Alternative 1. Use 20,000 units as a denominator; fixed manufacturing overhead per unit is $280,000 ÷20,000 = $14. 2012 2013 Together Revenues $300,000$ 300,000$600,000Cost of goods sold Beginning inventory 0 140,000*0 Allocated fixed manufacturing costs at $14 280,000 — 280,000 Deduct ending inventory (140,000) — — Adjustment for production-volume variance0280,000U 280,000U Cost of goods sold 140,000420,000560,000Gross margin 160,000 (120,000) 40,000 Operating costs 40,00040,00080,000Operating income $120,000$(160,000) $ (40,000) * Inventory carried forward from 2012 and sold in 2013.

9-26 Alternative 2. Use 10,000 units as a denominator; fixed manufacturing overhead per unit is $280,000 ÷10,000 = $28.

0

—

0

)

2. costingableunder varipointBreakeven = per tonmargin on ContributicostsFixed= $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 2012 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 2012?”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 2012, 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):

9-27 Let P = Production level Breakevensalesin units= marginon contributiUnit producedUnitsunitsinsalesBreakevenrateoverheadmanuf.FixedincomeoperatingTargetcostsfixedTotal⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−×⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛+⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛+⎟⎟⎠⎞⎜⎜⎝⎛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 40,000159,994Operating income (due to rounding) $ Given that production would be 20,000 tons in 2012, 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 = marginon contributiUnit producedUnitsNrateoverheadmanuf.Fixed

+

6