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Note that operating income under variable costing

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Note that operating income under variable costing follows sales and is not affected by inventory changes. Note also that students will understand the variable-costing presentation much more easily than the alternatives presented under absorption costing. 9-27
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2. Breakeven point under variable costing = per ton margin on Contributi costs Fixed = $30 $320,000 = 10,667 (rounded) tons per year or 21,334 for two years. If the company could sell 667 more tons per year at $30 each, it could get the extra $20,000 contribution margin needed to break even. Most students will say that the breakeven point is 10,667 tons per year under both absorption costing and variable costing. The logical question to ask a student who answers 10,667 tons for variable costing is: “What operating income do you show for 2008 under absorption costing?” If a student answers $120,000 (alternative 1 above), or $260,000 (alternative 2 above), ask: “But you say your breakeven point is 10,667 tons. How can you show an operating income on only 10,000 tons sold during 2008?” The answer to the above dilemma lies in the fact that operating income is affected by both sales and production under absorption costing. Given that sales would be 10,000 tons in 2008, solve for the production level that will provide a breakeven level of zero operating income. Using the formula in the chapter, sales of 10,000 units, and a fixed manufacturing overhead rate of $14 (based on $280,000 ÷ 20,000 units denominator level = $14): Let P = Production level = margin on contributi Unit produced Units units in sales Breakeven rate overhead manuf. Fixed income operating Target costs fixed Total - × + + 10,000 tons = 30 $ ) 000 10 ( 14 $ 0 $ 000 320 $ P - + + $300,000 = $320,000 + $140,000 – $14P $14P = $160,000 P = 11,429 units (rounded) Proof: Gross margin, 10,000 × ($30 – $14) $160,000 Production-volume variance, (20,000 – 11,429) × $14 $119,994 Marketing and administrative costs 40,000 159,994 Operating income (due to rounding) $ 6 9-28
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Given that production would be 20,000 tons in 2008, solve for the breakeven unit sales level. Using the formula in the chapter and a fixed manufacturing overhead rate of $14 (based on a denominator level of 20,000 units): Let N = Breakeven sales in units N = margin on contributi Unit produced Units N rate overhead manuf. Fixed income operating Target costs fixed Total - × + + N = $320,000 + $0 + $14(N 20,000) $30 - $30N = $320,000 + $14N – $280,000 $16N = $40,000 N = 2,500 units Proof: Gross margin, 2,500 × ($30 – $14) $40,000 Production-volume variance $ 0 Marketing and administrative costs 40,000 40,000 Operating income $ 0 We find it helpful to put the following comparisons on the board: Variable costing breakeven = f(sales) = 10,667 tons Absorption costing breakeven = f(sales and production) = f(10,000 and 11,429) = f(2,500 and 20,000) 3. Absorption costing inventory cost: Either $140,000 or $280,000 at the end of 2008 and zero at the end of 2009.
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