%) Expected net operating income (as above) Problem #2 Using the data below, construct a costvolume profit graph like the one in Exhibit 62 in the text:
– – – Selling price: Variable expenses: Fixed expenses: $10 per unit $ 6 per unit $40,000 total What is the breakeven point in units? What is the breakeven point in total sales dollars? Solution
Breakeven Point = Fixed expenses . in units sold Unit Contribution Margin = $ 40,000 . $ 4 per unit 10,000 units = Solution – part 2
Breakeven Point = Fixed expenses in total sales $ CM ratio* = $ 40,000 0.40 = $ 100,000 * CM ratio = Contribution margin Sales Solution – part #2 The breakeven point is 10,000 units or $100,000 in dollar sales. PROBLEM #3 Seaver Company produces and sells two products, X and Y. Data concerning the products follow: Product X Product Y $ 12 < 3> $9 Selling price/unit Variable Exp./unit CM* per unit $ 10 <6> $4 *Contribution Margin Required
In the most recent month, the company sold 400 units of Product X and 600 units of Product Y. Fixed expenses are $5,000 per month. Complete the following contribution format income statement for the most recent month (carry percentages to one decimal point). Compute the company’s overall monthly breakeven point in sales dollars. If the company continues to sell 1,000 units, in total, each month, but the sales mix shifts so that an equal number of units of each product is being sold, would you expect monthly net operating income to rise or fall? Explain. Refer to the data in part c above. If the sales mix shifts as explained, would you expect the company’s monthly breakeven point to rise or fall. Explain. Solution a Completed income statement Product Y Amount % Total Amount % Product X Amount % Sales $ 4,000 100 $ 7,200 100 $ 11,200 100.0 Less: variable cost <2,400> <60> <1,800> < 25> <4,200> 37.5 Contribution Margin $ 1,600 40 $ 5,400 75 $ 7,000 62.5 Less: Fixed exp. <5,000> Net operating income $ 2,000 Solution b Breakeven Point = Fixed Expenses in Total Sales $ CM ratio = $ 5,000 0.625 = $ 8,000 Solution c Monthly net operating income will fall. The shift in sales mix will mean that less of Product Y is being sold and more of Product X is being sold. Since Product Y has a higher contribution margin per unit than Product X, this means that less contribution margin in total will be available, and profits will therefore fall. Solution d The monthly breakeven point will rise. As explained above, the shift in sales mix will be toward the less profitable Product X, which has a CM ratio of only 40% as compared to 75% of Product Y. Thus, the company’s overall CM ratio will fall, and the breakeven point will rise since less contribution margin will be available per unit to cover the fixed costs. ...
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 Fall '09
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 Contribution Margin, Racing Bicycle Company

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