3-1 CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS 3-1 Cost-volume-profit (CVP) analysis examines the behavior of total revenues, total costs, and operating income as changes occur in the output level, selling price, variable costs per unit, or fixed costs. 3-2 The assumptions underlying the CVP analysis outlined in Chapter 3 are: 1. Changes in the level of revenues and costs arise only because of changes in the number of product (or service) units produced and sold. 2. Total costs can be divided into a fixed component and a component that is variable with respect to the level of output. 3. When graphed, the behavior of total revenues and total costs is linear (straight-line) in relation to output units within the relevant range. 4. The unit selling price, unit variable costs, and fixed costs are known and constant. 5. The analysis either covers a single product or assumes that the sales mix, when multiple products are sold, will remain constant as the level of total units sold changes. 6. All revenues and costs can be added and compared without taking into account the time value of money. 3-3 Operating income is total revenues from operations for the accounting period minus total costs from operations (excluding income taxes): Operating income = Total revenues – Total costs Net income is operating income plus nonoperating revenues (such as interest revenue) minus nonoperating costs (such as interest cost) minus income taxes. Chapter 3 assumes nonoperating revenues and nonoperating costs are zero. Thus, Chapter 3 computes net income as: Net income = Operating income – Income taxes 3-4 Contribution margin is computed as the difference between total revenues and total variable costs. Contribution margin per unit is the difference between selling price and variable cost per unit. Contribution-margin percentage is the contribution margin per unit divided by selling price. 3-5 Three methods to calculate the breakeven point are the equation method, the contribution margin method, and the graph method. 3-6 Breakeven analysis denotes the study of the breakeven point, which is often only an incidental part of the relationship between cost, volume, and profit. Cost-volume-profit relationship is a more comprehensive term than breakeven analysis.
Transcript
3-1
CHAPTER 3COST-VOLUME-PROFIT ANALYSIS
3-1 Cost-volume-profit (CVP) analysis examines the behavior of total revenues, total costs, andoperating income as changes occur in the output level, selling price, variable costs per unit, or fixedcosts.
3-2 The assumptions underlying the CVP analysis outlined in Chapter 3 are:
1. Changes in the level of revenues and costs arise only because of changes in the number ofproduct (or service) units produced and sold.
2. Total costs can be divided into a fixed component and a component that is variable withrespect to the level of output.
3. When graphed, the behavior of total revenues and total costs is linear (straight-line) inrelation to output units within the relevant range.
4. The unit selling price, unit variable costs, and fixed costs are known and constant.5. The analysis either covers a single product or assumes that the sales mix, when multiple
products are sold, will remain constant as the level of total units sold changes.6. All revenues and costs can be added and compared without taking into account the time value
of money.
3-3 Operating income is total revenues from operations for the accounting period minus totalcosts from operations (excluding income taxes):
Operating income = Total revenues – Total costs
Net income is operating income plus nonoperating revenues (such as interest revenue) minusnonoperating costs (such as interest cost) minus income taxes. Chapter 3 assumes nonoperatingrevenues and nonoperating costs are zero. Thus, Chapter 3 computes net income as:
Net income = Operating income – Income taxes
3-4 Contribution margin is computed as the difference between total revenues and total variablecosts. Contribution margin per unit is the difference between selling price and variable cost perunit. Contribution-margin percentage is the contribution margin per unit divided by selling price.
3-5 Three methods to calculate the breakeven point are the equation method, the contributionmargin method, and the graph method.
3-6 Breakeven analysis denotes the study of the breakeven point, which is often only anincidental part of the relationship between cost, volume, and profit. Cost-volume-profitrelationship is a more comprehensive term than breakeven analysis.
3-2
3-7 CVP certainly is simple, with its assumption of output as the only revenue and cost driver,and linear revenue and cost relationships. Whether these assumptions make it simplistic depends onthe decision context. In some cases, these assumptions may be sufficiently accurate for CVP toprovide useful insights. The examples in Chapter 3 (the software package context in the text andthe travel agency example in the Problem for Self-Study) illustrate how CVP can provide suchinsights. In more complex cases, the basic ideas of simple CVP analysis can be expanded.
3-8 An increase in the income tax rate does not affect the breakeven point. Operating income atthe breakeven point is zero, and thus no income taxes will be paid at this point.
3-9 Sensitivity analysis is a "what-if" technique that examines how a result will change if theoriginal predicted data are not achieved or if an underlying assumption changes. The advent ofspreadsheet software has greatly increased the ability to explore the effect of alternativeassumptions at minimal cost. CVP is one of the most widely used software applications in themanagement accounting area.
3-10 Examples include:Manufacturing––substituting a robotic machine for hourly wage workers.Marketing––changing a sales force compensation plan from a percent of sales dollars to afixed salary.Customer service––hiring a subcontractor to do customer repair visits on an annual retainerbasis rather than a per-visit basis.
3-11 Examples include:Manufacturing––subcontracting a component to a supplier on a per-unit basis to avoid
purchasing a machine with a high fixed depreciation cost.Marketing––changing a sales compensation plan from a fixed salary to percent of sales
dollars basis.Customer service––hiring a subcontractor to do customer service on a per-visit basis rather
than an annual retainer basis.
3-12 Operating leverage describes the effects that fixed costs have on changes in operatingincome as changes occur in units sold and hence in contribution margin. Knowing the degree ofoperating leverage at a given level of sales helps managers calculate the effect of fluctuations insales on operating incomes.
3-13 CVP analysis is always conducted for a specified time horizon. One extreme is a veryshort-time horizon. For example, some vacation cruises offer deep price discounts for people whooffer to take any cruise on a day's notice. One day prior to a cruise, most costs are fixed. Theother extreme is several years. Here, a much higher percentage of total costs typically is variable.
CVP itself is not made any less relevant when the time horizon lengthens. What happens isthat many items classified as fixed in the short run may become variable costs with a longer timehorizon.
3-3
3-14 A company with multiple products can compute a breakeven point by assuming there is aconstant mix of products at different levels of total revenue.
3-15 Yes, gross margin calculations emphasize the distinction between manufacturing andnonmanufacturing costs (gross margins are calculated after subtracting fixed manufacturing costs).Contribution margin calculations emphasize the distinction between fixed and variable costs.Hence, contribution margin is a more useful concept than gross margin in CVP analysis.
3-16 (10 min.) CVP computations.
Variable Fixed Total Operating Contribution ContributionRevenues Costs Costs Costs Income Margin Margin %
The $5 delivery fee results in a higher contribution margin which reduces both the breakeven pointand the tickets sold to attain operating income of $10,000.
b. Breakeven point under option 2$500Q − $350Q − (0.10 × $500Q) = 0
100Q = 0Q = 0
2. Operating income under Option 1 = $150Q − $5,000Operating income under Option 2 = $100Q
Find Q such that $150Q − $5,000 = $100Q$50Q = $5,000
Q = $5,000 ÷ $50 = 100 carpets
For Q = 100 carpets, operating income under both Option 1 and Option 2 = $10,000
3a. For Q > 100, say, 101 carpets,Option 1 gives operating income = $150 × 101 − $5,000 = $10,150Option 2 gives operating income = $100 × 101 = $10,100So Color Rugs will prefer Option 1.
3b. For Q < 100, say, 99 carpets,Option 1 gives operating income = $150 × 99 − $5,000 = $9,850Option 2 gives operating income = $100 × 99 = $9,900So Color Rugs will prefer Option 2.
3-10
3-25 (Cont’d.)
4. Degree of operating leverage =income Operating
marginon Contributi
Under option 1, Degree of operating leverage =$10,000
100 $150×= 1.5
Under option 2, Degree of operating leverage =$10,000
100 $100×= 1.0
5. The calculations in requirement 4 indicate that when sales are 100 units, a percentage changein sales and contribution margin will result in 1.5 times that percentage change in operating incomefor option 1, but the same percentage change in operating income for option 2. The degree ofoperating leverage at a given level of sales helps managers calculate the effect of fluctuations insales on operating incomes.
UVC = $ 4.00 variable production and marketing cost 3.15 variable author royalty cost (0.15 × $30.00 × 0.70)$ 7.15
UCM = $21.00 – $7.15 = $13.85
FC = $ 500,000 fixed production and marketing cost 3,000,000 up-front payment to Washington
$3,500,000
3-11
3-26 (Cont’d.)
Exhibit 3-26A shows the PV graph.
EXHIBIT 3-26A
PV Graph for Media Publishers
2. a.Breakevennumber of units =
FCUCM
=$3,500,000
$13.85
= 252,708 copies sold (rounded up)
b. Target OI =FC + OI
UCM
=$3,500,000 + $2,000,000
$13.85
=$5,500,000
$13.85
= 397,112 copies sold (rounded up)
100,000 200,000 300,000 400,000 500,000
0
Units sold
Ope
ratin
g in
com
e (0
00’s
)
(0; $3.5 million)
252,708; $0
FC = $3,500,000UCM = $13.85 per book sold
$4,000
3,000
2,000
1,000
-1,000
-2,000
-3,000
-4,000
3-12
3-26 (Cont’d.)
3. a. Decreasing the normal bookstore margin to 20% of the listed bookstore price of $30has the following effects:
USP = $30.00 × (1 – 0.20)= $30.00 × 0.80 = $24.00
UVC = $ 4.00 variable production and marketing cost+ 3.60 variable author royalty cost (0.15 × $30.00 × 0.80)$ 7.60
UCM = $24.00 – $7.60 = $16.40
Breakevennumber of units =
FCUCM
=$3,500,000
$16.40
= 213,415 copies sold (rounded)
The breakeven point decreases from 252,708 copies in requirement 2 to 213,415 copies.
b. Increasing the listed bookstore price to $40 while keeping the bookstore margin at 30%has the following effects:
USP = $40.00 × (1 – 0.30)= $40.00 × 0.70 = $28.00
UVC = $ 4.00 variable production and marketing cost+ 4.20 variable author royalty cost (0.15 × $40.00 × 0.70)$ 8.20
UCM = $28.00 – $8.20 = $19.80
Breakevennumber of units =
$3,500,000$19.80
= 176,768 copies sold (rounded)
The breakeven point decreases from 252,708 copies in requirement 2 to 176,768 copies.
c. The answer to requirements 3a and 3b decreases the breakeven point relative torequirement 2 because in each case fixed costs remain the same at $3,500,000 while contributionmargin per unit increases.
3-13
3-27 (10 min.) CVP analysis, international cost structure differences.
Thailand has the lowest breakeven point––it has both the lowest fixed costs ($4,500,000) and thelowest variable cost per unit ($17.00). Hence, for a given selling price, Thailand will always have ahigher operating income (or a lower operating loss) than Singapore or the U.S.
The U.S. breakeven point is 1,200,000 units. Hence, with sales of 800,000 units, it has anoperating loss of $4,000,000.
3c. As Zapo increases its percentage of new customers, which have a higher contribution marginper unit than upgrade customers, the number of units required to break even decreases:
New Customers Upgrade Customers Breakeven PointRequirement 3(a)Requirement 1Requirement 3(b)
3-30 (20 min.) Gross margin and contribution margin.
1a. Cost of Goods Sold $1,600,000Fixed Manufacturing Costs 500,000Variable Manufacturing Costs $1,100,000
Variable manufacturing costs per unit = $1,100,000 ÷ 200,000 = $5.50 per unit
1b. Total marketing and distribution costs $1,150,000Variable marketing and distribution (200,000 × $4) 800,000Fixed marketing and distribution costs $ 350,000
2. Selling price = $2,600,000 ÷ 200,000 units = $13 per unit
Foreman has confused gross margin with contribution margin. He has interpreted grossmargin as if it was all variable, and interpreted marketing and distribution costs as all fixed. In fact,the manufacturing costs, subtracted from sales to calculate gross margin, and marketing anddistribution costs contain both fixed and variable components.
3. Breakeven point in units =unitper margin on Contributi
costson distributi and marketing ing,manufactur Fixed
=50.3$
000,850$= 242,858 units (rounded up)
Breakeven point in revenues = 242,858 × $13 = $3,157,154.
The breakeven point is not unique because there are two cost drivers—quantity of pictureframes and number of shipments. Various combinations of the two cost drivers can yield zerooperating income.
3-19
3-32 (15–20 min.) Uncertainty, CVP analysis.
1. King pays Foreman $2 million plus $4 (25% of $16) for every home purchasing the pay-per-view. The expected value of the variable component is:
Demand(1)
Payment(2) = (1) ×× $4
Probability(3)
Expected payment(4)
100,000200,000300,000400,000500,000
1,000,000
$ 400,000800,000
1,200,0001,600,0002,000,0004,000,000
0.050.100.300.350.150.05
$ 20,00080,000
360,000560,000300,000
200,000$1,520,000
The expected value of King's payment is $3,520,000 ($2,000,000 fixed fee + $1,520,000).
b. Royal Rumble receives 62.5% of box-office receipts. Box-office receipts of$10,000,000 ($6,250,000 ÷ 62.5%) translate to $6,250,000 in revenues to RoyalRumble.
3-34 (20 min.) CVP analysis, cost structure differences, movie production.(Continuation of 3-33)
1. Contract AFixed costs for Contract A:
Production costs $21,000,000Fixed salary 15,000,000Total fixed costs $36,000,000
Unit variable cost = $0.25 per $1 revenue marketing feeUnit contribution margin = $0.75 per $1 revenue
Breakeven point in revenues =revenue $1per margin on contributiUnit
costs Fixed
=$0.75
0$36,000,00 = $48,000,000
Box-office receipts of $76,800,000 ($48,000,000 ÷ 62.5%) translate to $48,000,000 in revenues toRoyal Rumble.
Contract BFixed costs for Contract B:
Production costs $21,000,000Fixed salary 3,000,000
Total fixed costs $24,000,000
Unit variable cost = $0.25 per $1 revenue fee to Media Productions 0.15 per $1 revenue residual to directors/actors$0.40 per $1 revenue
Unit contribution margin = $0.60 per $1 revenue
Breakeven point in revenues =
$24, 000,0000.60
= $40,000,000
Box-office receipts of $64,000,000 ($40,000,000 ÷ 62.5%) translate to $40,000,000 in revenues toRoyal Rumble.
Difference in Breakeven PointsContract A has a higher fixed cost and a lower variable cost per sales dollar. In contrast,
Contract B has a lower fixed cost and a higher variable cost per sales dollar. In Contract B, there isrisk-sharing between Royal Rumble and Savage, Michaels, and Martel that lowers the breakevenpoint, but results in Royal Rumble receiving less operating income if Feature Creatures 2 is amega-success.
Feature Creatures 2 has a higher breakeven point and lower operating income at $300 millionin box-office receipts than Feature Creatures because of a higher level of fixed costs and a lowerunit contribution margin.
b. Breakeven point in revenues = $30 × 42,000 = $1,260,000
4. Fixed costs = $360,000Contribution margin per pair = $8.70
a. Breakeven point in units = $360,
$8.
000
70= 41,380 pairs (rounded up)
3-22
b. Breakeven point in revenues = $30 × 41,380 = $1,241,4003-35 (Cont’d.)
5. Breakeven point = 40,000 pairsStore manager receives commission on 10,000 pairs.Cost of commission = $0.30 × 10,000 = $3,000
Revenues, $30 × 50,000 $1,500,000Variable costs:
Cost of shoes $975,000Salespeople commission 75,000Manager commission 3,000 1,053,000
Contribution margin 447,000Fixed costs 360,000Operating income $ 87,000
An alternative approach is 10,000 units × $8.70 = $87,000.
3-23
3-36 (20–25 min.) CVP analysis, shoe stores. (Continuation of 3-35)
1. Because the unit sales level at the point of indifference would be the same for each plan, therevenue would be equal. Therefore, the unit sales level sought would be that which produces thesame total costs for each plan.
Let Q = unit sales level$19.50Q + $360,000 + $81,000 = $21.00Q + $360,000
$81,000 = $1.50QQ = 54,000 units
2. Commission Plan Salary Plan Sales in units 50,000 60,000 50,000 60,000Revenues @ $30.00 $1,500,000 $1,800,000 $1,500,000 $1,800,000Variable costs @ $21.00 and @ $19.50 1,050,000 1,260,000 975,000 1,170,000Contribution margin 450,000 540,000 525,000 630,000Fixed costs 360,000 360,000 441,000 441,000Operating income $ 90,000 $ 180,000 $ 84,000 $ 189,000
The decision regarding the plans will depend heavily on the unit sales level that is generatedby the fixed salary plan. For example, as part (1) shows, at identical unit sales levels in excess of54,000 units, the fixed salary plan will always provide a more profitable final result than thecommission plan.
3. Let TQ = Target number of units
a. $30.00TQ – $19.50TQ – $441,000 = $168,000$10.50TQ = $609,000
TQ = $609,000 ÷ $10.50TQ = 58,000 units
b. $30.00TQ – $21.00TQ – $360,000 = $168,000$9.00TQ = $528,000
TQ = $528,000 ÷ $9.00TQ = 58,667 units (rounded)
The decision regarding the salary plan depends heavily on predictions of demand. Forinstance, the salary plan offers the same operating income at 58,000 units as the commission planoffers at 58,667 units.
3-24
3-37 (10-20 min.) Sensitivity and inflation. (Continuation of 3-36)
Contribution margin 427,200Fixed costs 360,000Operating income $ 67,200
An alternative approach is:
Contribution margin on 48,000 pairs × $9.00 $432,000Deduct negative contribution margin on unsold pairs, 2,000 × [$18.00 – ($19.50 + $.90* commission)] 4,800Contribution margin 427,200Fixed costs 360,000Operating income $ 67,200
*5% of $18.00 = $.90
2. Optimal operating income, given perfect knowledge, would be the $432,000 [($30 – $19.50 –$1.50) × 48,000] contribution computed above, minus $360,000 fixed costs, or $72,000.
3. The point of indifference is where the operating incomes are equal. Let X = unit cost per pairthat would produce the identical operating income of $67,200. Then:
Therefore, any rise in purchase cost in excess of $19.60 per pair increases the operatingincome benefit of signing the long-term contract.
In a shortcut solution, you could take the $4,800 difference between the "ideal" operatingincome (of $72,000) at the current cost per pair and the operating income under the contract (of$67,200) and divide it by 48,000 units to get 10 cents per pair difference.
3-25
3-38 (30 min.) CVP analysis, income taxes, sensitivity.
1a. In order to break even, Almo Company must sell 500 units. This amount represents the pointwhere revenues equal total costs.
Let Q denote the quantity of canopies sold.Revenue = Variable costs + Fixed costs
$400Q = $200Q + $100,000$200Q = $100,000
Q = 500 units
The calculation can also be expressed asBreakeven = Fixed Costs ÷ Contribution margin per unit
= $100,000 ÷ $200= 500 units
1b. In order to achieve its net income objective, Almo Company must sell 2,500 units. Thisamount represents the point where revenues equal total costs plus the corresponding operatingincome objective to achieve net income of $240,000.
2. To achieve its net income objective, Almo Company should select the first alternative wherethe sales price is reduced by $40, and 2,700 units are sold during the remainder of the year. Thisalternative results in the highest net income and is the only alternative that equals or exceeds thecompany’s net income objective. Calculations for the three alternatives are shown below.
Total fixed costs 6,290,000 8,370,000Operating income $ 3,330,000 $ 3,330,000
leverage operating
of Degree =income Operating
marginon Contributi $9, ,
$3, ,
620 000
330 000= 2.89
$11, ,
$3, ,
700 000
330 000= 3.51
3-27
3-39 (Cont’d.)
The calculations indicate that at sales of $26,000,000, a percentage change in sales andcontribution margin will result in 2.89 times that percentage change in operating income if Marstoncontinues to use sales agents and 3.51 times that percentage change in operating income if Marstonemploys its own sales staff. The higher contribution margin per dollar of sales and higher fixedcosts gives Marston more operating leverage, that is greater benefits (increases in operatingincome) if revenues increase but greater risks (decreases in operating income) if revenues decrease.
4. Variable costs of marketing = 15% of RevenuesFixed marketing costs = $5,500,000
Operating income = Revenues − costs manuf.Variable − costs manuf.
Fixed − costs
marketingVariable
− costs
marketingFixed
Denote the revenues required to earn $3,330,000 of operating income by $R, then
A = 15,938 units of A (rounded)4A = 63,752 units of B5A = 79,690 units of C
Total = 159,380 units
Breakeven point increases because the new mix contains less of the higher contributionmargin per unit, product B, and more of the lower contribution margin per unit, product C.
Breakeven point in 2000 (in revenues) = 16,500 units × $50 = $825,000 in sales revenues
2. Breakeven point in 2001 (in units)Evenkeel expects to sell 3 units of Plumar for every 2 units of Ridex in 2001, so consider a
bundle consisting of 3 units of Plumar and 2 units of Ridex.
Unit Contribution Margin from Plumar = $50 − $20 = $30Unit Contribution Margin from Ridex = $25 − $15 = $10
The contribution margin for the bundle is
$30 × 3 units of Plumar + $10 × 2 units of Ridex = $110
So bundles to be sold to breakeven = 110$
000,495= 4,500 bundles
4,500 bundles× 3 × 2
13,500 units of Plumar 9,000 units of Ridex TotalSelling price × $50 × $25Revenue $675,000 $225,000 $900,000
3. Contribution margin percentage in 2000 =2000in price sellingUnit
2000in margin on contributiUnit
=50$
30$ = 60%
Contribution margin percentage in 2001 =Unit conribution margin on bundle in 2001
Selling price of bundle in 2001
=$25 2 $50 3
$110
×+× =
200$
110$ = 55%
The breakeven point in 2001 increases because fixed costs are the same in both years but thecontribution margin generated by each dollar of sales revenue at the given product mix decreases in2001 relative to 2000.
4. Despite the breakeven sales revenue being higher, I would advise Andy Minton to acceptGlaston’s offer. The breakeven points per se are irrelevant because I do not expect Evenkeel tooperate in the region of the breakeven dollars. By accepting Glaston’s offer, Andy has the abilityto sell all the 30,00 units of Plumar he expects to sell in 2001 and make more sales of Ridex toGlaston without incurring any more fixed costs.
3-30
3-41 (Cont’d.)
Profits in 2001 with and without Ridex are expected to be as follows:
The breakeven point is 120,000 Standard units plus 40,000 Deluxe units, a total of 160,000units.
2. Unit contribution margins are: Standard: $20 – $14 = $6; Deluxe: $30 – $18 = $12a. If only Standard carriers were sold, the breakeven point would be:
$1,200,000 ÷ $6 = 200,000 unitsb. If only Deluxe carriers were sold, the breakeven point would be:
$66Q = $1,200,000Q = 18,182 units of Deluxe (rounded)
9Q = 163,638 units of Standard
The breakeven point is 163,638 Standard + 18,182 Deluxe, a total of 181,820 units.
The major lesson of this problem is that changes in the sales mix change breakeven points andoperating incomes. In this example, the budgeted and actual total sales in number of units wereidentical, but the proportion of the product having the higher contribution margin declined.Operating income suffered, falling from $300,000 to $120,000. Moreover, the breakeven pointrose from 160,000 to 181,820 units.
3-32
3-43 (25 min.) CVP analysis, decision making.
1. Unit selling price $105Variable manufacturing costs per unit 45Variable marketing and distribution costs per unit 10Contribution margin per unit $ 50
Fixed manufacturing costs $ 800,000Fixed marketing and distribution costs 600,000Total fixed costs $1,400,000
Breakeven point in units =Total fixed costs
Contribution margin per unit=
$1, ,
$50
400 000= 28,000 units
Breakeven point in revenues = 28,000 units × $105 per unit = $2,940,000
2. Tocchet’s current operating income is as follows:
Hence the maximum increase in fixed marketing and distribution costs for which Tocchet willprefer to reduce the selling price is $200,000 ($1,600,000 – $1,400,000).
3. Let the selling price be $P.
We calculate $P for which, after increasing fixed manufacturing costs by $100,000 to $900,000 andvariable manufacturing cost per unit by $2 to $47, operating income = $600,000
Direct materials costs:Beginning inventory, 1/1 $12 $20Purchases of direct materials 15 50Direct materials available for use 27 70Ending inventory, 12/31 5 30 (W)
Direct materials used 22 (H) 40Direct manufacturing labor costs 30 15Manufacturing overhead costs:
Variable costs 5 5 (X)Fixed costs 18 (I) 20
Manufacturing overhead costs 23 25
Total manufacturing costs incurredduring year 75 80
Add beginning work in process, 1/1 0 9Total manufacturing costs to
3-35
account for 75 89Deduct ending work in process, 12/31 0 9Cost of goods manufactured $75 (G) $80 (U)
**If the loss is $5,000, total costs are $100,000 + $5,000 = $105,000***100 – 75 = 25
3-36
3-46 (20−30 min.) CVP analysis under uncertainty.
1. a. At a selling price of $100, the unit contribution margin is ($100 – $50) = $50, and it willrequire the sale of ($200,000 ÷ $50) = 4,000 units to break even. The sales in dollars is$400,000, and there is a 2/3 probability of equaling or exceeding this sales level.
b. At a selling price of $70, the unit contribution margin is ($70 – $50) = $20, and it willrequire the sale of ($200,000 ÷ $20) = 10,000 units to break even. At the lower price,this sales in dollars is $700,000, and there is a 2/3 probability of equaling or exceedingthis sales volume.
Therefore, if you seek to maximize the probability of showing an operating income, you areindifferent between the two strategies.
A selling price of $100 will maximize the expected operating income.
3-37
3-47 (15 min.) CVP analysis under uncertainty.
1. Both products have the same unit contribution margin:
Unit contribution margin = Selling price per unit − Variable costs per unit= $10 − $8 = $2
Breakeven point = Fixed costs
Unit contribution margin
= $400,000
$2
= 200,000 units for each product
2. The expected demand for the two umbrellas is:
Event Emerald Green Shocking Pink(1)
Demand(2)
Probability(1) × (2)
Units(3)
Probability(1) × (3)
Units50,000
100,000200,000300,000400,000500,000
Expected demand
0.00.10.20.40.20.11.0
10,00040,000
120,00080,000
50,000
300,000
0.10.10.10.20.40.11.0
5,00010,00020,00060,000
160,000 50,000
305,000
Expected operating income of Emerald Green umbrellas:$2(300,000) − $400,000 = $200,000
Expected operating income of Shocking Pink umbrellas:$2(305,000) − $400,000 = $210,000
The Shocking Pink umbrellas should be chosen because they have the higher expected operatingincome.
3. The expected operating income from the two products would be identical. If the choicecriterion is to maximize expected operating income, the company will be indifferent betweenEmerald Green and Shocking Pink umbrellas. However, assume that management considers riskfactors. Emerald Green umbrellas, for example, have a 10% chance of selling only 100,000 units,which would result in a net operating loss of $200,000. Also, there is a 30% chance that sales ofEmerald Green will exceed 300,000 units. If this event happens, the operating income of EmeraldGreen umbrellas will be higher than the operating income of Shocking Pink umbrellas.
The expected values are important, but the dispersion of the probability distribution is alsoimportant. Normally, the wider the dispersion, the greater the risk. Knowledge of the entireprobability distribution helps management assess the risk before reaching a decision.
3-38
3-48 (30 min.) Ethics, CVP analysis.
1. Contribution margin percentage =Revenues osts
Revenues
− Variable c
=$5, , $3, ,000 000 000 000−
$5,000,000
=$5,000,000
$2,000,000 = 40%
Breakeven revenues =percentagemargin on Contributi
costs Fixed
=0.40
$2,160,000= $5,400,000
2. If variable costs are 52% of revenues, contribution margin percentage equals 48% (100% −52%)
Breakeven revenues =percentagemargin on Contributi
4. Incorrect reporting of environmental costs with the goal of continuing operations is unethical.In assessing the situation, the specific “Standards of Ethical Conduct for ManagementAccountants” (described in Exhibit 1-7) that the management accountant should consider are listedbelow.
CompetenceClear reports using relevant and reliable information should be prepared. Preparing reports on thebasis of incorrect environmental costs in order to make the company’s performance look betterthan it is violates competence standards. It is unethical for Bush to not report environmental costsin order to make the plant’s performance look good.
IntegrityThe management accountant has a responsibility to avoid actual or apparent conflicts of interestand advise all appropriate parties of any potential conflict. Bush may be tempted to report lowerenvironmental costs to please Lemond and Woodall and save the jobs of his colleagues. Thisaction, however, violates the responsibility for integrity. The Standards of Ethical Conduct requirethe management accountant to communicate favorable as well as unfavorable information.
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3-48 (Cont’d.)
ObjectivityThe management accountant’s Standards of Ethical Conduct require that information should befairly and objectively communicated and that all relevant information should be disclosed. From amanagement accountant’s standpoint, underreporting environmental costs to make performancelook good would violate the standard of objectivity.
Bush should indicate to Lemond that estimates of environmental costs and liabilities should beincluded in the analysis. If Lemond still insists on modifying the numbers and reporting lowerenvironmental costs, Bush should raise the matter with one of Lemond’s superiors. If after takingall these steps, there is continued pressure to understate environmental costs, Bush should considerresigning from the company and not engage in unethical behavior.
3-49 (35 min.) Deciding where to produce.
1. The annual breakeven point in units at the Peoria plant is 73,500 units and at the Moline plantis 47,200 units, calculated as follows.
Unit contribution calculation:Peoria Moline
Selling price $150.00 $150.00Less variable costs:
Manufacturing 72.00 88.00Commissions 7.50 7.50Marketing and distribution 6.50 6 .50
Contribution margin per unit $ 64.00 $ 48.00
Fixed costs calculation:
Total fixed costs = (Fixed manufacturing costs per unit + Fixed marketing anddistribution costs per unit) × Production rate per day ×Normal working days
Breakeven units = Fixed costs ÷ Contribution margin per unit
Peoria = $4,704,000 ÷ $64 = 73,500 units
Moline = $2,265,600 ÷ $48 = 47,200 units
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3-49 (Cont’d.)
2. The operating income that would result from the division production manager’s plan toproduce 96,000 units at each plant is $3,628,800. The normal capacity at the Peoria plant is96,000 units (400 × 240); however, the normal capacity at the Moline plant is 76,800 units (320 ×240). Therefore, 19,200 units (96,000 − 76,800) will be manufactured at Moline at a reducedcontribution of $40.00 per unit ($48 − $8).
Total contribution margin 10,598,400Less total fixed costs, $4,704,000 + $2,265,600 6,969,600Operating income $ 3,628,800
3. The optimal production plan is to produce 120,000 units at the Peoria plant and 72,000 unitsat the Moline plant. The full capacity of the Peoria plant, 120,000 units (400 units × 300 days),should be utilized as the contribution from these units is higher at all levels of production than thecontribution from units produced at the Moline plant.
