Select Solutions to Chapter 7
7-14
East Company, which is highly automated, will have a cost structure dominated by fixed costs. West Company's cost structure will include a larger proportion 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 contribution margin divided by its net income. Since East Company has proportionately higher fixed costs, it will have a proportionately higher total contribution margin. Therefore, East Company's operating leverage factor will be higher.
7-15
When sales volume increases, Company X will have a higher percentage increase 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 by multiplying the percentage increase in sales volume by the firm's operating leverage factor.
7-16
The sales mix of a multiproduct organization is the relative proportion of sales of its products. The weighted-average unit contribution margin is the average of the 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
The car rental agency's sales mix is the relative proportion of its rental business 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-profit analysis shows the effect on profit of changes in expenses, sales prices, and sales mix. A change in the hotel's room rate (price) will change the hotel's unit contribution margin. This contribution-margin change will alter the relationship between volume and profit.
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.
EXERCISE 7-24 (25 MINUTES)
1
Sales Revenue $360,000
Variable Expenses $120,000
Total Contribution Margin $240,000
Fixed Expenses $90,000
Net Income $150,000
Break-Even Sales Revenue $135,000 a
2 3 4
55,000 320,000 c 160,000
11,000 80,000 130,000
44,000 240,000 30,000
25,000 60,000 30,000d
19,000 180,000 -0-
31,250b 80,000 160,000
Explanatory notes for selected items: $135,000 = $90,000 (2/3), where 2/3 is the contribution-margin ratio.
a
b
$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. 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
Loss area
$(200,000) Annual fixed expenses $(300,000) $(360,000)
Profit area
20,000
25,000
Tickets sold per year
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
= $408,000 = $17 per ticket
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.
$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
Operating leverage factor (at $1,000,000 sales level)
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.
PROBLEM 7-34 (30 MINUTES) 1.
Break-even point in sales dollars, using the contribution-margin ratio: fixed expenses contribution - margin ratio $540,000 $216,000 $756,000 $30 $12 $6 .4 $30 $1,890,000
Break - even point
2.
Target net income, using contribution-margin approach: fixed expenses target net income unit contribution margin $756,000 $540,000 $1,296,000 $30 $12 $6 $12 108,000 units
Sales units required to earn income of $540,000
3.
New unit variable manufacturing cost
= $12 110%
= $13.20 Break-even point in sales dollars: $756,000 $756,000 $30.00 $13.20 $6.00 .36 $30 $2,100,000
Break - even point
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 P $13.20 $6.00 $30.00 P P $19.20 .4 P .4P P $19.20 $19.20 .6P P $19.20/.6 P $32.00
Check: New contribution-margin ratio is: $32.00 $13.20 $6.00 .4 $32.00
PROBLEM 7-36 (30 MINUTES) 1.
Break-even point in units, using the equation approach: $24X – ($15 + $3)X – $1,800,000 = 0 $6X = $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 $2,400,000 $24 $19.50 $3 .0625 $24 $38,400,000
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 $3 $24 P P $22.50 .25 P .25 P P $22.50 $22.50 .75 P P $22.50/.75 P $30
Check: New contribution-margin ratio is: $30 $22.50 .25 $30
5. 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. 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……………………..
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
1,177,600 $1,472,000 $4,416,000 2,227,200
Net income……………………………………… 3.
$2,150,400
$2,188,800
Annual fixed costs will increase by $180,000 ($900,000 ÷ 5 years) because of straightline 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
PROBLEM 7-38 (25 MINUTES) 1.
Closing of mall store: Loss of contribution margin at Mall Store..................................................... $(108,000) Savings of fixed cost at Mall Store (75%)...................................................... Loss of contribution margin at Downtown Store (10%)................................ (14,400) Total decrease in operating income...............................................................$ (32,400)
2.
90,000
Promotional campaign: Increase in contribution margin (10%)........................................................... $10,800 Increase in monthly promotional expenses ($180,000/12)........................... (15,000) Decrease in operating income........................................................................ $(4,200)
3.
Elimination of items sold at their variable cost: We can restate the November 20x4 data for the Mall Store as follows:
Sales................................................................................... Less: variable expenses................................................... Contribution margin..........................................................
Mall Store Items Sold at Their Variable Cost Other Items $180,000* $180,000* 180,000 72,000 $ -0$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)
*$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. 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
Mister Ice Cream.......... Cold King..................... Total........................ (c)
Plan A
Units
Sales Mix
Units
Sales Mix
21,000 39,000 60,000
35% 65% 100%
19,500 45,500 65,000
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.............................................................
$ 721,500 1,956,500 $2,678,000
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)
Current
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.............................
19,500 45,500 65,000
Sales Mix 30% 70% 100%
Plan B Units 39,000 26,000 65,000
Sales Mix 60% 40% 100%
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..............................................................................................
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
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 25,000 tubs $3.50 $2.86
Break - even volume
$22,000 27,500 tubs $3.50 $2.70
Break - even volume
$40,000 40,816 tubs (rounded) $3.50 $2.52
Super model:
Giant model:
PROBLEM 7-41 (CONTINUED) 2. Profit-volume graph:
Dollars per year (in thousands)
Profit
$40
$20 Break-even point: 40,816 tubs 0
10
20
30
Profit area
40
50
Loss
Loss area ($20)
($40)
Fixed rental cost: $40,000 per year
Tubs sold per year (in thousands)
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 + 2.86X = 22,000 + 2.70X Rearranging terms yields the following:
(2.86 – 2.70)X = 22,000 – 16,000 .16X = 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.
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.
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
$450,000
72,000 $522,000 $198,000
----__ $450,000 $270,000
33,000
99,000
$165,000
$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: Plan A
Plan B
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%……...
$600,000
$600,000
$375,000
$375,000
60,000
Total variable cost……………………….. Contribution margin……………………………… Fixed costs………………………………………… Net income………………………………………….
$435,000
---__ $375,000
$165,000
$225,000
33,000
99,000
$132,000
$126,000
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.
CASE 7-55 (50 MINUTES) 1.
Break-even point for 20x4, based on current budget: $15,000,000 $9,000,000 $3,000,000 .20 $15,000,000 fixed expenses Break - even point contribution - margin ratio $150,000 $750,000 .20
Contribution - margin ratio
2.
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........................................................................................................ ........................................................................................$15,000,000 Cost of goods sold................................................................................. Gross margin.......................................................................................... 6,000,000 Commissions (at 5%).............................................................................. Contribution margin............................................................................... Contribution - margin ratio
$5,250,000 .35 $15,000,000
fixed expenses contribution - margin ratio $525,000 $1,500,000 .35
Estimated break - even point
9,000,000 $ 750,000 $ 5,250,000
CASE 7-55 (CONTINUED) 1.
Assuming a 25% sales commission: New contribution-margin ratio: Sales........................................................................................................ ........................................................................................$15,000,000 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
9,000,000 $ 6,000,000 3,750,000 $ 2,250,000
$2,250,000 .15 $15,000,000
target after - tax net income (1 t ) contribution - margin ratio
fixed expenses
$1,995,000 $3,000,000 (1 .3) .15 .15 $20,000,000 $150,000
Check: Sales.................................................................... 20,000,000 Cost of goods sold (60% of sales)..................... 12,000,000 Gross margin...................................................... 8,000,000 Selling and administrative expenses: Commissions................................................ All other expenses (fixed)............................ Income before taxes........................................... 2,850,000 Income tax expense (30%)................................. Net income.......................................................... 1,995,000
$
$ $ 5,000,000 150,000
5,150,000 $ 855,000 $
CASE 7-55 (CONTINUED) 2.
Sales dollar volume at which Lake Champlain Sporting Goods Company is indifferent: Let X denote the desired volume of sales. Since the tax rate is the same regardless of which approach management chooses, we can find X so that the company’s before-tax income is the same under the two alternatives. (In the following equations, the contribution-margin ratios of .35 and .15, respectively, were computed in the preceding two requirements.) .35X – $525,000 = .15X – $150,000 .20X = $375,000 X = $375,000/.20 X = $1,875,000 Thus, the company will have the same before-tax income under the two alternatives if the sales volume is $1,875,000. 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................................................................... *$1,875,000 5% = $93,750 † $1,875,000 25% = $468,750
Alternatives Employ Sales Pay 25% Personnel Commission $1,875,000 $1,875,000 1,125,000 1,125,000 $ 750,000 $ 750,000 93,750* 525,000 $ 131,250 39,375 $ 91,875
468,750† 150,000 $ 131,250 39,375 $ 91,875
