# 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.

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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.

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).

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?

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

3 - 5 Example of Relationships For a particular item, Unit Price\$2.50 100% Unit VC 1.75 70% (VC%) Unit CM\$.75 30% (CM%)

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]

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

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.

3 - 9 Product-Mix Problem PRODUCT PRODUCT A B C A B C Price \$10 \$15 \$25The Weighted VC 8 7 10Average CM% CM \$ 2 \$ 8 \$15will depend on actual mix sold CM% 20% 53.33% 60%

3 - 10 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 5000 10000 15000 30000 Sales \$50,000 150,000 375,000 575,000 1.000 VC 40,000 70,000 150,000 260,000.452 CM 10,000 80,000 225,000 315,000.548

3 - 11 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.20 + 10/30 x.533 + 15/30 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

3 - 12 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.

3 - 13 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

3 - 14 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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