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3 - 1 Preview of Chapter 3 Cost-Volume-Profit (CVP) Analysis Purpose Purpose To model how revenues and costs (and profit!) will behave during a given period of time, depending upon the level of activity.

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3 - 2 CVP Model Assumes a contribution margin income statement: Contribution Mgn Approach vs Absorption Costing Sales 100% Sales Sales 100% Sales - Variable Costs: - VC% - CGS (Var. CGS, Selling, Admin.) = Gross Margin = Cont. Margin = CM% - Period Costs - Fixed Costs: (Selling, Admin.) (Mfg., Selling, Admin.) (Mfg., Selling, Admin.) Operating Income Operating Income Operating Income Operating Income Same only if inventories are constant (production = sales).

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3 - 3 Questions Besides “Where’s the breakeven point,” other questions are of more interest: How will the BEP increase if FC or VC increases? How much higher could VC/unit rise before we’d have a loss for the period? How far could sales drop below the forecast before Operating Income would fall below last year’s?

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3 - 4 Equations For CVP Analysis Graphs are for exposition only. We must solve using equations. A “definitional” equation, defining income: Sales – Var Cost – Fixed Cost = Operating Income – Good starting point to attack unusual CVP questions

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3 - 5 Example of Relationships For a particular item, Unit Price$ % Unit VC % (VC%) Unit CM$.75 30% (CM%)

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3 - 6 Equations For CVP Analysis Recognizing that VC and CM are % of sales: Sales – (VariableCost%)Sales – FixedCost = Operating Income Contribution Margin {OR} {OR} Sales x (CM%) – FC = Operating Income CM CM If FC = $10,000, how many must we sell to BE? S -.7S – 10,000 = 0.3S = 10,000.3S = 10,000 S = $33,333 [÷ $2.50 = 13,333 units] S = $33,333 [÷ $2.50 = 13,333 units]

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3 - 7 Other Handy Equation Forms Sales Dollars = (FC + Oper. Inc.) / CM% Units Sold = (FC + Oper. Inc.) / (CM per unit)

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3 - 8 Wide Applicability of CVP CVP applies to any question about proposed changes in cost structures and related volume effects. »Widely applicable. »Assigned problems are representative.

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3 - 9 Product-Mix Problem PRODUCT PRODUCT A B C A B C Price $10 $15 $25The Weighted VC Average CM% CM $ 2 $ 8 $15will depend on actual mix sold CM% 20% 53.33% 60%

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Product-Mix Problem Weighted Average based on previous year’s results (assumed numbers): A B C Tot. Wtd Avg A B C Tot. Wtd Avg Units Sold Sales $50, , , , VC 40,000 70, , , CM 10,000 80, , ,

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Product-Mix Problem What’s wrong with the following approach? Product mix is 5/30 “A”, 10/30 “B” and 15/30 “C” So 5/30 x /30 x /30 x.60 =.511 ≠.548 Error: Done in terms of units, but the CM% is contribution/$, not contribution/unit! contribution/$, not contribution/unit!Correct: (50/575)(.20) + (150/575)(.533) + (375/575)(.60) =.548 (50/575)(.20) + (150/575)(.533) + (375/575)(.60) =.548

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Considering Income Tax Recall the “definitional” equation, defining income: Sales – Var Cost – Fixed Cost = Operating Income (1-r)*(Sales – Var Cost – Fixed Cost) = Income after tax Sales – Var Cost – Fixed Cost = (Income after tax)/ (1-r) So, divide desired after-tax income by (1-r) to get the desired before-tax income and use the formulas as usual.

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Effect of Income Taxes Any amount “after tax” or net of taxes = (1-r) (The amount before taxes) (1-r) (The amount before taxes) [Applies to an expense, revenue, or Operating Income] [Applies to an expense, revenue, or Operating Income] $1,000 expense is tax deductible So at 40% rate: (1-.4) 1,000 = $600 net expense $1,000 revenue is taxable So at 40% rate: (1-.4) 1,000 = $600 net So at 40% rate: (1-.4) 1,000 = $600 net

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Effect of Income Taxes All numbers in the CVP equations are before tax. Therefore questions involving “after tax” effects require you to convert to “before tax” before using the equation. Ex. How many units sold to earn $900,000 after tax at a 45% tax rate? AT amt. = (1-r) BT amt. 900,000 = (1-.45) BT amt. BT amt. = 900,000/.55 = $1,636,364 Thus, using my Eq. 4: Units = FC + 1,636,364 CM/unit CM/unit

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