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CHAPTER 20
DISCUSSION QUESTIONS
20-1
Q20-1. Direct costs are direct materials, direct labor,and other costs directly assignable to a product.Direct costing is a procedure by which onlyprime costs plus variable factory overheadare assigned to a product or inventory; allfixed costs are considered period costs.
Q20-2. Product costs are associated with the manu-facture of a product and include direct materi-als, direct labor, and factory overhead. Thesecosts are charged against revenue as cost ofgoods sold, or shown on the balance sheet asinventories of work in process and finishedgoods. Period costs are associated with thepassage of time and are included as expensesin the income statement. Under direct costing,fixed factory overhead is treated as a periodcost rather than as a product cost.
Q20-3. Under direct costing, only variable manufactur-ing costs are included in inventory. Underabsorption costing (the current, generallyaccepted method of costing inventory for exter-nal reporting), all manufacturing costs, bothvariable and fixed, are included in inventory.
Q20-4. It is argued that fixed manufacturing costs arethe expenses of maintaining productivecapacity. Such expenses are more closelyassociated with the passage of time than withproduction activity and should, therefore, becharged to period expense rather than to theproduct.
Q20-5. The direct costing method is useful for inter-nal reporting because it focuses attention onthe fixed-variable cost relationship and thecontribution margin concept. It facilitates man-agerial decision making, product pricing, andcost control. It allows certain calculations tobe readily made, such as break-even pointsand contribution margins of products, salesterritories, operating divisions, etc. The focuson the contribution margin (sales revenueless variable costs) enables management toemphasize profitability in making short-runbusiness decisions. Fixed costs are not easilycontrollable in the short run and hence maynot be particularly relevant for short-run busi-ness decisions.
Q20-6. Arguments for the use of direct costinginclude the following:(a) For profit-planning and decision-making
purposes, management requires cost-volume-profit relationship data that aremore readily available from direct coststatements than from absorption coststatements.
(b) Since fixed factory overhead is absorbedas a period cost, fluctuations in produc-tion and differences between the numberof units produced and the number sold donot affect the per unit product cost.
(c) Direct costing reports are more easilyunderstood by management because thestatements follow management’s deci-sion-making processes more closely thando absorption cost statements.
(d) Reporting the total fixed cost for theperiod in the income statement directsmanagement’s attention to the relation-ship of such cost to profits.
(e) The elimination of allocated joint fixed costpermits a more objective appraisal ofincome contributions according to prod-ucts, sales areas, kinds of customers, etc.Cost-volume relationships are highlighted.
(f) The similarity of the underlying conceptsof direct costing and flexible budgets facil-itates the adoption and use of thesemethods for reporting and cost control.
(g) Direct costing provides a means of costinginventory that is similar to management’sconcept of inventory cost as the currentout-of-pocket expenditures necessary toproduce or replace the inventory.
(h) Clerical costs are lower under direct cost-ing because the method is simpler anddoes not require involved allocations offixed costs or special analyses of absorp-tion data.
(i) The computation of product costs is sim-pler and more reliable under direct costingbecause a basis for allocating the fixedcosts, which involves estimates and per-sonal judgment, is eliminated.
Q20-7. Arguments against the use of direct costinginclude the following:(a) Separation of costs into fixed and variable
might be difficult, especially when suchcosts are semivariable in nature.Moreover, all costs—including fixedcosts—are variable at some level of pro-duction and in the long run.
(b) Long-range pricing of products and otherlong-range policy decisions require aknowledge of complete manufacturingcost, which would require additional sep-arate computations to allocate fixed over-head.
(c) The pricing of inventories by the directcosting method is not acceptable forincome tax computation purposes.
(d) Direct costing has not been recognizedas conforming with generally acceptedaccounting principles applied in thepreparation of financial statements forstockholders and the general public.
(e) Profits determined by direct costing are not“true and proper” because of the exclusionof fixed production costs that are part oftotal production costs and inventory.Production would not be possible withoutplant facilities, equipment, etc.To disregardthese fixed costs violates the general prin-ciple of matching costs with revenue.
(f) The elimination of fixed costs from inven-tory results in a lower figure and conse-quent reduction of reported workingcapital for financial analysis purposes.
Q20-8. Assuming that the quantity of ending inven-tory is larger than the quantity of beginninginventory and the lifo method is used, operat-ing income using direct costing would besmaller than operating income using absorp-tion costing. Direct costing excludes fixed fac-tory overhead from inventories because suchcosts are considered to be period costs whichare expensed when incurred. In contrast,absorption costing includes fixed factory over-head in inventories because such costs areconsidered to be product costs, which areexpensed only when the products are sold.When the quantity of inventory increases dur-ing a period, direct costing produces a lowerdollar increase in inventory than absorptioncosting, because fixed costs are expensedrather than charged to inventory. Since asmaller amount of current period cost is
charged against income under the absorptioncosting method when inventories increase,absorption costing income would be largerthan direct costing income.
Q20-9.The break-even point is the point at whichcosts and revenue are in equilibrium, showingneither profit nor loss for the business.
Q20-10.The contribution margin is the result of sub-tracting variable cost from the sales figure. Thecontribution margin indicates the amount avail-able for the recovery of fixed cost and for profit.
Q20-11.(a) R(BE) = F1 – V
or (in words):Revenue at the = Total fixed costbreak-even point Contribution margin
per dollar of sales(b) Q(BE) = F
P – Cor (in words):Units of sales at = Total fixed costbreak-even point Contribution margin
per unit of salesQ20-12. (1) Dollars of revenue and costs.
(2) Volume of output, expressed in units, per-cent of capacity, sales, or some othermeasure.
(3) Total cost line.(4) Variable cost area.(5) Fixed cost area.(6) Break-even point.(7) Loss area.(8) Profit area.(9) Sales line.
Q20-13.An analysis of the expected behavior of afirm’s expenses and revenue for the purposeof constructing a break-even chart is usuallyrestricted to the output levels at which the firmis likely to operate. Assumptions about thelevel of fixed cost, the rate of variable cost,and sales prices are based on the operatingconditions and managerial policies that will bein effect over the expected output levels.These expected output levels represent thefirm’s relevant range, and the cost-volume-profit relationships shown in a break-evenchart are applicable only to output levelswithin this range. The behavior of fixed cost,variable cost, and sales prices at levels of out-put below or above the relevant range arelikely to result in an entirely different set ofcost-volume-profit relationships because of
20-2 Chapter 20
changed operating conditions or managerialpolicies. The fact that the cost and revenuelines on a break-even chart are typicallyextended past the upper and lower limits ofthe relevant range should not, therefore, beinterpreted to mean that they are valid forthese levels of output.
A break-oven chart showing cost-volume-profit relationships for all levels of output couldbe developed. The shapes of the cost and rev-enue lines in such a chart could not, however,be expected to approximate straight-line (lin-ear) patterns. By restricting the underlying costand revenue behavior assumptions in break-even analyses to a relatively narrow outputrange (the range over which the firm is likely tooperate), it is usually possible to assume linearbehavior patterns without any significant distor-tions in cost-volume-profit relationships,thereby simplifying the analysis.
If the range over which a firm is likely tooperate is quite wide, curvilinear functionsmay be employed; or it may be desirable todevelop a number of break-even charts, eachhaving its own relevant range, for which theunderlying cost and revenue behaviorassumptions are valid.
Q20-14. Weaknesses inherent in the preparation anduse of break-even analysis are:(a) When more than one product is pro-
duced, the contribution margin of eachproduct will probably differ. Accordingly, abreak-even analysis for the whole opera-tion will not indicate the contribution ofeach product to fixed cost and the volumerequired for each product.
(b) Some costs are almost impossible toclassify conclusively as being either fixedor variable.
(c) General economic conditions and otherexternal factors may affect the data usedin the analysis.
(d) In the final analysis, fixed cost is related toproduction and sales and, therefore, maydecrease somewhat due to decreasedproduction and sales—and vice versa.
(e) Quite often costs increase sharply at cer-tain points in production and sales levelsand then level out until a certain greaterstage of production and/or sales isreached, at which time the phenomenonis repeated as production and/or salesare again increased.
(f) Performance must be constantly com-pared to the break-even analysis in orderto determine whether the conditions thatexisted at the time of the calculationshave held true, and whether any changeshave been considered.
Q20-15. (a) With sales price per unit and total fixedcost remaining constant, the break-evenpoint moves up rapidly as unit variablecost is increased; at the same time, thebreak-even point moves down as unitvariable cost is decreased.
(b) A decrease in fixed cost lowers the break-even point. An increase in fixed costmoves the break-even point higher.
Q20-16. The margin of safety is a selected sales figureless break-even sales. The margin of safety isa cushion against sales decreases. Thegreater the margin, the greater the cushionagainst suffering a loss.
Q20-17. Cost-volume-profit relationship is the relation-ship of profit to sales volume.This relationshipis important to management because man-agement tries at all times to keep volume,cost, price, and product mix in a ratio that willachieve a desired level of profit.
Q20-18. The Theory of Constraints is a specializedversion of direct costing for use in short-runoptimization decisions. A distinction betweenTOC and direct costing is that TOC focuseson only the purely variable costs and does notconsider direct labor to be purely variable.
Q20-19. Most companies that classify costs into fixedand variable categories treat direct labor asvariable, so in direct costing, direct labor isassigned to products as a variable or incre-mental cost of production. In the Theory ofConstraints, direct labor is stipulated to be notpurely variable and therefore is not treated asan incremental cost of output.
The difference between the contributionmargin measure in direct costing and thethroughput measure in TOC is that directlabor is one of the costs deducted from salesto calculate contribution margin, but directlabor is not a cost to be deducted from salesin calculating throughput.
There are many differences in emphasisbetween direct costing and the Theory ofConstraints. For example, while direct cost-ing is widely used as an accountingapproach for internal reporting of incomeand product cost, TOC deals heavily with the
Chapter 20 20-3
improvement of constraints or bottlenecks in aproduction system.
Q20-20. Throughput is the rate at which a system gen-erates money through sales. It is calculatedas sales minus the purely variable costs, andoften the only purely variable cost is the costof materials.
Q20-21. Elevating a constraint means improving theconstraint—improving the conditions at a bot-tleneck in the system. Its significance is great-est if the constraint is the tightest one in the
system; there, any improvement will increasethe total throughput of the entire system.
An improvement in product quality can helpelevate a constraint because it can reduce theworkload on a bottleneck resource. For exam-ple, removing defective units before ratherthan after they reach the bottleneck meansthere will be fewer units passing through thebottleneck. This has approximately the sameeffect on the bottleneck as increasing itscapacity.
20-4 Chapter 20
EXERCISES
E20-1
Operating income for 20A using direct costing:Sales (90,000 × $12) .................................................................. $1,080,000Variable cost of goods sold (90,000 × $4) .............................. 360,000Gross contribution margin....................................................... $ 720,000Variable marketing and administrative expenses
(90,000 × $20) ................................................................ 18,000Contribution margin.................................................................. $ 702,000Less fixed expenses:
Factory overhead........................................ $200,000Marketing and administrative expenses .. 90,000 290,000
Operating income...................................................................... $ 412,000
E20-2
(1) Variable cost per unit:$7,000,000 total variable cost
60% manufacturing cost portion$4,200,000 total variable manufacturing cost
$4,200,000 total variable manufacturing cost140,000 units actually produced
= $30 per unit
Fixed cost per unit:$11,200,000 total fixed cost
50% manufacturing cost portion$5,600,000 total fixed factory overhead
$5,600,000 total fixed factory overhead160,000 units normal production volume
= 35 per unit
Full cost per unit at standard $65Number of units sold during the year × 100,000Cost of goods sold at standard under
absorption costing $6,500,000
(2) Units actually produced during the year.................... 140,000Units sold during the year ........................................... 100,000Unit increase in inventory ........................................... 40,000Standard variable manufacturing cost per unit......... × 30Ending inventory at standard direct cost .................. $1,200,000
Chapter 20 20-5
E20-2 (Concluded)
(3) Normal production volume..................................................... 160,000Units actually produced during the year .............................. 140,000Excess of budget over actual production............................. 20,000Fixed factory overhead per unit............................................. × $35Factory overhead volume variance ....................................... $ 700,000
(4) Sales (100,000 units × $180)................................................... $18,000,000Standard variable cost of goods sold (100,000 units × $30
unit variable cost)........................................................... 3,000,000Gross contribution margin ..................................................... $15,000,000Variable selling expense ($7,000,000 variable cost × 40%). 2,800,000Contribution margin................................................................ $12,200,000Less fixed costs ...................................................................... 11,200,000Operating income under direct costing................................ $1,000,000
E20-3
(1) Income statement using absorption costing:Sales (9,000 × $30) .................................................................. $270,000Cost of goods sold (9,000 × ($10 + $5)) ................................ 135,000Gross profit .............................................................................. $135,000Less commercial expenses.................................................... 44,000Operating income.................................................................... $ 91,000
(2) Income statement using direct costing:Sales (9,000 × $30) .................................................................. $270,000Variable cost of goods sold (9,000 × $10)............................. 90,000Contribution margin................................................................ $180,000Less fixed expenses:
Factory overhead .................................. $40,000Commercial expenses .......................... 44,000 84,000
Operating income.................................................................... $ 96,000
(3) Computations explaining the difference in operating income:Absorption costing operating income .................................. $ 91,000Direct costing operating income ........................................... 96,000Difference................................................................................. $ (5,000)
Units produced during the period ......................................... 8,000Units sold during the period .................................................. 9,000Unit decrease in finished goods inventory ......................... (1,000)Fixed factory overhead charged to each unit of product
under absorption costing.............................................. × $5Difference................................................................................. $ (5,000)
20-6 Chapter 20
E20-4
$10,000 ÷ $2 = 5,000 break-even point in units(or)
E20-5
Materials................................................................................... $ 1.00Direct labor .............................................................................. 1.20Variable factory overhead....................................................... .50Variable marketing expense ................................................... .30Total variable cost per unit..................................................... $ 3.00
Sales price per unit ................................................................. $ 5.00Variable cost per unit.............................................................. 3.00Contribution margin per unit.................................................. $ 2.00
Fixed factory overhead........................................................... $15,000Fixed marketing expense ....................................................... 5,000Fixed administrative expense ................................................ 6,000Total fixed expense ................................................................. $26,000
(1) $26,000 total fixed cost $2 contribution margin
= 13,000 units of sales to break even
(2) 13,000 units × $5 per unit = $65,000 sales to break even
(3) $26,000 fixed cost + $10,000 profit$2 contribution margin
= 18,000 units
(4) 18,000 units × $5 per unit = $90,000 sales
E20-6
Planned sales .......................................................................... $2,000,000Break-even sales ..................................................................... 1,500,000Margin of safety....................................................................... $ 500,000
$ ,$ , $.
$ ,$ .
,6 000
2 00 806 0001 20
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= = break-even point in units
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$ ,$ .
$ .
$ ,.
$ ,.
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1 802 00
6 0001 40
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Chapter 20 20-7
E20-6 (Continued)
$500,000 Margin of safety = 25% Margin of safety ratio$2,000,000 Planned sales
E20-7
(1)
(2)
(3) PR = C/M × M/S; PR = .62 × .25 = .155$20,000 × .155 = $3,100 profit for the month
E20-8
(1)
(2)
PR = C/M × M/S; PR = .20 × .60 = .12$62,500 × .12 = $7,500 profit for the year
(3) Sales ......................................................................................... $62,500Variable cost ($62,500 × (1 – .60)).......................................... 25,000Contribution margin ($62,500 × .60) ...................................... $37,500
E20-9
Chip A Chip B TotalSales:
(100,000 × $8)....................................... $800,000(200,000 × $6)....................................... $1,200,000 $2,000,000
Variable cost:($800,000 × 30%).................................. 240,000
($1,200,000 × 25%)............................... 300,000 540,000Contribution margin......................................... $560,000 $ 900,000 $1,460,000
Planned operating profit ................................. 270,000Fixed cost ......................................................... $1,190,000
$ ,.
$ ,.
$ ,50 0001 20
50 00080
62 500−
= = sales for the year
$ ,.
$ ,30 000
6050 000= break-even sales
$ ,.
$ ,.
$ ,15 0001 25
15 00075
20 000−
= = actual sales
$ ,.
$ ,9 300
6215 000= break-even point sales
20-8 Chapter 20
E20-10
Tables ChairsSales price per unit ...................................................... $110 $35Variable cost per unit ................................................... 50 20Contribution margin per unit....................................... $ 60 $15
or alternatively:
or alternatively:
6,000 packages × 1 table per package = 6,000 tables to break even6,000 packages × 4 chairs per package = 24,000 chairs to break even6,000 tables × $110 per table.............. = $ 660,00024,000 chairs × $ 35 per chair ............ = 840,000Total sales to break even.................... $1,500,000
E20-11
Product L Product MSales price per unit ............................. $20 $15Variable cost per unit.......................... 12 10Unit contribution margin .................... $ 8 $ 5Expected sales mix ............................. × 2 × 3Contribution margin per
hypothetical package................. $16 + $15 = $31
$ ,$ ( $ )
,720 00060 4 15
6 000fixed cost
CMhypothetical packages
+ ×=
$ ,($ ( $ )) ($ ( $ ))
$ , ,720 000
60 4 15 110 4 351 500 000
fixed costsa
+ × ÷ + ×= lles to break even
saleshypotheti
$ , ,$ ( $ )
,1 500 000110 4 35
6 000+ ×
= ccal packages
$ ,((($ ( $ )) ($ ( $ )))
$ , ,720 000
1 50 4 20 110 4 351 500
fixed cost− + × ÷ + ×
= 0000 sales to break even
Chapter 20 20-9
E20-11 (Concluded)
(1) $372,000 fixed cost$31 contribution margin
= 12,000 packages to break even
12,000 packages × 2 units of L = 24,000 units of L12,000 packages × 3 units of M = 36,000 units of M24,000 units of L × $20 = $ 480,000 sales of L36,000 units of M × $15 = 540,000 sales of MBreak-even sales....................................................... $1,020,000
(2) $372,000 fixed cost + $93,000 profit$31 contribution margin
= 15,000 packages to achieve profit
15,000 packages × 2 units of L = 30,000 units of L15,000 packages × 3 units of M = 45,000 units of M30,000 units of L × $20 = $600,000 sales of L45,000 units of M × $15 = 675,000 sales of MSales to achieve profit.............................................. $1,275,000
E20-12
(1) Variable manufacturing cost............................................................... $210,000Fixed manufacturing cost ................................................................... 80,000Variable marketing expense................................................................ 105,000Fixed marketing and administrative expenses ................................. 60,000Total costs to produce and sell 70,000 units .................................... $455,000
$455,000 total cost = $6.50 sales price per unit to break even70,000 units
(2) ($80,000 + $60,000) fixed cost = 51,852 units$8 – $4.50 – (10% × $8)
(3) ($147,000 + $60,000) fixed cost = 90,000 units$8 – $4.50 – (15% × $8)
CGA-Canada (adapted). Reprint with permission.
20-10 Chapter 20
Chapter 20 20-11
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E20
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E20-14
(1) throughput/unit = sales – materials cost = $45 – ($14 + $1) = $30
(2) Maximum throughput per month is $144,000. Total throughput for a period is the$30/unit (from requirement 1) multiplied by the number of units shipped; unitsare limited by the lowest-capacity operation, which is Surface Prep’s 4,800 unitsper month: 4,800 units/month × $30/unit = $144,000/month.
(3) Surface Prep is the tightest constraint, with a 4,800-unit capacity.
E20-15
(1) No, they should not acquire the equipment. Gloss Coat is not the tightest con-straint, so increasing its capacity will not help.
(2) Zero. Maximum monthly throughput will not increase.
(3) Yes, an additional Surface Prep (SP) crew should be hired. The increase in over-all throughput more than justifies the cost.
(4) Maximum throughput will increase by about $15,000 per month (500 units/month× $30/unit). SP is the tightest constraint, so increasing its capacity will increasethroughput of the entire system until SP’s improvement causes another con-straint to become the tightest. Gloss Coat, the second-tightest constraint,presently has capacity 500 units higher than SP’s.
E20-16
(1) Yes, an inspection should be created just prior to Surface Prep (SP). For each1,000 shipped, 50 defectives enter SP—26, 14, and 10 arising in the three preced-ing operations, respectively. SP is the tightest constraint, so removing defec-tives prior to SP will increase total system throughput. At $30 throughput perunit, the 50 added units (per thousand shipped) do justify the added inspection.
(2) Removing all defectives just prior to SP will increase the number of good unitsentering SP by 50/1,000 or about 5%. With SP presently handling 4,800 units permonth, a 5% increase in units shipped is .05 × 4,800 = 240. Additional through-put will be 240 units/month × $30/unit = $7,200 per month. Because the inspec-tion will cost $1,800 per month, the monthly advantage of the added inspectionoperation will be $7,200 minus $1,800, or $5,400 per month.
20-12 Chapter 20
PROBLEMS
P20-1TAYLOR TOOL CORPORATIONProduct-Line Income Statement(Contribution Margin Approach)
Electronic Pneumatic HandTotal Tools Tools Tools
Sales....................................................... $3,000,000 $1,500,000 $1,000,000 $500,000Less variable cost of goods sold ........ 1,400,000 700,000 500,000 200,000
Gross contribution margin................... $1,600,000 $ 800,000 $ 500,000 $300,000Less variable marketing expenses
(packing and shipping) .................... 250,000 100,000 100,000 50,000
Contribution margin.............................. $1,350,000 $ 700,000 $ 400,000 $250,000
Less traceable fixed expenses:Manufacturing................................... $ 250,000 $ 100,000 $ 100,000 $ 50,000Marketing (advertising).................... 450,000 200,000 200,000 50,000
Total traceable fixed expense...... $ 700,000 $ 300,000 $ 300,000 $100,000
Product contribution............................. $ 650,000 $ 400,000 $ 100,000 $150,000
Less common fixed expenses:Manufacturing1 ................................. $ 300,000Marketing2 ......................................... 100,000Administration .................................. 150,000
Total common fixed expenses .... $ 550,000
Operating income.................................. $ 100,000
1 $1,950,000 absorption cost of goods sold – $1,400,000 variable costs – $250,000 traceable fixed cost2 $800,000 total marketing costs – $250,000 variable expense – $450,000 advertising expense
Chapter 20 20-13
P20-2(1) ROBERTS CORPORATION
Income StatementFor Year Ended 12-31-20–
Sales (52,000 × $25)...................................................................... $1,300,000Cost of goods sold:
Standard full cost (52,000 × $15) ......................... $780,000Net unfavorable variable cost variances............. 2,000Unfavorable volume variance* ............................. 5,000 787,000
Gross profit ................................................................................... $ 513,000Less commercial expenses:
Variable expenses (52,000 × $1)........................... $ 52,000Fixed expenses...................................................... 180,000 232,000
Operating income under absorption costing ............ $ 281,000
*Units budgeted for production during the year......................... 50,000Units actually produced during the year.................................... 49,000
1,000Fixed factory overhead charged to each unit ............................ $ × 5Unfavorable volume variance ...................................................... $ 5,000
(2) ROBERTS CORPORATIONIncome Statement
For Year Ended 12-31-20–
Sales (52,000 × $25)...................................................................... $1,300,000Cost of goods sold:
Standard variable cost (52,000 × $10) ................. $520,000Net unfavorable variable cost variances............. 2,000 522,000
Gross contribution margin .......................................... $ 778,000Variable commercial expenses (52,000 × $1)............................. 52,000Contribution margin ..................................................................... $ 726,000Less fixed costs:
Factory overhead(50,000 units budgeted × $5) .......................... $250,000
Commercial expenses........................................... 180,000 430,000Operating income under direct costing ..................................... $ 296,000
(3) Operating income under absorption costing............................. $ 281,000Operating income under direct costing ..................................... 296,000Difference ...................................................................................... $ (15,000)
Units produced during the year .................................................. 49,000Units sold during the year ........................................................... 52,000Unit decrease in finished goods inventory................................ (3,000)Fixed factory overhead charged to each unit under
absorption costing .................................................................... $ × 5Difference ...................................................................................... $ (15,000)
20-14 Chapter 20
P20-3(1) PLACID CORPORATION
Income StatementFor Year Ended 12-31-20–
Sales (48,000 × $16)...................................................................... $768,000Cost of goods sold:
Standard full cost (48,000 × $9) ........................... $432,000Net unfavorable variable cost variances............. 1,000Favorable volume variance* ................................. (3,000) 430,000
Gross profit ................................................................................... $338,000Less commercial expenses:
Variable expenses (48,000 × $1)........................... $48,000Fixed expenses...................................................... 99,000 147,000
Operating income under absorption costing............................. $191,000
*Units budgeted for production during the year......................... 50,000Units actually produced during the year.................................... 51,000
(1,000)Fixed factory overhead charged to each unit ............................ × $3Favorable volume variance.......................................................... $ (3,000)
(2) PLACID CORPORATIONIncome Statement
For Year Ended 12-31-20–
Sales (48,000 × $16)...................................................................... $768,000Cost of goods sold:
Standard variable cost (48,000 × $6) ................... $288,000Net unfavorable variable cost variances............. 1,000 289,000
Gross contribution margin .......................................................... $479,000Variable commercial expenses (48,000 × $1)............................. 48,000Contribution margin ..................................................................... $431,000Less fixed costs:
Factory overhead(50,000 units budgeted × $3) ............................ $150,000
Commercial expenses........................................... 99,000 249,000Operating income under direct costing ..................................... $182,000
(3) Operating income under absorption costing ............ $191,000Operating income under direct costing ..................... 182,000Difference ...................................................................... $ 9,000
Units produced during the year .................................. 51,000Units sold during the year ........................................... 48,000Unit increase in finished goods inventory................. 3,000Fixed factory overhead charged to each unit under
absorption costing.................................................... × $3Difference ...................................................................... $ 9,000
Chapter 20 20-15
P20-4
(1) Absorption costing: QuarterFirst Second
Sales................................................................ $200,000 $260,000Direct materials .............................................. $ 30,000 $ 20,000Direct labor ..................................................... 60,000 40,000Variable factory overhead ............................. 45,000 30,000Fixed factory overhead.................................. 62,400 62,400Cost of goods manufactured ........................ $197,400 $152,400Beginning inventory....................................... 65,800Cost of goods available for sale................... $197,400 $218,200Ending inventory............................................ 65,800 1 30,480 2
Cost of goods sold ........................................ $131,600 $187,720Gross profit..................................................... $68,400 $72,280Marketing and administrative expenses...... 25,000 28,000Operating income........................................... $ 43,400 $ 44,280
1 $1 + $2 + $1.50 + ($62,400 ÷ 30,000) = $6.58$6.58 × 10,000 units = $65,800
2 $1 + $2 + $1.50 + ($62,400 ÷ 20,000) = $7.62$7.62 × 4,000 units = $30,480
(2) Direct Costing: QuarterFirst Second
Sales................................................................ $200,000 $260,000Direct materials .............................................. $ 30,000 $ 20,000Direct labor ..................................................... 60,000 40,000Variable factory overhead ............................. 45,000 30,000Variable cost of goods manufactured.......... $135,000 $ 90,000Beginning inventory....................................... 45,000Variable cost of goods available for sale..... $135,000 $135,000Ending inventory............................................ 45,000 18,000Variable cost of goods sold .......................... $90,000 $117,000Gross contribution margin............................ $110,000 $143,000Variable marketing and administrative
expenses................................................ 10,000 13,000Contribution margin....................................... $100,000 $130,000Less fixed expenses:
Factory overhead .................................. $ 62,400 $ 62,400Marketing and administrative .............. 15,000 15,000
Total fixed expense ........................................ $ 77,400 $ 77,400Operating income........................................... $ 22,600 $ 52,600
20-16 Chapter 20
P20-4 (Concluded)Quarter
(3) First SecondOperating income under absorption costing $43,400 $ 44,280Operating income under direct costing....... 22,600 52,600Difference........................................................ $20,800 $ (8,320)
Change in inventory under absorption costing:Ending inventory................................... $65,800 $ 30,480Beginning inventory.............................. 0 65,800Increase (decrease) in inventory ......... $65,800 $(35,320)
Change in inventory under direct costing:Ending inventory................................... $45,000 $18,000Beginning inventory.............................. 0 45,000Increase (decrease) in inventory ......... $45,000 $(27,000)
Difference between absorption anddirect costing......................................... $20,800 $ (8,320)
P20-5
Capital LaborIntensive Intensive
Sales price ...................................................... $30.00 $30.00Variable costs:
Materials................................................. $5.00 $5.60Direct labor ............................................ 6.00 7.20Variable factory overhead .................... 3.00 4.80Variable marketing expenses............... 2.00 16.00 2.00 19.60
Contribution margin per unit ........................ $14.00 $10.40
(a) Capital-intensive manufacturing method:Fixed factory overhead.................................................. $2,440,000Fixed marketing expenses ............................................ 500,000Total fixed cost ............................................................... $2,940,000
$2,940,000 fixed cost = 210,000 units of sales to break even$14 contribution margin per unit(b) Labor-intensive manufacturing method:
Fixed factory overhead.................................................. $1,320,000Fixed marketing expenses ............................................ 500,000Total fixed cost ............................................................... $1,820,000
$1,820,000 fixed cost = 175,000 units of sales to break even$10.40 contribution margin per unit
Chapter 20 20-17
P20-5 (Concluded)
(2) Kimbrell Company would be indifferent between the two alternative manufactur-ing methods at the volume of sales for which total cost was equal under bothalternatives. Let Q equal the quantity of units of product manufactured and sold.
($16 × Q) + $2,940,000 = ($19.80 × Q) + $1,820,000$2,940,000 – $1,820,000 = ($19.60 × Q) – ($16 × Q)
$1,120,000 = $ 3.60 × Q311,111 = Q
Total cost will be the same for both manufacturing methods at 311,111 units ofsales.
P20-6
(1) The number of units to break even at a per unit sales price of $38.50:
Variable costs:Direct materials...................................................................... $ 60,000Direct labor............................................................................. 40,000Variable factory overhead..................................................... 20,000Variable marketing and administrative expenses .............. 10,000
$130,000
*$130,000 ÷ 5,000 units = $26 variable cost per unit
(2) Units that must be sold to produce an $18,000 profit, at a $40 per unit sales price:
(3) The price Castleton must charge at a 5,000-unit sales level, in order to producea profit equal to 20% of sales:
Let x = sales price per unit5,000x = 5,000($26) + $45,000 + 5,000 (.2x)4,000x = $175,000
x = $43.75 sales price per unit
CGA-Canada (adapted). Reprint with permission.
$ , $ ,$ $
$ ,$
,45 000 18 000
40 2663 000
144 500
+−
= = units
$ , $ ,$ . $ . *
$ ,$ .
,30 000 15 00038 50 26 00
45 00012 50
3 600+
−= = break-evenn units
20-18 Chapter 20
P20-7B2 B4
Sales price per unit........................................ $180.00 $176.00*Less:
Variable manufacturing cost per unit . $121.00 $ 96.00Variable selling expense per unit
(5% of sales price) .......................... 9.00 8.80Total variable cost per unit .................. $130.00 $104.80
Contribution margin per unit ........................ $ 50.00 $ 71.20
*$160 sales price per unit in 20A + ($160 × 10% increase in 20B)
Total fixed factory overhead((20,000 B2’s + 40,000 B4’s) × $25 per unit)................. $1,500,000
Total fixed selling and administrative expenses.................. 207,330Total fixed costs ...................................................................... $1,707,330
$1,707,330 fixed cost + ($135,000 profit ÷ (1 – .4)) =(2 B2’s × $50 CM each) + (3 B4’s × $71.20 CM each)
$1,707,330 fixed cost + $225,000 pretax profit =$313.60 CM per package
$1,932,330 = 6,162 packages$313.60
6,162 packages × 2 units of B2 = 12,324 units of B26,162 packages × 3 units of B4 = 18,486 units of B4
Chapter 20 20-19
P20-8
(1) The 20A sales mix in units is 1:2 (70,000 tape recorders; 140,000 electronic cal-culators).
Let x = Number of tape recorders to break even2x = Number of electronic calculators to break even
At break even:Sales = Variable cost + Fixed cost
$15x + 2 ($22.50x) = $8x + 2 ($9.50x) + $1,320,0001
$15x + $45x = $8x + $19x + $1,320,000$60x = $27x + $1,320,000$33x = $1,320,000
x = 40,000 tape recorders2x = 80,000 electronic calculators
1Fixed costs:Factory overhead ..................................... $ 280,000Marketing and administrative ................. 1,040,000
Total........................................................ $1,320,000
20-20 Chapter 20
P20-8 (Continued)
(2) The following formula can be used to calculate the sales dollars required to earnan aftertax profit of 9% on sales, using 20B estimates:
S = VC(S) + FC + P(S)1 – T
Where: S = Necessary sales dollarsVC = Variable cost stated as a percentage of sales dollars (S)FC = Fixed costs
P = Desired profit stated as a percentage of sales dollars (S)T = Income tax rate
S = .46S1 + $1,377,0002 + .09(S)(1 – .55)
S = .46S + $1,377,000 + .2S.34S = $1,377,000
S = $4,050,000
1Variable cost rate for tape recorders and electronic calculators:Tape Electronic
Recorders CalculatorsPer PerUnit % Unit %
Sales price ......................................................$15.00 100% $20.00 100.0% Variable costs:
Materials................................................. $3.80 $ 3.60Direct labor ............................................ 2.20 3.30Factory overhead .................................. 2.00 2.00
Total variable cost............................. $7.80 52% $ 8.90 44.5%
Contribution margin....................................... $7.20 48% $11.10 55.5%
Composite variable cost rate per dollar of sales:(.20 × Tape recorder variable cost rate) + (.80 × Calculator variable cost rate) = .20 (.52) + .80 (.445) = .104 + .356 = .462Fixed costs:
Factory overhead ........................................................... $ 280,000Marketing and administrative ....................................... 1,040,000Additional advertising.................................................... 57,000
Total ............................................................................. $1,377,000
Chapter 20 20-21
P20-8 (Concluded)
(3) Let: x = Number of tape recorders to break even3x = Number of electronic calculators to break even
At break even:Sales = Variable cost + Fixed cost
$15x + 3($20x) = $7.80x + 3($8.90x) + $1,377,000$15x + $60x = 7.80x + $26.70x + $1,377,000
$75x = $34.50x + $1,377,000$40.50x = $1,377,000
x = 34,000 tape recorders3x = 102,000 electronic calculators
P20-9
(1) (a) In order to break even, Almo must sell 500 units determined as follows:
where F = fixed cost, P = sales price per unit, and C = variable cost per unit.
(b) To achieve an after-tax profit of $240,000, Almo must sell 2,500 units determined as follows:
where P, F, and C are defined the same as in (1)(a), and ππ is the after-tax profit objective.
Q =F +P C
π−
=+ ÷ −
−=
+$ , ($ , ( . ))$ $
$ , $100 000 240 000 1 40400 200
100 000 4000 000200
500 000200
2 500
,$
$ ,$
,
=
= units
Q(BE) =F
P Cunits
−=
−=
$ ,$ $
100 000400 200
500
20-22 Chapter 20
P20-9 (Concluded)
(2) Almo Company should choose alternative (a) because it will result in the largestafter tax profit.
Alternative (a):
Revenue = ($400 unit sales price × 350 units) + (($400 – $40 price reduction) × 2,700 units)= $140,000 + $972,000= $1,112,000
Variable Cost = $200 per unit × (350 units sold + 2,700 units to be sold)= $610,000
After-tax Profit = (Revenue – Variable Cost – Fixed Cost) × (1 – Tax Rate)= ($1,112,000 – $610,000 – $100,000) × (1 – .4)= $402,000 × .6= $241,200
Alternative (b):
Revenue = ($400 unit sales price × 350 units) + (($400 – $30 price reduction) × 2,200 units= $140,000 + $814,000= $954,000
Variable Cost = ($200 per unit × 350 units) + (($200 – $25 cost reduction) × 2,200 units)= $70,000 + $385,000= $455,000
After-tax Profit = (Revenue – Variable Cost – Fixed Cost) × (1 – Tax Rate)= ($954,000 – $455,000 – $100,000) × (1 –.4)= $399,000 × .6= $239,400
Alternative (c):
Revenue = ($400 unit sales price × 350 units) + ($400 × (1 – 5% price reduction) × 2,000 units)= $140,000 + $760,000= $900,000
Variable Cost = $200 per unit × (350 units sold + 2,000 units to be sold)= $470,000
After-tax Profit = (Revenue – Variable Cost – Fixed Cost) × (1 – Tax Rate)= ($900,000 – $470,000 – ($100,000 – $10,000 cost reduction)) × (1 – .4)= $340,000 × .6= $204,000
Chapter 20 20-23
P20-10
(1) Estimated break-even point based on pro forma income statement:
Sales ......................................................................................... $10,000,000Variable costs:
Cost of goods sold ............................... $6,000,000Commissions paid to agents............... 2,000,000 8,000,000
Contribution margin................................................................ $2,000,000
Contribution margin ratio = $2,000,000 = 20% C/M$10,000,000
$100,000 fixed cost = $500,000 break-even point20% C/M
(2) Estimated break-even point with the company employing its own salespersons:
Variable cost ratios:Cost of goods sold to sales ($6,000,000 ÷ $10,000,000) 60%Commissions on sales .................................................. 5%
Total variable cost ratio ............................................. 65%
Contribution margin ratio = 1 – 65% variable cost ratio = 35%
Fixed costs:Administrative ................................................................ $100,000Sales manager................................................................ 160,000Salaries of salespersons (3 × $30,000) ........................ 90,000
Total fixed costs ......................................................... $350,000
$350,000 fixed cost = $1,000,000 break-even point35% C/M
20-24 Chapter 20
P20-10 (Concluded)
(3) Estimated sales volume to yield net income projected in pro forma income state-ment with independent sales agents receiving 25% commission:
Total income before income tax ............................................ $1,900,000Fixed cost................................................................................. 100,000Total fixed cost and profit ...................................................... $2,000,000
Variable cost ratios:Cost of goods sold to sales..................................................... 60%Commissions on sales............................................................. 25%
Total variable cost ratio.................................................... 85%
Contribution margin ratio = 1 – 85% variable cost ratio = 15%
$2,000,000 fixed cost and profit = $13,333,333 sales15% C/M
(4) Estimated sales volume to yield an identical income regardless of whether thecompany employs its own salespersons or continues with independent salesagents and pays them a 25% commission:
Total cost with agents = Total cost with company’sreceiving 25% commission own sales force
(85% variable cost × sales) = (65% variable cost × sales)+ $100,000 fixed cost + $350,000 fixed cost
20% × sales = $250,000
sales = $1,250,000
Chapter 20 20-25
CASES
C20-1
(1) Because Star Company uses absorption costing, income from operations isinfluenced by both sales volume and production volume. Sales volume wasincreased in the November 30 forecast, and at standard gross profit rates thiswould increase income from operations by $5,600. However, during this sameperiod, production volume was below the January 1 forecast, causing anunplanned volume variance of $6,000. The volume variance and the increasedmarketing expenses (due to the 10% increase in sales) overshadowed the addedprofits from sales, as follows:
Increased sales ................................................ $26,800Increased cost of goods sold at standard .... 21,200Increased gross profit at standard ................ $ 5,600Less:
Volume variance......................................... $6,000Increased marketing expense .................. 1,340 7,340
Decrease in income from operations ............ $(1,740)
20-26 Chapter 20
C20-1 (Concluded)
(2) Star Company could adopt direct costing. Under direct costing, fixed manufac-turing costs would be treated as period costs and would not be assigned to pro-duction. Consequently, earnings would not be affected by production volume,but only by sales volume. Statements prepared on a direct-costing basis are asfollows:
STAR COMPANYForecasts of Operating Results for 20—
Forecasts as ofJanuary 1 November 30
Sales................................................................ $268,000 $294,800Variable costs:
Manufacturing........................................... $182,000 $200,200*Marketing .................................................. 13,400 14,740
Total variable cost.............................. $195,400 $214,940Contribution margin....................................... $ 72,600 $ 79,860Fixed costs:
Manufacturing........................................... $ 30,000 $ 30,000Administrative .......................................... 26,800 26,800
Total fixed cost ................................... $ 56,800 $ 56,800Income from operations ................................ $ 15,800 $ 23,060
*$182,000 × 110% = $200,200
Reconciliation of differences in income from operations:January 1: No difference in absorption vs. direct costing because $30,000 fixedfactory overhead was expensed in both cases.
November 30: Income fromOperations
Direct costing ................................................. $23,060Absorption costing ........................................ 14,060Difference........................................................ $ 9,000
Fixed factory overhead included in cost of goods sold at standard:November 30 forecast ($30,000 in January 1 forecast+ 10% sales volume increase) .................... $33,000
January 1 forecast ......................................... 30,000$ 3,000
Underapplied fixed factory overhead........... 6,000Difference........................................................ $ 9,000
Chapter 20 20-27
C20-2
(1) In absorption costing, as currently employed by RGS Corporation, fixed factoryoverhead is considered a product cost rather than a period cost. Fixed factoryoverhead is applied to production based on a normal capacity of 1,000,000 units.Thus, the fixed factory overhead is applied to products in the same manner asvariable costs, even though it does not vary with production. In addition, if pro-duction and sales are not equal during the year, fixed factory overhead isdeferred as part of inventory costs (when production exceeds sales) or releasedupon sales of the inventory (when sales exceed production).
During 20A, production exceeded sales, resulting in a portion of the fixed fac-tory overhead being inventoried in finished goods rather than being expensed in20A. This resulted in 20A operating income being larger than it would have beenif all fixed factory overhead had been charged against 20A sales revenue. Thenin 20B, sales exceeded production, resulting In more fixed factory overheadbeing charged against 20B sales revenue than was incurred in 20B. First, fin-ished goods were sold out of inventory, which meant that the part of fixed fac-tory overhead that was incurred in 20A and inventoried in 20A was chargedagainst 20B sales revenue. Second, fixed factory overhead was underapplied in20B because only 850,000 units were produced (150,000 units less than normalcapacity used in determining the factory overhead rate).This resulted in an unfa-vorable volume variance that was charged to the cost of goods sold in 20B. Bothof these occurrences increased the cost of goods sold and resulted in a reduc-tion of gross profit and operating income in 20B.
20-28 Chapter 20
C20-2 (Continued)
(2)(a) RGB CORPORATION
Operating Income StatementFor the Years Ended November 30, 20A and 20B
(in thousands)
20A 20B
Sales....................................................... $9,000 $11,200Variable cost of goods sold:
900,000 units at $5.00 .................... 4,500300,000 units at $5.00 .................... $1,500700,000 units at $5.50 .................... 3,850 5,350
Contribution margin.............................. $4,500 $ 5,850Fixed expenses:
Fixed factory overhead.................. $3,000 $3,300Selling and administrative ............ 1,500 4,500 1,500 4,800
Operating income.................................. 0 $ 1,050
(b) Reconciliation:20A 20B
Operating income—absorption costing......................... $ 900 $ 645
Operating income—direct costing ................................. 0 1,050
Difference............................................... $ 900 $ (405)
Difference accounted for as follows:Inventory change underabsorption costing:
Ending inventory:300,000 units at $8.00 ............ $2,400150,000 units at $8.80 ............ $1,320
Beginning inventory: ................. 0 $2,400300,000 units at $8.00 ............ 2,400 $(1,080)
Inventory change under direct costing:Ending inventory:
300,000 units at $5.00 ............ $1,500150,000 units at $5.50 ............ $ 825
Beginning inventory .................. 0 1,500300,000 units at $5.00 ............ 1,500 (675)
Difference .............................................. $ 900 $ (405)
Chapter 20 20-29
C20-2 (Concluded)
(3) The advantages of direct costing for internal reporting include the following:(a) Direct costing aids in forecasting and in evaluating reported income for
internal management decision-making purposes, because fixed costs arenot arbitrarily allocated between accounting periods (or among differentproducts, sales territories, operating divisions, etc.).
(b) Fixed costs are reported at incurred values (and not absorbed values),increasing opportunity for more effective control of these costs.
(c) Profits vary directly with sales volume and are unaffected by changes ininventory levels.
(d) Analysis of the cost-volume-profit relationship is facilitated, and manage-ment is able to determine the break-even point and total profit for a givenvolume of production and sales.
The disadvantages of direct costing for internal reporting include the following:(a) Management may fail to consider properly the fixed cost element in long-
range pricing decisions.(b) Direct costing lacks acceptability for external financial reporting or as a
basis for computing taxable income. As a consequence, additional record-keeping costs must be incurred to use direct costing.
(c) The separation of costs into fixed and variable elements is a costly process.In addition, the distinction between fixed and variable cost is not precise andnot reliable at all levels of activity.
C20-3(1) Daly would determine the number of units of Product Y that it would have to sell
to attain a 20% profit on sales, by dividing total fixed costs plus desired profit(i.e., 20% of sales price per unit multiplied by the units to attain a 20% profit) byunit contribution margin (i.e., sales price per unit less variable cost per unit).
(2) If variable cost per unit increases as a percentage of the sales price, Daly wouldhave to sell more units of Product Y to break even. Because the unit contributionmargin (i.e., sales price per unit less variable cost per unit) would be lower, Dalywould have to sell more units to cover the fixed cost in order to break even.
20-30 Chapter 20
C20-3 (Concluded)
(3) The limitations of break-even and cost-volume-profit analysis in managerialdecision making follow:(a) The analysis is fundamentally a static analysis, and, in most cases, changes
can be determined only by recomputing results. If a break-even chart isused, changes can be shown only by drawing a new chart or series ofcharts.
(b) The amount of fixed and variable cost, as well as the slope of the sales line,is meaningful in a defined range of activity and must be redefined for activ-ity outside the relevant range.
(c) The analysis is highly dependent upon a meaningful separation of fixed andvariable costs, which may be difficult to obtain in actual practice.
(d) The analysis is based on a single mix of products. If the mix is expected tochange, the results must be recomputed.
(e) The analysis assumes that production technology (i.e., labor productivity,level of automation, and product specifications) will be unchanged. Ifchanges in production technology are expected to occur, the analyst mustconsider the expected effects on costs.
(f) The analysis assumes that selling prices, input prices, and other marketconditions will not change. Expected changes must be incorporated into theanalysis. If a range of possible changes can occur, a different result must bedetermined for each possible combination.
Chapter 20 20-31
