CHAPTER 7
Cost-Volume-Profit Analysis ANSWERS TO REVIEW QUESTIONS 7-1 7-1
a. In the the con contr trib ibut utio ion-m n-mar argi gin n appr approa oach ch,, the the brea breakk-ev even en poi point nt in in unit unitss is calc calcul ulat ated ed using the following formula: Break -even point
fixed expenses unit contributi on margin
b. In the equatio equation n approach, approach, the followi following ng profit profit equation equation is used: used:
unit sales volume unit variable sales volume − × × sales price in units expense in units
fixed expenses
=
0
This equation is solved for the sales volume in units. c. In the graphica graphicall approa approach, ch, sales sales reven revenue ue and total total expense expensess are are graphe graphed. d. The break-even point occurs at the intersection of the total revenue and total expense lines. 7-2
The term unit contribution margin refers to the contribution that each unit of sales makes toward covering fixed expenses and earning a profit. The unit contribution margin is defined as the sales price minus the unit variable expense.
7-3
In addit addition ion to to the breakbreak-eve even n point, point, a CVP graph graph shows shows the the impa impact ct on total total expen expenses ses,, total revenue, and profit when sales volume changes. The graph shows the sales volume required to earn a particular target net profit. The firm's profit and loss areas are also indicated on a CVP graph.
7-4 7-4
The The safet safetyy margi margin n is the amou amount nt by whic which h budge budgete ted d sales sales reven revenue ue exce exceed edss break break-even sales revenue.
7-5 7-5
An incre increas asee in the fixed fixed expen expense sess of any enter enterpr pris isee will will incre increas asee its its brea breakk-ev even en point. In a travel agency, more clients must be served before the fixed expenses are covered by the agency's service fees.
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7-6
A decre decrease ase in in the variab variable le expe expense nse per per poun pound d of oyst oysters ers resu results lts in in an incr increas easee in the the contribution margin per pound. This will reduce the company's break-even sales volume.
7-7 7-7
The The pres presid iden entt is corre correct ct.. A pric pricee incr increa ease se resul results ts in a high higher er unit unit cont contri ribu buti tion on margin. An increase in the unit contribution margin causes the break-even point to decline. The financial vice president's reasoning is flawed. Even though the break-even point will be lower, the price increase will not necessarily reduce the likelihood of a loss. Customers will probably be less likely to buy the product at a higher price. Thus, the firm may be less likely to meet the lower break-even point (at a high price) than the higher break-even point (at a low price).
7-8 7-8
When When the the sales sales pric pricee and uni unitt varia variabl blee cost cost incre increas asee by the same same amou amount nt,, the unit unit contribution contribution margin remains remains unchanged. unchanged. Therefore Therefore,, the firm's firm's break-eve break-even n point remains the same.
7-9 7-9
The The fixed fixed annu annual al dona donati tion on will will offs offset et some some of the the museu museum' m'ss fixed fixed expe expens nses es.. The reduction in net fixed expenses will reduce the museum's break-even point.
7-10
A profit-vo profit-volume lume graph shows the profit profit to to be earne earned d at each each level level of sales sales volume. volume.
7-11
The most most import important ant assump assumptions tions of a cost-volum cost-volume-pro e-profit fit analys analysis is are are as follows: follows: (a) The behavior of total revenue is linear (straight line) over the relevant range. range. This behavior implies that the price of the product or service will not change as sales volume varies within the relevant range. (b) The behavior behavior of total expenses expenses is linear linear (straight (straight line) over the relevant relevant range. This behavior implies the following more specific assumptions: (1) Expenses can be categorized categorized as fixed, variable, or semivariable. (2) Efficiency Efficiency and product productivity ivity are consta constant. nt. (c) In multiproduct multiproduct organizati organizations, ons, the sales mix remains constant constant over the relevant range. (d) In manufact manufacturi uring ng firms, firms, the inventor inventoryy levels levels at the beginni beginning ng and end of the period are the same.
7-12 7-12
Opera Operatin ting g managers managers frequ frequent ently ly prefer prefer the contri contribut bution ion income income statem statement ent becaus becausee it sepa separa rate tess fixe fixed d and and vari variab able le cost costs. s. This This form format at make makess cost cost-vo -volu lume me-p -pro rofi fitt relationships more readily discernible.
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7-13
The gross margin is defi define ned d as sale saless reve revenu nuee minu minuss all all vari variab able le and and fixe fixed d manufacturing expenses. The total contribution margin is defined as sales revenue minus all variable expenses, including manufacturing, selling, and administrative expenses.
7-14 7-14
East East Company, Company, which which is highly highly autom automate ated, d, will have have a cost struc structur turee dominate dominated d by fixed fixed costs. costs. West West Compan Company's y's cost cost struct structure ure will will includ includee a larger larger propor proportio tion n of variable costs than East Company's cost structure. A firm's operating leverage factor, at a particular sales volume, is defined as its total total contri contribut bution ion margin margin divide divided d by its net income income.. Since Since East East Compan Companyy has propor proportio tionat nately ely higher higher fixed fixed costs, costs, it will will have have a propor proportio tionat nately ely higher higher total total contribution margin. Therefore, East Company's operating leverage factor will be higher.
7-15 7-15
When When sales sales volume volume incre increase ases, s, Compan Companyy X will have have a higher higher percen percentag tagee increas increasee in profit than Company Y. Company X's higher proportion of fixed costs gives the firm a higher operating leverage factor. The company's percentage increase in profit can be found found by multip multiplyi lying ng the percen percentag tagee incre increase ase in sales sales volume volume by the firm's firm's operating leverage factor.
7-16 7-16
The sales sales mix mix of a multipro multiproduc ductt organiz organizati ation on is the relat relative ive propo proporti rtion on of sales sales of its products. The The weig weight hted ed-a -ave vera rage ge unit unit cont contri ribu buti tion on marg margin in is the the aver averag agee of the the unit unit contribution margins for a firm's several products, with each product's contribution margin weighted by the relative proportion of that product's sales.
7-17 7-17
The The car car rent rental al agency agency's 's sales sales mix is the the rela relati tive ve propo proport rtio ion n of its renta rentall busi busine ness ss associated with each of the three types of automobiles: subcompact, compact, and full-size. In a multi-product CVP analysis, the sales mix is assumed to be constant over the relevant range of activity.
7-18
Cost-volume Cost-volume-prof -profit it analysis analysis shows the effect effect on profit profit of of changes changes in in expense expenses, s, sales sales prices, and sales mix. A change in the hotel's room rate (price) will change the hotel' hotel'ss unit unit contri contribut bution ion margin margin.. This This contri contribut bution ion-ma -margi rgin n change change will will alter alter the relationship between volume and profit.
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7-19
Budgeting begins with a sales forecast. Cost-volume-profit analysis can be used to determine the profit that will be achieved at the budgeted sales volume. A CVP analysis also shows how profit will change if the sales volume deviates from budgeted sales. Cost-volume-profit analysis can be used to show the effect on profit when variable or fixed expenses change. The effect on profit of changes in variable or fixed advertising expenses is one factor that management would consider in making a decision about advertising.
7-20
The low-price company must have a larger sales volume than the high-price company. By spreading its fixed expense across a larger sales volume, the low-price firm can afford to charge a lower price and still earn the same profit as the high-price company. Suppose, for example, that companies A and B have the following expenses, sales prices, sales volumes, and profits.
Company A Sales revenue: 350 units at $10.............................................. 100 units at $20.............................................. Variable expenses: 350 units at $6................................................ 100 units at $6................................................ Contribution margin............................................. Fixed expenses.................................................... Profit.....................................................................
Company B
$3,500 $2,000 2,100 $1,400 1,000 $ 400
600 $1,400 1,000 $ 400
7-21
The statement makes three assertions, but only two of them are true. Thus the statement is false. A company with an advanced manufacturing environment typically will have a larger proportion of fixed costs in its cost structure. This will result in a higher break-even point and greater operating leverage. However, the firm's higher break-even point will result in a reduced safety margin.
7-22
Activity-based costing (ABC) results in a richer description of an organization's cost behavior and CVP relationships. Costs that are fixed with respect to sales volume may not be fixed with respect to other important cost drivers. An ABC system recognizes these nonvolume cost drivers, whereas a traditional costing system does not.
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SOLUTIONS TO EXERCISES EXERCISE 7-23 (20 MINUTES) 1.
2.
3.
fixed expenses
Break-even point (in units) = unit contributi on margin
Contribution-margin ratio
=
$54,000 = 13,500 pizzas $10 $6
=
unit contributi on margin unit sales price
=
$10 $6 = .4 $10
Break-even point (in sales dollars)
fixed expenses
= contribution-margin ratio =
4.
$54,000 = $135,000 .4
Let X denote the sales volume of pizzas required to earn a target net profit of $60,000. $10 X – $6 X – $54,000 = $60,000 $4 X = $114,000 X = 28,500 pizzas
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EXERCISE 7-24 (25 MINUTES)
1 2 3 4
Sales Revenue $360,000 55,000 320,000 c 160,000
Variable Expenses $120,000 11,000 80,000 130,000
Total Contribution Margin $240,000 44,000 240,000 30,000
Fixed Expenses $90,000 25,000 60,000 30,000 d
Net Income $150,000 19,000 180,000 -0-
Break-Even Sales Revenue $135,000 a 31,250 b 80,000 160,000
Explanatory notes for selected items: a
$135,000 = $90,000
b
(2/3), where 2/3 is the contribution-margin ratio.
$31,250 = $25,000/.80, where .80 is the contribution-margin ratio.
c
Break-even sales revenue............................................................................... Fixed expenses................................................................................................ Variable expenses............................................................................................
$80,000 60,000 $20,000
Therefore, variable expenses are 25 percent of sales revenue. When variable expenses amount to $80,000, sales revenue is $320,000. d
$160,000 is the break-even sales revenue, so fixed expenses must be equal to the contribution margin of $30,000 and profit must be zero.
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EXERCISE 7-25 (25 MINUTES) 1.
Cost-volume-profit graph:
Dollars per year Total revenue $600,000
Total expenses
Break-even point: 20,000 tickets
$500,000
Profit area Variable expense (at 30,000 tickets)
$400,000
$300,000 Loss area $200,000
Annual fixed expenses
$100,000
5,000
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15,000
20,000
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25,000
30,000
Tickets sold per year
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EXERCISE 7-25 (CONTINUED) 2.
Stadium capacity................................................ Attendance rate................................................... Attendance per game......................................... Break - even point (tickets) Attendance per game
20,000 4,000
6,000 2/3 4,000
5
The team must play 5 games to break even.
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EXERCISE 7-26 (25 MINUTES) 1.
Profit-volume graph:
Dollars per year
$300,000
$200,000
$100,000 Break-even point: 20,000 tickets 0
$(100,000)
5,000
10,000
15,000
Profit area •
20,000
25,000
Tickets sold per year
Loss area
$(200,000) Annual fixed expenses $(300,000) $(360,000)
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EXERCISE 7-26 (CONTINUED) 2.
Safety margin: Budgeted sales revenue (10 games 6,000 seats .45 full $20)............................................... Break-even sales revenue (20,000 tickets $20)............................................................................... Safety margin.................................................................................................
3.
$540,000 400,000 $140,000
Let P denote the break-even ticket price, assuming a 10-game season and 40 percent attendance: (10)(6,000)(.40)P – (10)(6,000)(.40)($2) – $360,000 = 0 24,000P P
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= $408,000 = $17 per ticket
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EXERCISE 7-27 (25 MINUTES) 1.
Break-even point (in units)
fixed costs
= unit contributi on margin 2,000,000 p = 4,000 components 1,000 p
= 1,500 p p denotes Argentina’s peso.
2.
New break-even point (in units)
= =
(2,000,000 p ) (1.05) 1,500 p
1,000 p
2,100,000 p = 4,200 components 500 p
3.
Sales revenue (7,000 1,500 p) ................................................. 10,500,000 p Variable costs (7,000 1,000 p)........................................................ 7,000,000 p Contribution margin......................................................................... 3,500,000 p Fixed costs........................................................................................ 2,000,000 p Net income........................................................................................ 1,500,000 p
4.
New break-even point (in units) = 1,400 p
2,000,000 p 1,000 p
= 5,000 components 5.
Analysis of price change decision: Price 1,500 p 10,500,000 p Sales revenue: (7,000 1,500 p)................................. (8,000 1,400 p)................................. 7,000,000 p Variable costs: (7,000 1,000 p)................................. (8,000 1,000 p)................................. 3,500,000 p Contribution margin.................................................... 2,000,000 p Fixed expenses............................................................ 1,500,000 p Net income (loss).........................................................
1,400 p 11,200,000 p 8,000,000 p 3,200,000 p 2,000,000 p 1,200,000 p
The price cut should not be made, since projected net income will decline by 300,000 p.
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EXERCISE 7-28 (25 MINUTES) 1.
(a) Traditional income statement: PACIFIC RIM PUBLICATIONS, INC. INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20XX
Sales ......................................................................... Less: Cost of goods sold......................................... Gross margin............................................................... Less: Operating expenses: Selling expenses............................................ Administrative expenses............................... Net income...................................................................
$1,000,000 750,000 $ 250,000 $75,000 75,000
150,000 $ 100,000
(b) Contribution income statement: PACIFIC RIM PUBLICATIONS, INC. INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20XX
Sales ......................................................................... Less: Variable expenses: Variable manufacturing.................................. Variable selling............................................... Variable administrative.................................. Contribution margin.................................................... Less: Fixed expenses: Fixed manufacturing...................................... Fixed selling................................................... Fixed administrative....................................... Net income................................................................... 2.
Operating leverage factor (at $1,000,000 sales level)
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$1,000,000 $500,000 50,000 15,000
$ 250,000 25,000 60,000
565,000 $ 435,000
335,000 $ 100,000
contribution margin net income $435,000 4.35 $100,000
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EXERCISE 7-28 (CONTINUED) 3.
percentage increase operating Percentage increase in et income = × i nsalesrev nue lev ragefactor = 12%
4.35
= 52.2% 4.
Most operating managers prefer the contribution income statement for answering this type of question. The contribution format highlights the contribution margin and separates fixed and variable expenses.
EXERCISE 7-29 (30 MINUTES) Answers will vary on this question, depending on the airline selected as well as the year of the inquiry. In a typical year, most airlines report a breakeven load factor of around 65 percent.
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EXERCISE 7-30 (30 MINUTES) 1. Bicycle Type High-quality Medium-quality 2.
Sales Price $1,000 600
Unit Variable Cost $600 ($550 + $50) 300 ($270 + $30)
Unit Contribution Margin $400 300
Sales mix: High-quality bicycles........................................................................................ Medium-quality bicycles...................................................................................
3.
Weighted-average unit contribution margin
= ($400
30%) + ($300
30% 70%
70%)
= $330 4.
Break - even point (in units)
fixed expenses weighted - average unit contribution ma $148,500 $330
Bicycle Type High-quality bicycles Medium-quality bicycles Total 5.
450 bicycles
Break-Even Sales Volume 135 (450 .30) 315 (450 .70)
Sales Price $1,000 600
Sales Revenue $135,000 189,000 $324,000
Target net income: Sales volume required to earn target net income of $99,000
$148,500 $99,000 $330 750 bicycles
This means that the shop will need to sell the following volume of each type of bicycle to earn the target net income: High-quality........................................................................... Medium-quality.....................................................................
225 (750 525 (750
.30) .70)
EXERCISE 7-31 (25 MINUTES) 1.
The following income statement, often called a common-size income statement, provides a convenient way to show the cost structure.
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Revenue....................................................... Variable expenses...................................... Contribution margin................................... Fixed expenses........................................... Net income..................................................
Amount $1,500,000 900,000 $600,000 450,000 $ 150,000
Percent 100 60 40 30 10
2. Decrease in Revenue $300,000* *$300,000 = $1,500,000
Contribution Margin Percentage 40%†
Decrease in Net Income $120,000
=
20%
†
40% = $600,000/$1,500,000
3.
Operating leverage factor (at revenue of $1,500,000)
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contribution margin net income $600,000 4 $150,000
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4.
percentageincrease operatingleverage Percentagechangein etincome inrevenue factor 5%2 4 10 %
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EXERCISE 7-32 (10 MINUTES) Revenue....................................................... Less: Variable expenses........................... Contribution margin.................................... Less: Fixed expenses................................ Net Income (loss)........................................
Requirement (1) $1,875,000 1,125,000 $ 750,000 675,000 $ 75,000
Requirement (2) $1,500,000 1,800,000 $ (300,000) 350,000 $ (650,000)
EXERCISE 7-33 (20 MINUTES) 1.
Break - even volume of service revenue
fixed expenses contribution margin ratio $200,000 .25
2.
3.
4.
Target before - tax income
$800,000
target after - tax net income 1 tax rate $120,000 $200,000 1 .40
Service revenue required to earn target after-tax income of $120,000
target after - tax net income (1 t ) contribution margin ratio
fixed expenses
$120,000 1 .40 .25
$200,000
$1,600,000
A change in the tax rate will have no effect on the firm's break-even point. At the breakeven point, the firm has no profit and does not have to pay any income taxes.
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SOLUTIONS TO PROBLEMS PROBLEM 7-34 (30 MINUTES) 1.
Break-even point in sales dollars, using the contribution-margin ratio: Break - even point
fixed expenses contribution - margin ratio $540,000 $216,000 $30 $12 $6 $30 $1,890,000
2.
$756,000 .4
Target net income, using contribution-margin approach: Sales units required to earn income of $540,000
fixed expenses target net incom unit contribution margin $756,000 $540,000 $30 $12 $6 108,000 units
3.
New unit variable manufacturing cost = $12
$1,296,000 $12
110%
= $13.20 Break-even point in sales dollars: Break - even point
=
$756,000 $30.00 −$13.20 −$6.00
=
$756,000 .36
$30 =$2,100,000
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PROBLEM 7-34 (CONTINUED) 4.
Let P denote the selling price that will yield the same contribution-margin ratio: $30.00
$12.00
$6.00
$13.20
P
$30.00
$6.00
P
.4
P
$19.20
P
$19.20
P
.4P $19.20
.6 P
P
$19.20/.6
P
$32.00
Check: New contribution-margin ratio is: $32.00
$13.20 $32.00
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PROBLEM 7-35 (30 MINUTES) 1.
Break - even point (in units)
fixed costs unit contribution margin $702,000 $25.00 $19.80
2.
Break - even point (in sales dollars)
135,000 units
fixed cost contribution - margin ratio $702,000 $25.00 $19.80 $25.00
3.
4.
Number of sales units required to earn target net profit
fixed costs
$3,375,000
target net profit
unit contribution margin $702,000 $25.00
$390,000 $19.80
210,000 units
Margin of safety = budgeted sales revenue – break-even sales revenue = (140,000)($25) – $3,375,000 = $125,000
5.
Break-even point if direct-labor costs increase by 10 percent: New unit contribution margin
= $25.00 – $8.20 – ($4.00)(1.10) – $6.00 – $1.60 = $4.80
Break-even point
fixed costs new unit contribution margin $702,000 $4.80
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146,250 units
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PROBLEM 7-35 (CONTINUED) 6.
Contribution margin ratio Old contribution-margin ratio
=
unit contribution margin sales price
$25.00 $19.80 $25.00 .208 −
=
=
Let P denote sales price required to maintain a contribution-margin ratio of .208. Then P is determined as follows: P
$8.20 ($4.00)(1.10)
$6.00
$1.60
P P
$20.20 .208P .792 P P
Check:
New contributionmargin ratio
.208
$20.20 $25.51 (rounded)
$25.51
$8.20
($4.00)(1. 10) $25.51
$6.00
$1.60
.208 (rounded)
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PROBLEM 7-36 (30 MINUTES) 1.
Break-even point in units, using the equation approach: $24 X – ($15 + $3) X – $1,800,000 = 0 $6 X = $1,800,000 X =
$1,800,000 $6
= 300,000 units 2.
New projected sales volume = 400,000
110%
= 440,000 units Net income = (440,000)($24 – $18) – $1,800,000 = (440,000)($6) – $1,800,000 = $2,640,000 – $1,800,000 = $840,000 3.
Target net income = $600,000 (from original problem data) New disk purchase price = $15
130% = $19.50
Volume of sales dollars required: Volume of sales dollars required
fixed expenses target net profit contribution - margin ratio $1,800,000 $600,000 $24 $19.50 $3 $24 $38,400,00 0
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PROBLEM 7-36 (CONTINUED) 4.
Let P denote the selling price that will yield the same contribution-margin ratio: $24
$15
$3
P
$19.50
$24
$3
P
.25
P
$22.50
P
$22.50
P
.25 P $22.50
.75 P
P
$22.50/.75
P
$30
Check: New contribution-margin ratio is: $30
5.
$22.50 $30
.25
The electronic version of the Solutions Manual “BUILD A SPREADSHEET SOLUTIONS” is available on your Instructors CD and on the Hilton, 8e website: www.mhhe.com/hilton8e.
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PROBLEM 7-37 (30 MINUTES) 1.
Unit contribution margin: Sales price………………………………… Less variable costs: Sales commissions ($32 x 5%)…… System variable costs……………… Unit contribution margin………………..
$32.00 $ 1.60 8.00
9.60 $22.40
Break-even point = fixed costs ÷ unit contribution margin = $1,971,200 ÷ $22.40 = 88,000 units 2.
Model A is more profitable when sales and production average 184,000 units.
Sales revenue (184,000 units x $32.00)……... Less variable costs: Sales commissions ($5,888,000 x 5%)… System variable costs:…………………… 184,000 units x $8.00…………………. 184,000 units x $6.40…………………. Total variable costs……………………….. Contribution margin…………………………... Less: Annual fixed costs…………………….. Net income……………………………………… 3.
Model A
Model B
$5,888,000
$5,888,000
$ 294,400
$ 294,400
1,472,000 $1,766,400 $4,121,600 1,971,200 $2,150,400
1,177,600 $1,472,000 $4,416,000 2,227,200 $2,188,800
Annual fixed costs will increase by $180,000 ($900,000 ÷ 5 years) because of straight-line depreciation associated with the new equipment, to $2,407,200 ($2,227,200 + $180,000). The unit contribution margin is $24 ($4,416,000 ÷ 184,000 units). Thus: Required sales = (fixed costs + target net profit) ÷ unit contribution margin = ($2,407,200 + $1,912,800) ÷ $24 = 180,000 units
4.
Let X = volume level at which annual total costs are equal $8.00X + $1,971,200 = $6.40X + $2,227,200 $1.60X = $256,000 X = 160,000 units
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PROBLEM 7-38 (25 MINUTES) 1.
Closing of mall store: Loss of contribution margin at Mall Store..................................................... $(108,000) Savings of fixed cost at Mall Store (75%)...................................................... 90,000 Loss of contribution margin at Downtown Store (10%)................................ (14,400) Total decrease in operating income............................................................... $ (32,400)
2.
Promotional campaign: Increase in contribution margin (10%)........................................................... Increase in monthly promotional expenses ($180,000/12)........................... Decrease in operating income........................................................................
3.
$10,800 (15,000) $(4,200)
Elimination of items sold at their variable cost: We can restate the November 20x4 data for the Mall Store as follows: Mall Store Items Sold at Their Variable Cost $180,000* 180,000 $ -0-
Other Items $180,000* 72,000 $108,000
If the items sold at their variable cost are eliminated, we have: Decrease in contribution margin on other items (20%).............................. Decrease in fixed expenses (15%)................................................................ Decrease in operating income......................................................................
$(21,600) 18,000 $ (3,600)
Sales................................................................................... Less: variable expenses................................................... Contribution margin..........................................................
*$180,000 is one half of the Mall Store's dollar sales for November 20x4. 4.
The electronic version of the Solutions Manual “BUILD A SPREADSHEET SOLUTIONS” is available on your Instructors CD and on the Hilton, 8e website: www.mhhe.com/hilton8e.
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PROBLEM 7-39 (40 MINUTES) 1.
Sales mix refers to the relative proportion of each product sold when a company sells more than one product.
2.
(a)
Yes. Plan A sales are expected to total 65,000 units (19,500 + 45,500), which compares favorably against current sales of 60,000 units.
(b)
Yes. Sales personnel earn a commission based on gross dollar sales. As the following figures show, Cold King sales will comprise a greater proportion of total sales under Plan A. This is not surprising in light of the fact that Cold King has a higher selling price than Mister Ice Cream ($43 vs. $37). Current
Units Mister Ice Cream.......... Cold King..................... Total........................ (c)
21,000 39,000 60,000
Plan A
Sales Mix 35% 65% 100%
Units 19,500 45,500 65,000
Sales Mix 30% 70% 100%
Yes. Commissions will total $267,800 ($2,678,000 x 10%), which compares favorably against the current flat salaries of $200,000. Mister Ice Cream sales: 19,500 units x $37............. Cold King sales: 45,500 units x $43........................ Total sales...........................................................
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$ 721,500 1,956,500 $2,678,000
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7- 27
PROBLEM 7-39 (CONTINUED) (d)
No. The company would be less profitable under the new plan.
Sales revenue: Mister Ice Cream: 21,000 units x $37; 19,500 units x $37.............. Cold King: 39,000 units x $43; 45,500 units x $43.......................... Total revenue.............................................................................. Less variable cost: Mister Ice Cream: 21,000 units x $20.50; 19,500 units x $20.50.... Cold King: 39,000 units x $32.50; 45,500 units x $32.50................ Sales commissions (10% of sales revenue)................................... Total variable cost...................................................................... Contribution margin............................................................................... Less fixed cost (salaries)....................................................................... Net income.............................................................................................. 3.
(a)
Plan A
$ 777,000 1,677,000 $2,454,000
$ 721,500 1,956,500 $2,678,000
$ 430,500 1,267,500
$ 399,750 1,478,750 267,800 $2,146,300 $ 531,700 ----___ $ 531,700
$1,698,000 $ 756,000 200,000 $ 556,000
The total units sold under both plans are the same; however, the sales mix has shifted under Plan B in favor of the more profitable product as judged by the contribution margin. Cold King has a contribution margin of $10.50 ($43.00 - $32.50), and Mister Ice Cream has a contribution margin of $16.50 ($37.00 - $20.50). Plan A
Units Mister Ice Cream.............. Cold King.......................... Total.............................
McGraw-Hill/Irwin Inc. 7-28
Current
19,500 45,500 65,000
Plan B
Sales Mix 30% 70% 100%
© 2009
Units 39,000 26,000 65,000
Sales Mix 60% 40% 100%
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PROBLEM 7-39 (CONTINUED) (b)
Plan B is more attractive both to the sales force and to the company. Salespeople earn more money under this arrangement ($274,950 vs. $200,000), and the company is more profitable ($641,550 vs. $556,000).
Sales revenue: Mister Ice Cream: 21,000 units x $37; 39,000 units x $37 ................................................................................................................. Cold King: 39,000 units x $43; 26,000 units x $43 ................................................................................................................. Total revenue ................................................................................................................. Less variable cost: Mister Ice Cream: 21,000 units x $20.50; 39,000 units x $20.50 ................................................................................................................. Cold King: 39,000 units x $32.50; 26,000 units x $32.50 ................................................................................................................. Total variable cost ................................................................................................................. Contribution margin............................................................................... Less: Sales force compensation: Flat salaries ................................................................................................................. Commissions ($916,500 x 30%) ................................................................................................................. Net income..............................................................................................
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Current
Plan B
$ 777,000
$1,443,000
1,677,000
1,118,000
$2,454,000
$2,561,000
$ 430,500
$ 799,500
1,267,500
845,000
$1,698,000
$1,644,500
$ 756,000
$ 916,500
200,000 274,950 $ 556,000
$ 641,550
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7- 29
PROBLEM 7-40 (35 MINUTES) 1.
Current income: Sales revenue………………………... Less: Variable costs………………… $1,008,000 Fixed costs……………………. 2,736,000 Net income…………………………….
$4,032,000 3,744,000 $ 288,000
CompTronics has a contribution margin of $72 [($4,032,000 - $1,008,000) ÷ 42,000 sets] and desires to increase income to $576,000 ($288,000 x 2). In addition, the current selling price is $96 ($4,032,000 ÷ 42,000 sets). Thus: Required sales = (fixed costs + target net profit) ÷ unit contribution margin = ($2,736,000 + $576,000) ÷ $72 = 46,000 sets, or $4,416,000 (46,000 sets x $96) 2.
If operations are shifted to Mexico, the new unit contribution margin will be $74.40 ($96.00 - $21.60). Thus: Break-even point = fixed costs ÷ unit contribution margin = $2,380,800 ÷ $74.40 = 32,000 units
3.
(a) CompTronics desires to have a 32,000-unit break-even point with a $72 unit contribution margin. Fixed costs must therefore drop by $432,000 ($2,736,000 $2,304,000), as follows: Let X = fixed costs X ÷ $72 = 32,000 units X = $2,304,000 (b)
As the following calculations show, CompTronics will have to generate a contribution margin of $85.50 to produce a 32,000-unit break-even point. Based on a $96.00 selling price, this means that the company can incur variable costs of only $10.50 per unit. Given the current variable cost of $24.00 ($96.00 - $72.00), a decrease of $13.50 per unit ($24.00 - $10.50) is needed. Let X = unit contribution margin $2,736,000 ÷ X = 32,000 units X = $85.50
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PROBLEM 7-40 (CONTINUED) 4.
(a)
Increase
(b)
No effect
(c)
Increase
(d)
No effect
PROBLEM 7-41 (45 MINUTES) 1.
Break-even sales volume for each model: Break-even volume
(a)
(b)
(c)
=
annual rental cost unit contribution margin
Standard model: Break - even volume
$16,000 $3.50 $2.86
25,000 tubs
Break - even volume
$22,000 $3.50 $2.70
27,500 tubs
Break - even volume
$40,000 $3.50 $2.52
40,816 tubs (rounded)
Super model:
Giant model:
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PROBLEM 7-41 (CONTINUED) 2. Profit-volume graph:
Dollars per year (in thousands)
$40
t i f o r P
$20 Break-even point: 40,816 tubs 0
10
20
30
Profit area •
40
50
Tubs sold per year (in thousands)
Loss area s s o L
($20)
Fixed rental cost: $40,000 per year ($40)
McGraw-Hill/Irwin Inc. 7-32
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PROBLEM 7-41 (CONTINUED) 3.
The sales price per tub is the same regardless of the type of machine selected. Therefore, the same profit (or loss) will be achieved with the Standard and Super models at the sales volume, X , where the total costs are the same. Model Standard..................................................... Super..........................................................
Variable Cost per Tub $2.86 2.70
Total Fixed Cost $16,000 22,000
This reasoning leads to the following equation: 16,000 + 2.86 X = 22,000 + 2.70 X Rearranging terms yields the following:
(2.86 – 2.70) X = 22,000 – 16,000 .16 X = 6,000 X = 6,000/.16 X = 37,500
Or, stated slightly differently: Volume at which both machines produce the same profit
fixed cost differential variable cost differential $6,000 $.16 37,500 tubs
Check: the total cost is the same with either model if 37,500 tubs are sold. Standard Variable cost: Standard, 37,500 $2.86........................... Super, 37,500 $2.70................................ Fixed cost: Standard, $16,000...................................... Super, $22,000............................................ Total cost.........................................................
Super
$107,250 $101,250 16,000 $123,250
22,000 $123,250
Since the sales price for popcorn does not depend on the popper model, the sales revenue will be the same under either alternative.
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PROBLEM 7-42 (40 MINUTES) 1. CVP graph:
Total revenue Dollars per year (in millions) 20 18 16 14
Profit area
Break-even point: 80,000 units or $8,000,000 of sales
Total expenses
12 10 8 6
Loss 4 area
Fixed expenses
2 50
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100
150
200
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Units sold per year (in thousands)
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PROBLEM 7-42 (CONTINUED) 2.
Break-even point: Contribution - margin ratio Break - even point
contribution margin sales fixed expenses
$12,000,000
.75 $16,000,000 $6,000,000
contribution - margin ratio
.75
$8,000,000
3.
Margin of safety
= budgeted sales revenue – break-even sales revenue = $16,000,000 – $8,000,000 = $8,000,000
4.
5.
Operating leverage factor (at budgeted sales)
Dollar sales required to earn target net profit
contribution margin (at budgeted sales) net income (at budgeted sales) $12,000,000 $6,000,000
2
fixed expenses
target net profit
contribution - margin ratio $6,000,000 $9,000,000 .75
6.
$20,000,00 0
Cost structure:
Sales revenue....................................................... Variable expenses................................................ Contribution margin............................................. Fixed expenses.................................................... Net income............................................................
McGraw-Hill/Irwin Inc. Managerial Accounting, 8/e
Amount $16,000,000 4,000,000 $12,000,000 6,000,000 $ 6,000,000
© 2009
Percent 100.0 25.0 75.0 37.5 37.5
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PROBLEM 7-43 (35 MINUTES) 1.
Plan A break-even point = fixed costs ÷ unit contribution margin = $33,000 ÷ $33* = 1,000 units Plan B break-even point = fixed costs ÷ unit contribution margin = $99,000 ÷ $45** = 2,200 units * $120 - [($120 x 10%) + $75] ** $120 - $75
2.
Operating leverage refers to the use of fixed costs in an organization’s overall cost structure. An organization that has a relatively high proportion of fixed costs and low proportion of variable costs has a high degree of operating leverage.
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PROBLEM 7-43 (CONTINUED) 3.
Calculation of contribution margin and profit at 6,000 units of sales:
Sales revenue: 6,000 units x $120………………. Less variable costs: Cost of purchasing product: 6,000 units x $75…………………….…… Sales commissions: $720,000 x 10%……... Total variable cost……………………….. Contribution margin……………………………… Fixed costs…………………………………………. Net income………………………………………….
Plan A
Plan B
$720,000
$720,000
$450,000 72,000 $522,000 $198,000 33,000 $165,000
$450,000 ----__ $450,000 $270,000 99,000 $171,000
Plan A has a higher percentage of variable costs to sales (72.5%) compared to Plan B (62.5%). Plan B’s fixed costs are 13.75% of sales, compared to Plan A’s 4.58%. Operating leverage factor = contribution margin ÷ net income Plan A: $198,000 ÷ $165,000 = 1.2 Plan B: $270,000 ÷ $171,000 = 1.58 (rounded) Plan B has the higher degree of operating leverage. 4 & 5. Calculation of profit at 5,000 units:
Sales revenue: 5,000 units x $120………………. Less variable costs: Cost of purchasing product: 5,000 units x $75………………………….. Sales commissions: $600,000 x 10%……... Total variable cost……………………….. Contribution margin……………………………… Fixed costs………………………………………… Net income………………………………………….
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Plan A
Plan B
$600,000
$600,000
$375,000 60,000 $435,000 $165,000 33,000 $132,000
$375,000 ---- __ $375,000 $225,000 99,000 $126,000
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PROBLEM 7-43 (CONTINUED) Plan A profitability decrease: $165,000 - $132,000 = $33,000; $33,000 ÷ $165,000 = 20% Plan B profitability decrease: $171,000 - $126,000 = $45,000; $45,000 ÷ $171,000 = 26.3% (rounded) PneumoTech would experience a larger percentage decrease in income if it adopts Plan B. This situation arises because Plan B has a higher degree of operating leverage. Stated differently, Plan B’s cost structure produces a greater percentage decline in profitability from the drop-off in sales revenue. Note: The percentage decreases in profitability can be computed by multiplying the percentage decrease in sales revenue by the operating leverage factor. Sales dropped from 6,000 units to 5,000 units, or 16.67%. Thus: Plan A: 16.67% x 1.2 = 20.0% Plan B: 16.67% x 1.58 = 26.3% (rounded) 6.
Heavily automated manufacturers have sizable investments in plant and equipment, along with a high percentage of fixed costs in their cost structures. As a result, there is a high degree of operating leverage. In a severe economic downturn, these firms typically suffer a significant decrease in profitability. Such firms would be a more risky investment when compared with firms that have a low degree of operating leverage. Of course, when times are good, increases in sales would tend to have a very favorable effect on earnings in a company with high operating leverage.
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PROBLEM 7-44 (45 MINUTES) 1.
Break-even point in units: Break-even point
=
fixed costs unit contribution margin
Calculation of contribution margins:
Selling price...................................... Variable costs: Direct material.............................. Direct labor................................... Variable overhead........................ Variable selling cost..................... Contribution margin per unit (a)
$8.40 10.80 7.20 3.00
29.40 $15.60
ComputerAssisted Manufacturing System $45.00 $7.50 9.00 4.50 3.00
24.00 $21.00
Labor-intensive production system: Break - even point in units
(b)
LaborIntensive Production System $45.00
$1,980,000 $750,000 $15.60 $2,730,000 $15.60 175,000 units
Computer-assisted manufacturing system: Break - even point in units
McGraw-Hill/Irwin Inc. Managerial Accounting, 8/e
$3,660,000 $750,000 $21 $4,410,000 $21 210,000 units
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PROBLEM 7-44 (CONTINUED) 2.
Zodiac’s management would be indifferent between the two manufacturing methods at the volume ( X ) where total costs are equal. $29.40 X + $2,730,000 =
$24 X + $4,410,000
$5.40 X =
$1,680,000
X =
311,111 units* *Rounded
3.
Operating leverage is the extent to which a firm's operations employ fixed operating costs. The greater the proportion of fixed costs used to produce a product, the greater the degree of operating leverage. Thus, the computer-assisted manufacturing method utilizes a greater degree of operating leverage. The greater the degree of operating leverage, the greater the change in operating income (loss) relative to a small fluctuation in sales volume. Thus, there is a higher degree of variability in operating income if operating leverage is high.
4.
Management should employ the computer-assisted manufacturing method if annual sales are expected to exceed 311,111 units and the labor-intensive manufacturing method if annual sales are not expected to exceed 311,111 units.
5.
Zodiac’s management should consider many other business factors other than operating leverage before selecting a manufacturing method. Among these are: •
Variability or uncertainty with respect to demand quantity and selling price.
•
The ability to produce and market the new product quickly.
•
The ability to discontinue production and marketing of the new product while incurring the least amount of loss.
McGraw-Hill/Irwin Inc. 7-40
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PROBLEM 7-45 (40 MINUTES) 1.
In order to break even, during the first year of operations, 10,220 clients must visit the law office being considered by Steven Clark and his colleagues, as the following calculations show. Fixed expenses: Advertising............................................................................... $ 980,000 Rent (6,000 $56).................................................................... 336,000 Property insurance.................................................................. 54,000 Utilities ..................................................................................... 74,000 Malpractice insurance............................................................. 360,000 Depreciation ($120,000/4)........................................................ 30,000 Wages and fringe benefits: Regular wages ($50 + $40 + $30 + $20) 16 hours 360 days......... $806,400 Overtime wages (200 $30 1.5) + (200 $20 1.5).......................... 15,000 Total wages............................................................ $821,400 Fringe benefits at 40%....................................................... 328,560 1,149,960 Total fixed expenses...................................................................... $2,983,960
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PROBLEM 7-45 (CONTINUED) Break-even point: 0 = revenue – variable cost – fixed cost 0 = $60 X + ($4,000
.2 X .3)* – $8 X – $2,983,960
0 = $60 X + $240 X – $8 X – $2,983,960 $292 X = $2,983,960 X = 10,220 clients (rounded)
*Revenue calculation: $60 X represents the $60 consultation fee per client. ($4,000 .2 X .30) represents the predicted average settlement of $4,000, multiplied by the 20% of the clients whose judgments are expected to be favorable, multiplied by the 30% of the judgment that goes to the firm. 2.
Safety margin: Safety margin = budgeted sales revenue
break-even sales revenue
Budgeted (expected) number of clients = 50
360 = 18,000
Break-even number of clients = 10,220 (rounded) Safety margin = [($60
18,000) + ($4,000 – [($60
10,220) + ($4,000
= [$60 + ($4,000 = $300
18,000
.20
.30)]
.20
.30)]
10,220
.20
.30)]
(18,000 – 10,220)
7,780
= $2,334,000
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PROBLEM 7-46 (35 MINUTES) Unit contribution margin
1.
$1,2 $20 p
Break - even point (in units)
unit $300 $
2.
fixed costs target net profit unit contribution margin
Number of sales units required to earn target net profit
$300,000 $280,000 $20
3.
New break - even point (in units) = =
29,000 units
new fixed costs new unit contributi on margin $300,000 + ($36,000/6) * $20 − $4 †
=
19,125 units
*Annual straight-line depreciation on new machine †
$4.00 = $9.00 – $5.00 increase in the unit cost of the new part
4.
Number of sales units re uired to earn target net profit, given manufacturing changes
=
= =
new fixed costs + target net profit new unit contributi on margin $306,000 +$200,000 * $16 31,625 units
*Last year's profit: ($50)(25,000) – $1,050,000 = $200,000
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PROBLEM 7-46 (CONTINUED)
Contributi on - margin ratio
5.
Old contribution - margin ratio
=
=
unit contribution margin $20 $50 *
sales price =
.40
*Sales price, given in problem. Let P denote the price required to cover increased direct-material cost and maintain the same contribution margin ratio: P
−
$30 * $4 † −
P P
=
$34 .60P
−
P
*Old unit variable cost = $30 = $750,000
= = =
.40 .40P $34 $56.67 (rounded)
25,000 units
†
Increase in direct-material cost = $4
Check: New contribution - margin ratio
= =
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$56.67 − $30 − $4 $56.67 .40 (rounded)
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PROBLEM 7-47 (40 MINUTES) 1.
Memorandum
Date:
Today
To:
Vice President for Manufacturing, Saturn Game Company
From:
I.M. Student, Controller
Subject:
Activity-Based Costing
The $300,000 cost that has been characterized as fixed is fixed with respect to sales volume. This cost will not increase with increases in sales volume. However, as the activitybased costing analysis demonstrates, these costs are not fixed with respect to other important cost drivers. This is the difference between a traditional costing system and an ABC system. The latter recognizes that costs vary with respect to a variety of cost drivers, not just sales volume. 2.
New break-even point if automated manufacturing equipment is installed: Sales price..................................................................................................... Costs that are variable (with respect to sales volume): Unit variable cost (.8 $750,000 25,000)........................................... Unit contribution margin.............................................................................. Costs that are fixed (with respect to sales volume): Setup (300 setups at $100 per setup)........................................... Engineering (800 hours at $56 per hour)..................................... Inspection (100 inspections at $90 per inspection).................... General factory overhead.............................................................. Total.......................................................................................... Fixed selling and administrative costs.............................................. Total costs that are fixed (with respect to sales volume)........... Break - even point (in units)
$52 24 $28
$ 30,000 44,800 9,000 332,200 $416,000 60,000 $476,000
fixed costs unit contribution margin $476,000 $28 17,000 units
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PROBLEM 7-47 (CONTINUED) 3.
Sales (in units) required to show a profit of $280,000: Number of sales units required to earn target net profit
=
= =
4.
fixed cost + target net profit unit contribution margin $476,000 + $280,000 $28 27,000 units
If management adopts the new manufacturing technology: (a)
Its break-even point will be higher (17,000 units instead of 15,000 units).
(b)
The number of sales units required to show a profit of $280,000 will be lower (27,000 units instead of 29,000 units).
(c)
These results are typical of situations where firms adopt advanced manufacturing equipment and practices. The break-even point increases because of the increased fixed costs due to the large investment in equipment. However, at higher levels of sales after fixed costs have been covered, the larger unit contribution margin ($28 instead of $20) earns a profit at a faster rate. This results in the firm needing to sell fewer units to reach a given target profit level.
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PROBLEM 7-47 (CONTINUED) 5.
The controller should include the break-even analysis in the report. The Board of Directors needs a complete picture of the financial implications of the proposed equipment acquisition. The break-even point is a relevant piece of information. The controller should accompany the break-even analysis with an explanation as to why the break-even point will increase. It would also be appropriate for the controller to point out in the report that the advanced manufacturing equipment would require fewer sales units at higher volumes in order to achieve a given target profit, as in requirement (3) of this problem. To withhold the break-even analysis from the controller's report would be a violation of the following ethical standards: (a)
Competence: Prepare complete and clear reports and recommendations after appropriate analysis of relevant and reliable information.
(b)
Integrity: Communicate unfavorable as well as favorable information and professional judgments or opinions.
(c)
Objectivity: Communicate information fairly and objectively. Disclose fully all relevant information that could reasonably be expected to influence an intended user's understanding of the reports, comments, and recommendations presented.
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PROBLEM 7-48 (45 MINUTES) 1.
2.
Unit contributi on margin
=
$810,000 1,800
Break - even volume in tons
=
fixed costs unit contributi on margin
=
$495,000 $450
$450 per ton
=
1,100 tons
=
Projected net income for sales of 2,100 tons: Projected contribution margin (2,100 $450)....................................... Projected fixed costs............................................................................... Projected net income...............................................................................
3.
$945,000 495,000 $450,000
Projected net income including foreign order: Variable cost per ton = $990,000/1,800 = $550 per ton Sales price per ton for regular orders = $1,800,000/1,800 = $1,000 per ton
Sales in tons..................................................................... Contribution margin per ton: Foreign order ($900 – $550)....................................... Regular sales ($1,000 – $550).................................... Total contribution margin................................................
Foreign Order 1,500 $350 $525,000
Contribution margin on foreign order....................................................... Contribution margin on Regular sales...................................................... Total contribution margin........................................................................... Fixed costs.................................................................................................. Net income...................................................................................................
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Regular Sales 1,500
$450 $675,000 $ 525,000 675,000 $1,200,000 495,000 $ 705,000
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PROBLEM 7-48 (CONTINUED) 4.
New sales territory: To maintain its current net income, Central Pennsylvania Limestone Company just needs to break even on sales in the new territory. Break - even point in tons
fixed costs in new territory unit contribution margin on sales in new territory $123,000 $450 $50
5.
307.5 tons
Automated production process: Break - even point in tons
Break - even point in sales dollars
$495,000 $450
$1 $5
$612,000 $500
1,
1,224 tons
$
$1,224,000
6.
Changes in selling price and unit variable cost: New unit
contributio
New contribution ma
Dollar
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sales required to earn target
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PROBLEM 7-49 (45 MINUTES) 1. TOLEDO TOOL COMPANY BUDGETED INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20X4
Unit Unit sellin selling g price. price..... ....... ...... ...... ...... ........ ......... .... Variable manufacturing cost....... Variable selling cost.................... Total variable cost....................... Contribution margin per unit. . . . . . Unit sales...................................... Total contribution margin.......
Hedge Clippers $84 $39 15 $54 $30 50,000 $1,500,000
Line Trimmers $108 $108 $ 36 12 $ 48 $ 60 50,000 $3,000,000
Leaf Blowers $144 $144 $ 75 18 $ 93 $ 51 100,000 $5,100,000
Fixed manufacturing overhead... Fixed selling and administrative costs................ Total fixed costs...................... Income before taxes.................... Income taxes (40%)..................... Budgeted net income..................
Total
$9,600,000 $6,000,000 1,800,000 $7,800,000 $1,800,000 720,000 $1,080,000
2.
Hedge Clippers....................................... Line Trimmers........................................ Leaf Blowers........................................... Weighted-average unit contribution margin.......................... Total unit sales to break even
(a) Unit Contribution $30 60 51
(a) (b) $ 7. 7.50 15.00 25.50 $48.00
total fixed costs weighted - average unit contribution margin $7,800,000 $48
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(b) Sales Proportion .25 .25 .50
162,500 units
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PROBLEM 7-49 (CONTINUED) Sales proportions:
Hedge Cl Clippers............................................. Line Trimmers............................................... Leaf Blowers................................................. Total...............................................................
Sales Proportion .25 .25 .50
Total Unit Sales 162,500 162,500 162,500
Product Line Sales 40,625 40,625 81,250 162,500
3.
Hedge Clippers.............................................. Line Trimmers*............................................... Leaf Blowers†................................................. Weighted-average unit contribution margin
(a) (b) Unit Sales Contribution Proportion $30 .20 57 .20 36 .60
(a) (b) $ 6.00 11.40 21.60 $39.00
*Variable selling cost increases. Thus, the unit contribution decreases to $57 [$108 – ($36 + $12 + $3)]. †
The variable manufacturing cost increases 20 percent. Thus, the unit contribution decreases to $36 [$144 – (1.2 $75) – $18]. Total unit sales to break even
total fixed costs weighted - average unit contribution margin $7,800,000 $39
200,000 units
Sales proportions: Sales Proportions Hedge Clippers............................................. .20 Line Trimmers.............................................. .20 Leaf Blowers................................................. .60 Total..............................................................
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Total Unit Sales 200,000 200,000 200,000
Product Line Sales 40,000 40,000 120,000 200,000
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PROBLEM 7-50 (35 MINUTES) 1.
sales
Unit contribution margin
(a)
var units
$2,000,000 10 fixe unit contri
Break - even point (in units)
$420,000 $6 contri
Contribution - margin ratio
(b)
sale $2,000
Break - even point (in sales dollars)
contri $420,0 .3
2.
Number of units of sales required to earn target after-tax net income
fixed costs +
(1 − t ) unit contribution margin
=
$420,000 + =
=
3.
target after - tax net income
$180,000 (1
−
$6
.4)
=
$720,000 $6
120,000 units
If fixed costs increase by $63,000: Break - even point (in units)
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$420,000
$63,000 $6
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80,500 units
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PROBLEM 7-50 (CONTINUED) 4. Profit-volume graph:
Dollars per year
$1,500,000
$1,000,000
$500,000
0
Break-even point: 70,000 units
Loss 25,000 area
50,000
75,000
Profit area
100,000
Units sold per year
$(500,000)
$(1,000,000)
$(1,500,000)
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PROBLEM 7-50 (CONTINUED) 5.
Number of units of sales required to earn target after-tax net income
target after - tax net income (1 t ) unit contribution margin
fixed costs
$180,000 (1 .5)
$420,000 $6
$780,000 $6
130,000 units
6.
The electronic version of the Solutions Manual “BUILD A SPREADSHEET SOLUTIONS” is available on your Instructors CD and on the Hilton, 8e website: WWW.MHHE.COM/HILTON8E.
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PROBLEM 7-51 (35 MINUTES) 1.
2.
Contribution margin ratio
$120.00
$79.20
$120.00
fixed expenses
target after - tax net income
(1 t) unit contribution margin
Number of units of sales required to earn target after-tax income
$475,200 X X
3.
.34
Break-even point (in units) for the touring model
$120.00
$33,120 (1 .40) $79.20
$530,400 $40.80
13,000 units
$554,400 $132.00
$79.20
10,500 units
Let Y denote the variable cost of the mountaineering model such that the break-even point for the mountaineering model is 10,500 units. Then we have: 10,500 Y )
$120.00 $475,200
10,500Y
$475,200
10,500Y
$784,800
(10,500) ($120.00 $1,260,000
$475,200
Y
Y
$74.74 (rounded)
Thus, the variable cost per unit would have to decrease by $4.46 ($79.20 – $74.74).
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PROBLEM 7-51 (CONTINUED) 4.
New break - even point
$475,200 110% $120.00 ($79.20)(90%) $522,720 $48.72 10,729 units (rounded)
5.
Weighted-average unit contribution margin
Break-even point
(50%
$52.80)
(50%
$40.80)
$46.80 fixed costs weighted - average unit contribution margin $514,800 $46.80
11,000 units (or 5,500 of each type)
PROBLEM 7-52 (45 MINUTES) 1.
SUMMARY OF EXPENSES
Manufacturing.................................................................... Selling and administrative................................................ Interest............................................................................... Costs from budgeted income statement..................... If the company employs its own sales force: Additional sales force costs......................................... Reduced commissions [(.15 – .10) $24,000]............ Costs with own sales force............................................... If the company sells through agents: Deduct cost of sales force............................................ Increased commissions [(.225 – .10) $24,000]......... Costs with agents paid increased commissions............
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Expenses per Year (in thousands) Variable Fixed $ 10,800 $3,510 3,600 2,880 810 $ 14,400 $7,200 3,600 (1,200 ) $ 13,200
$10,800 (3,600)
3,000 $ 16,200
$7,200
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PROBLEM 7-52 (CONTINUED) Break -even sales dollars =
total fixed expenses contribution margin ratio
Contribution-margin ratio =1 −
(a)
Contributi on margin ratio
total variable expenses sales revenue
1 1 .40
Break - even sales dollars
(b)
Contribution margin ratio
$14,400,000 $24,000,000 .60
$7,200,000 .40 $18,000,00 0 1 1
$13,200,000 $24,000,000 .55
.45 Break - even sales dollars
2.
Required sales dollars
$10,800,000 .45 $24,000,000
total fixed costs target income before income taxes contribution margin ratio
Contribution margin ratio
1 1
$16,2 $24,0 .675
.325 Required sales dollars to break even
$7,200,0 $9,600,0 .325 $29,538,
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PROBLEM 7-52 (CONTINUED) 3.
The volume in sales dollars ( X ) that would result in equal net income is the volume of sales dollars where total expenses are equal. Total expenses with agents paid increased commission $16,200,000 X $24,000,000 .675 X
= total expenses with own sales force
$7,200,000 $7,200,000 .125 X X
$13,200,000 X $10,800,000 $24,000,000 .55 X $10,800,000 $3,600,000 $28,800,000
Therefore, at a sales volume of $28,800,000, the company will earn equal before-tax income under either alternative. Since before-tax income is the same, so is after-tax net income. A different approach to the solution seeks to equate total profit (instead of total expenses). This approach uses the contribution-margin ratio, as follows: $24, 000000 - $16, 200, 000
$24, 000, 000 - $13, 200, 000 X - $7, 200, 000 =
$24, 000, 000
X - $10, 800, 000 $24, 000, 000
..325X - $7, 200, 000 = ..45X - $10, 800, 000 .125X = $3, 600, 000 X = $28, 800, 000
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PROBLEM 7-53 (45 MINUTES) 1.
a. In order to break even, Columbus Canopy Company must sell 500 units. This amount represents the point where revenue equals total costs. Revenue
variable costs
$800X
$400X
$400X
$200,000
X
500 units
fixed costs
$200,000
b. In order to achieve its after-tax profit objective, Columbus Canopy Company must sell 2,500 units. This amount represents the point where revenue equals total costs plus the before-tax profit objective. Revenue
2.
variable costs
fixed costs
$800X
$400X
$200,000
[$480,000
$800X
$400X
$200,000
$800,000
$400X
$1,000,000
X
2,500 units
before - tax profit (1
.4)]
To achieve its annual after-tax profit objective, management should select the first alternative, where the sales price is reduced by $80 and 2,700 units are sold during the remainder of the year. This alternative results in the highest profit and is the only alternative that equals or exceeds the company’s profit objective. Calculations for the three alternatives follow.
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PROBLEM 7-53 (CONTINUED) Alternative (1): Re venue
($800)(350)
($720)( 2,700)
$2,224,000 Variable cost
$400
3,050
$1,220,000 Before - tax profit
$2,224,000
$1,220,000
$200,000
$804,000 After - tax profit
$804,000
(1
.4 )
$ 482,400
Alternative (2): Re venue
($800)(350)
($740)( 2,200)
$1,908,000 Variable cost
( $400)(350)
($350)( 2,200)
$910,000 Before - tax profit
$1,908,000
$910,000
$200,000
$798,000 After - tax profit
$798,000
(1
.4 )
$ 478,800
Alternative (3): Re venue
($800)(350)
($760)( 2,000)
$1,800,000 Variable cost
$400
2,350
$940,000 Before - tax profit
$1,800,000
$940,000
$180,000
$680,000 After - tax profit
$680,000
(1
.4 )
$ 408,000
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SOLUTIONS TO CASES CASE 7-54 (50 MINUTES) 1.
The break-even point is 16,900 patient-days calculated as follows: SUSQUEHANNA MEDICAL CENTER COMPUTATION OF BREAK-EVEN POINT IN PATIENT-DAYS: PEDIATRICS FOR THE YEAR ENDED JUNE 30, 20X6
Total fixed costs: Medical center charges......................................................................................... Supervising nurses ($30,000 4)....................................................................... Nurses ($24,000 10)..................................................................... Aids ($10,800 20)..................................................................... Total fixed costs .............................................................................................
$3,480,000 120,000 240,000 216,000 $4,056,000
Contribution margin per patient-day: Revenue per patient-day.......................................................................................
$360
Variable cost per patient-day: ($7,200,000 ÷ $360 = 20,000 patient-days) ($2,400,000 ÷ 20,000 patient-days).................................................................. Contribution margin per patient-day....................................................................
120 $240
Break-even point in patient-days
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total fixed costs contribution margin per patient - day 16,900 patient days
$4,056,000 $240
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CASE 7-54 (CONTINUED) 2. Net earnings would decrease by $728,000, calculated as follows: SUSQUEHANNA MEDICAL CENTER COMPUTATION OF LOSS FROM RENTAL OF ADDITIONAL 20 BEDS: PEDIATRICS FOR THE YEAR ENDED JUNE 30, 20X6
Increase in revenue (20 additional beds
$360 charge per day)....................................
$ 648,000
Increase in expenses: Variable charges by medical center (20 additional beds 90 days $120 per day)...........................................
$ 216,000
Fixed charges by medical center ($3,480,000 60 beds = $58,000 per bed) ($58,000 20 beds).......................................................................................
1,160,000
Salaries (20,000 patient-days before additional 20 beds + 20 additional beds 90 days = 21,800, which does not exceed 22,000 patient-days; therefore, no additional personnel are required)......................................... Total increase in expenses..................................................................................... Net change in earnings from rental of additional 20 beds...................................
-0$1,376,000 $ (728,000)
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CASE 7-55 (50 MINUTES) 1.
Break-even point for 20x4, based on current budget: Contributi on - margin ratio Break - even point
$15,000,000
=
=
2.
$9,000,000 $15,000,000 fixed expenses
=
−
$3,000,000
−
.20
=
contributi on - margin ratio $150,000 .20
=
$750,000
Break-even point given employment of sales personnel: New fixed expenses: Previous fixed expenses........................................................................ Sales personnel salaries (3 x $45,000).................................................. Sales managers’ salaries (2 $120,000)............................................... Total.........................................................................................................
$
$
150,000 135,000 240,000 525,000
New contribution-margin ratio: Sales........................................................................................................ Cost of goods sold................................................................................. Gross margin.......................................................................................... Commissions (at 5%).............................................................................. Contribution margin............................................................................... Contribution - margin ratio
Estimated break - even point
$5,250,000 $15,000,000
.35
fixed expenses contribution - margin ratio $525,000 .35
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$15,000,000 9,000,000 $ 6,000,000 750,000 $ 5,250,000
$1,500,000
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CASE 7-55 (CONTINUED) 3.
Assuming a 25% sales commission: New contribution-margin ratio: Sales........................................................................................................ Cost of goods sold................................................................................. Gross margin.......................................................................................... Commissions (at 25%)............................................................................ Contribution margin............................................................................... Contribution - margin ratio
Sales volume in dollars required to earn after-tax net income
$2,250,000 $15,000,000
fixed expenses + =
.15
target after - tax net income
(1 − t ) contribution - margin ratio
$150,000 + =
$15,000,000 9,000,000 $ 6,000,000 3,750,000 $ 2,250,000
$1,995,000 (1 − .3)
.15 = $20,000,000
=
$3,000,000 .15
Check: Sales.................................................................... Cost of goods sold (60% of sales)..................... Gross margin...................................................... Selling and administrative expenses: Commissions................................................ All other expenses (fixed)............................ Income before taxes........................................... Income tax expense (30%)................................. Net income..........................................................
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$ 20,000,000 12,000,000 $ 8,000,000 $ 5,000,000 150,000
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5,150,000 $ 2,850,000 855,000 $ 1,995,000
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