Ch9 Raiborn SM.doc
Short Description
Download Ch9 Raiborn SM.doc...
Description
Chapter 9
CHAPTER 9 BREAK-EVEN POINT AND COST-VOLUME-PROFIT ANALYSIS QUESTIONS 1.
The variable costing income statement classifies costs by the way they react relative to changes in volume. Variable costs are deducted from revenues to determine contribution margin and then fixed costs are deducted from contribution margin to determine operating profit. Breakeven analysis involves a study of fixed costs, variable costs, and revenues to determine the volume at which total costs equal total revenues. Hence, variable costing provides the variable and fixed cost classifications needed to compute breakeven. The absorption costing income statement uses functional classifications—manufacturing and nonmanufacturing costs—to compute gross profit and operating income, respectively. A functional classification requires a cost to be classified based on the reason it was incurred, i.e., selling, administrative, or production. This classification does not separate variable from fixed costs and is therefore not useful in computing breakeven.
2.
The breakeven point is the starting point for CVP analysis, because before a company can earn profits, it must first cover all of its variable and fixed costs; the point at which all costs are just covered is the breakeven point. The formula approach requires solving for the exact breakeven using the following algebraic equation: R(X) – V(X) – FC = 0; where R is revenue per unit, X is volume, V is variable cost per unit, and FC is fixed cost. The graph approach provides a visual relationship between revenues and costs. The breakeven point is where the total revenue line intersects the total cost line on the traditional or costvolumeprofit graph or where the profit line intersects the xaxis on the profitvolume graph. Unlike the formula approach, the graph approach does not provide a precise solution because exact points cannot be determined from a visual view of the graph. The income statement approach requires preparing an income statement to prove the accuracy of the computations of breakeven. Only by trialanderror can the exact breakeven be determined using the income statement approach.
3. The contribution margin ratio is contribution margin per unit divided by selling price per unit. It represents the proportion of revenue that remains after variable costs are covered. The contribution margin ratio can be used to calculate break even in sales dollars by dividing fixed costs by the contribution margin ratio. 4. The usefulness of CVP analysis is its ability to clearly forecast income expected to result from the shortrun interplay of cost, volume, price, and quantity. It is often useful in analyzing current problems regarding product mix, make or buy, sell or process further, and pricing. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
6
Chapter 9
In the long run, however, all of these factors and their relationships and the assumptions that underlie CVP regarding these factors are likely to change. This emphasizes that CVP only holds true for the short run. Results must be recalculated periodically to maintain validity. 5.
The “bag” or “basket” assumption means that a multiproduct firm will consider that the products it sells are sold in a constant, proportional sales mix—as if in a bag of goods. It is necessary to make this assumption to determine the contribution margin for the entire company product line, since individual products’ contribution margins may differ significantly. A single contribution margin must be used in CVP analysis so the “bag” or “basket” assumption allows CVP computations to be made.
6.
If the company includes more of its higher contribution margin products— squigees—than its lower contribution margin products—widgees—in its multiproduct mix, then its weighted average contribution margin will be higher and its breakeven point lower. This is because the contribution margin is weighted based on the relative quantities of each product. In the contribution margin weighting process, the product making up the larger proportion of the bag has the greatest impact on the average contribution margin. Previously, the product widgees, with the lowest contribution margin had the greater impact on the average contribution margin. However when the sales mix changed, the product squigees, with the higher contribution margin, has the greater impact on the average contribution margin.
7.
Margin of safety is the difference between actual or projected sales and break even level sales. Margin of safety can be expressed in units, in dollars, or as a percentage of total sales dollars. It identifies the amount by which sales could fall and still leave the firm’s bottom line in the black. Margin of safety measures provide either comfort or risk depending on whether the margin of safety is positive or negative. Operating leverage refers to the amount of fixed costs relative to variable costs in a company’s cost structure. It indicates how sensitive a company’s sales are to sales volume increases and decreases. Higher operating leverage is associated with a higher proportion of fixed costs; lower operating leverage is associated with a lower level of fixed costs. The level of operating leverage varies with the level of revenues. Further, operating leverage provides information about how profit will change when revenue changes. High operating leverage indicates that the level of profit is very sensitive to a change in revenue level. The reverse is true for low operating leverage. Margin of safety percentage is 1 ÷ Degree of operating leverage; degree of operating leverage is 1 ÷ Margin of safety percentage. Thus, the margin of safety percentage is the reciprocal of the degree of operating leverage and the degree of operating level is the reciprocal of the margin of safety percentage.
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
EXERCISES Ingredients Labor Variable overhead Total variable cost Divided by units Variable production cost per unit
a.
b.
$ 56,000 26,000 48,000 $ 130,000 ÷ 104,000 $1.25
Variable cost of goods sold = 98,000 × $1.25 = $122,500
c.
and d. Contribution margin ratio is: Sales (98,000 × $3.10) Less variable costs Cost of goods sold Variable selling & admin. Contribution margin and ratio
Dollars
Percent
$ 303,800
100
$122,500 10,000 (132,500) $ 171,300
44 56
Contribution margin per unit = $171,300 ÷ 98,000 = $1.75 per bottle (rounded) 9. a.
Direct material Direct labor Manufacturing overhead Total variable production cost Divided by units produced Variable production cost per cap
b.
Contribution margin per unit: Revenue Less variable costs Cost of goods sold (180,000 × $1.00) Selling and administrative Contribution margin Divided by units sold Contribution margin per unit
c.
$ 150,000 100,000 75,000 $ 325,000 ÷ 325,000 $1.00 $450,000 $180,000 90,000
270,000 $180,000 ÷180,000 $1.00
Top Disc Income Statement For 2013 Sales revenue Less variable costs Cost of goods sold (180,000 × $1.00) Selling and administrative Contribution margin Less fixed expenses
$ 450,000 $180,000 90,000
(270,000) $ 180,000
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
8
Chapter 9
Manufacturing overhead Selling and administrative Net loss
$112,500 100,000
(212,500) $ (32,500)
10. a. Total revenue rises by $25 + $21 = $46 b.
Total costs rise by the amount of variable costs, $21
c. Total pretax profit rises at the rate of the CM per unit, $25 11. a. Breakeven in units = $90,000 ÷ ($70 $40) = 3,000 units b. In dollars breakeven = 3,000 × $70 = $210,000 12. a. Breakeven point in rings = $345,000 ÷ ($600 $300) = 1,150 b. c.
Breakeven point in sales dollars = 1,150 × $600 = $690,000
(rounded)
d.
Breakeven point $345,000 ÷ ($600 $306) = 1,174 rings Breakeven point would be $339,000 ÷ ($600 $300) = 1,130
rings 13. a. The breakeven point is the point at which total revenue equals total cost. Fixed costs ÷ Contribution margin = Breakeven point $52,200 ÷ ($8 $3.50) = $52,200 ÷ $4.50 = 11,600 units or $92,800 in revenue b.
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
10
Chapter 9
c.
Breakeven point
d.
e.
Graph (b) demonstrates how total costs and total revenues change as volume changes. Profit or loss is the distance between the total revenue and total cost lines. In graph (c), variable costs are not explicitly shown but can be inferred as the distance between the total cost and fixed cost lines. Graph (c) shows only how profit changes with changes in volume. The shaded area to the right of the profit line is the profit area; the shaded area to the left is the loss area. No actual revenues or costs can be determined by looking at this graph. Pittsburg Tar Co.
Income Statement For the Year Ended 2013
Sales (11,600 gal. × $8 per gal.) Variable costs Production (11,600 gal. × $3.00 per gal.) Selling (11,600 × $0.50 per gal.) Contribution margin Fixed costs Production Selling and administrative Net income
$92,800 $34,800 5,800 $46,000 6,200
40,600 $52,200 52,200 $ 0
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
14. Sales Less variable cost Contribution margin Less fixed costs Profit
Given Plugged $ ? 0.7(S) $ ? $ 900,000 (600,000) (600,000) $ 300,000 $ 300,000
Let S = sales Then S 0.7S = $900,000 0.3S = $900,000 S = $3,000,000 Then the minimum selling price is $3,000,000 ÷ 30,000 units = $100. 15. a. Breakeven in units is $260,000 ÷ ($1,800 $1,000) = 325 garden sheds. b. To earn a pretax profit of $200,000 = ($260,000 + $200,000) ÷ $800 = 575 garden sheds c. To earn a pretax profit of $280,000 = ($260,000 + $280,000) ÷ $800 = 675 garden sheds 16. a. Contribution margin per unit = Sales less variable costs $180 – ($30 + $25 + $17) = $108 b. Contribution margin ratio = Contribution margin ÷ Sales $108 ÷ $180 = 60% c. Breakeven in units is fixed costs ÷ Contribution margin per unit $62,640 ÷ $108 = 580 units d. Breakeven in dollars is fixed costs ÷ Contribution margin ratio $62,640 ÷ 0.60 = $104,400 e. To earn $51,840 in pretax profit, Austin Automotive must sell: ($62,640 + $51,840) ÷ $108 = 1,060 units 17. a. Convert aftertax to pretax profit: $182,000 ÷ (1 0.35) = $280,000 The number of garden sheds that must be sold to generate $280,000 = ($260,000 + $280,000) ÷ $800 = 675 garden sheds. b. Let R = revenue; then 0.08R = Aftertax income desired Beforetax income = 0.08R ÷ (1 – 0.35) = 0.123R Revenue – Variable costs – Fixed costs = Income before tax Let X = Units sold SP(X) – VC(X) – FC = Income before tax © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
12
Chapter 9
$1,800X $1,000X $260,000 = 0.123($1,800)X $800X $260,000 = $221.4X $578.6X = $260,000 X = 450 units (rounded) sold to earn 8 percent of revenue after tax Amount of revenue = 450 × $1,800 = $810,000
Check: $810,000 × 0.08 = $64,800 aftertax income needed (round to $65,000) $64,800 ÷ 0.65 = $99,692 beforetax income (round to $100,000) $1,800(450) $1,000(450) $260,000 = $100,000 (beforetax income) $100,000 0.35($100,000) = $100,000 $35,000 = $65,000 $65,000 ÷ $810,000 = 8% 18. a. Convert the aftertax income to pretax desired income: $135,800 ÷ (1 – 0.30) = $194,000 The number of units required to earn an aftertax profit of $135,800: ($62,640 + $194,000) ÷ $108 = 2,376.3 or 2,376 units b.
19.
Convert the aftertax to pretax profit: $7.20 ÷ $180 = 0.04, or 4%; 0.04 ÷ (1 – 0.30) = 5.7% of sales A pretax return on sales of 5.7 percent is required to generate an aftertax profit of $7.20 per unit Let R = the Level of revenue that generates a pretax return of 5.7%: Variable costs = ($30 + $25 + 17) ÷ $180 = 0.4, or 0.4R R – $62,640 – 0.4R = 0.057R 0.543R = $62,640 R = $115,359 $115,359 ÷ $180 = 640.88 or 641 units (rounded)
Let Y = Level of sales generating income equal to 30% of sales, then: Y – 0.60Y – ($25,000 per month × 12 months) = 0.30Y 0.10Y = $300,000 Y = $3,000,000 Since existing sales are $2,250,000, sales would need to increase by $3,000,000 $2,250,000 = $750,000.
20.
a.
First, convert the desired aftertax income to a pretax desired income: $600,000 ÷ (1 0.40) = $1,000,000 Note that total variable costs per unit = $3,000, and total fixed costs = $370,000. Next, let P represent the number of golf carts that must be sold to generate $1,000,000 in pretax income: $5,000P $3,000P $370,000 = $1,000,000 $2,000P = $1,370,000 = 685 golf carts © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
b.
Find aftertax equivalent of 20%: 20% ÷ (1 0.40) = 33.33% Variable costs as a percentage of sales: $3,000 ÷ $5,000 = 60% Let R = Level of revenue that generates a pretax return of 33.33%: R – 0.6R – $370,000 = 0.3333R 0.0667R = $370,000 R = $5,547,226
Proof: Sales $ 5,547,226 Variable costs (60%) (3,328,336) Contribution margin $ 2,218,890 Fixed costs (370,000) Income before tax $ 1,848,890 Income tax (40%) (739,556) Net income $ 1,109,334 $1,109,334 ÷ $5,547,226 = 20% 21.
Each student will have a different answer; no solution provided.
22. a. $1,450 ÷ $0.50 = 2,900 passengers per day b.
Breakeven: $2,000 ÷ 2,900 = $0.69 (rounded) per passenger Earn $250: ($2,000 + $250) ÷ 2,900 = $0.78 (rounded)
c.
Total variable cost = $2,000 – ($2,000 × 0.80) = $400 Variable cost per passenger = $400 ÷ 2,900 = $0.14 (rounded) Profit if fare is $0.60 = (2,900 × 0.90 × $0.60) – (2,900 × 0.9 × $0.14) $1,600 = $(399.40) Current loss = $1,450 $2,000 = $(550) County will be better off by $(399.40) – ($550) = $150.60.
d.
At a fare of $0.70: (2,900 × $0.70 × 0.95) – (2,900 × $0.14 × 0.95) $1,600 = $(57.20) The county would incur a slight loss at a fare of $0.70. At a fare of $0.90: (2,900 × $0.90 × 0.90) – (2,900 × $0.14 × 0.90) $1,600 = $383.60 The company would first make a profit when the fare is set at $0.90.
e.
Increasing volume will help improve profitability only if the volume change increases total contribution margin. Because an increase in volume can often be achieved only with a decrease in price, the change in contribution margin may be negative rather than positive.
23. a. Current sales volume for both companies = $2,000,000 ÷ $40 = 50,000 New selling price $40 – (0.3 × $40) = $28; Variable costs = $1,400,000 ÷ 50,000 = $28 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
14
Chapter 9
Ainsley: (50,000 × 1.60 × $28) – (50,000 × 1.60 × $28) $0 = $0 Bard: (50,000 × 1.60 × $28) – (50,000 × 1.60 × $0) $1,400,000 = $840,000 This strategy is best used by Bard. b. New selling price: $40 × 1.3 = $52 Ainsley: (50,000 × 0.85 × $52) – (50,000 × 0.85 × $28) $0 = $1,020,000 Bard: (50,000 × 0.85 × $52) – (50,000 × 0.85 × $0) $1,400,000 = $810,000 This strategy is best used by Ainsley. c.
Ainsley: (65,000 × $40) – (65,000 × $28) $200,000 = $580,000 Bard: (65,000 × $40) – (65,000 × $0) $1,600,000 = $1,000,000 This strategy is best used by Bard.
24. a. CM per unit of sales mix = ($3 × 8) + (1 × $6) = $30 Breakeven = $180,000 ÷ $30 = 6,000 units of sales mix, or 18,000 wallets and 6,000 money clips Total revenue = (18,000 × $30) + (6,000 × $15) = $630,000 b.
Sales mix units = ($180,000 + $150,000) ÷ $30 = 11,000 = 33,000 wallets and 11,000 money clips Total revenue = (33,000 × $30) + (11,000 × $15) = $1,155,000
c.
Equivalent pretax profit = $150,000 ÷ (1 0.40) = $250,000 Sales mix units = ($180,000 + $250,000) ÷ $30 = 14,333.33 = 43,000 wallets and 14,333 money clips Total revenue = (43,000 × $30) + (14,333 × $15) = $1,504,995
d.
Units of sales mix = $1,155,000 ÷ [(5 × $30) + (2 × $15)] = 6,417 (rounded) = 32,085 wallets and 12,834 money clips Income = (32,085 × $8) + (12,834 × $6) $180,000 = $153,684 The sales mix shifted such that the ratio of wallets to money clips declined, and the breakeven point was reduced because money clips have a higher contribution margin ratio than money clips. Hence, at a sales level of $1,155,000, more contribution margin is generated at the actual sales mix than at the planned sales mix.
25. a. Fixed costs ÷ Contribution margin = Breakeven point in units $1,080,000,000 ÷ [(3 × $300) + (5 × $700) + (2 × $1,000)] = $1,080,000,000 ÷ $6,400 = 168,750 bags Mod = 3 × 168,750 = 506,250 units × $2,200 = Rad = 5 × 168,750 = 843,750 units × $3,700 = Xtreme = 2 × 168,750 = 337,500 units × $6,000 = Revenue to breakeven
$1,113,750,000 3,121,875,000 2,025,000,000 $6,260,625,000
b.Convert aftertax to pretax income. $1,000,000,000 ÷ (1 0.5) = $2,000,000,000 ($2,000,000,000 + $1,080,000,000) ÷ $6,400 = 481,250 bags Mod = 3 × 481,250 = 1,443,750 units × $2,200 =
$ 3,176,250,000
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
Rad = 5 × 481,250 = 2,406,250 units × $3,700 = Xtreme = 2 × 481,250 = 962,500 units × $6,000 = Total revenue needed c.
8,903,125,000 5,775,000,000 $17,854,375,000
This change will increase the number of units required to break even because fewer units of Rad and Xtreme, which have the greatest contribution margin, are being sold and more units of Mod, which has the lowest contribution margin, are being sold.
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
16
Chapter 9
Scooter Mod Rad Xtreme Total
Contribution Margin 5 × $300 = $1,500 4 × $700 = 2,800 1 × $1,000 = 1,000 $5,300
Now the contribution margin is $5,300 per bag, which is less than the contribution margin per bag of $6,400 in (a) above. d.
If Green Rider sells more of its scooters with the greatest contribution margin (Xtreme) and fewer of the scooters with the lowest contribution margin (Mod), then fewer scooters would be needed to be sold to break even.
26. a. Breakeven is $264,000 ÷ ($9.60 $7.60) = 132,000 bushels 132,000 bushels × $9.60 = $1,267,200 Bushels per acre = 132,000 ÷ 1,200 = 110 bushels per acre b.
Bushels sold Breakeven bushels = Margin of safety 174,000 – 132,000 = 42,000 bushels (174,000 × $9.60) $1,267,200 = $403,200 $403,200 ÷ $1,670,400 = 24.1%
27. a. Breakeven = Fixed costs ÷ Contribution margin $450,000 ÷ $30 = 15,000 tires per month 15,000 × $60 = $900,000 per month b.
Profit before tax desired is 25% of sales revenue PBT = 0.25 × $60 = $15 CM(X) – PBT(X) = FC $30(X) $15(X) = $450,000 $15(X) = $450,000 X = 30,000 units
c.
Degree of operating leverage = Contribution margin ÷ Profit before tax ($30 × 20,000) ÷ $150,000a = 4 a
d.
Profit = Contribution margin – Fixed costs $30(20,000) $450,000 = $150,000
(Total contribution margin × 1.15) = $30 × 20,000 × 1.15 = $690,000 Contribution margin – Fixed cost = Net income $690,000 $450,000 = $240,000 new net income Increase in net income is $240,000 $150,000 = $90,000
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
Racine Tire Co. Income Statement For the Month XXX Current Proposed Sales $60 (20,000; 23,000) $1,200,000 $1,380,000 Less variable expense $30 (20,000; 23,000) (600,000) (690,000) Contribution margin $ 600,000 $ 690,000 Less fixed costs (450,000) (450,000) Net income $ 150,000 $ 240,000 28.
a. Sales ($7.20 × 125,000) Variable costs ($4.32 × 125,000) Contribution margin Fixed costs Net income
$ 900,000 (540,000) $ 360,000 (316,600) $ 43,400
Breakeven point = $316,600 ÷ 0.40a = $791,500 or 109,931 packages (rounded) Margin of safety, dollars: $900,000 $791,500 = $108,500 Margin of safety in units: $108,500 ÷ $7.20 = 15,069 packages (rounded)
($7.20 $4.32) ÷ $7.20 = Contribution margin ratio
a
b. $360,000 ÷ $43,400 = 8.295 c.Income will increase by: 8.295 × 30% = 249% Proof: Sales ($7.20 × 125,000 × 1.30) Variable costs ($4.32 × 125,000 × 1.30) Contribution margin Fixed costs Net income
$1,170,000 (702,000) $ 468,000 (316,600) $ 151,400
($151,400 $43,400) ÷ $43,400 = 249% d. Breakeven point = ($316,600 + $41,200) ÷ 0.40 = $894,500 Sales ($7.20 × 125,000 × 1.15) Variable costs ($4.32 × 125,000 × 1.15) Contribution margin Fixed costs ($316,600 + $41,200) Net income
$1,035,000 (621,000) $ 414,000 (357,800) $ 56,200
Operating leverage = $414,000 ÷ $56,200 = 7.37 29.
Substantial cost structure implications must be considered in selecting from the alternative production technologies. Machinebased technologies will tend to have much higher levels of fixed costs and lower levels of variable costs than laborintense technologies. Accordingly, the machinebased technologies will © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
18
Chapter 9
have higher operating leverage. Having higher operating leverage means that the firm’s income will be much more sensitive to changes in the level of sales. Because higher operating leverage is associated with higher income sensitivity to volume changes, high operating leverage is desired if future sales are expected to be increasing. Higher leverage allows net income to grow at a higher rate as sales increase. Alternatively, if sales will be decreasing, firms will prefer to have low operating leverage because costs will tend to fall more rapidly as sales diminish. With high operating leverage, costs will remain more constant as sales drop causing net income to drop very rapidly. In an ideal world, one would desire to have a very low level of fixed costs below the breakeven point and only fixed costs above the breakeven point. If the cost structure contained only fixed costs, then each dollar of revenue above the break even point would generate a dollar of income before profit. CVP analysis is useful to determine when a firm should consider trading variable costs for fixed costs in order to shift the cost structure from more variable to more fixed, or vice versa. For a given level of sales, a company with mostly variable costs will have a higher margin of safety than a similar firm with mostly fixed costs. If a firm had only variable costs, its sales could fall to zero without causing the firm to incur a loss. Consequently, its breakeven point is zero. The firm with a high level of fixed costs would have a much higher breakeven point. 30.
An issue in the use of CVP analysis is that CVP analysis requires costs to be classified as either variable or fixed. The outcome of CVP analysis is sensitive to variations in this classification. In making decisions that rely on CVP analyses, it is important to be mindful of the requirement to dichotomize costs between these two categories (fixed and variable). Further, it is important to recognize that in the long term, all costs are variable. A problem arises when shortterm decisions have longterm consequences. In this circumstance, costs will have been incorrectly considered in the CVP analysis because too many of the costs would have been classified as fixed. Accordingly, the greatest potential for problems arises in situations in which a longterm decision is made on the basis of a shortterm classification of costs. A final observation is that CVP decisions are made in an incremental fashion. This means that each decision is made independently of all other decisions. The reality is that past decisions affect future decisions and short term decisions can affect longterm decisions. CVP analysis can be used in long, medium, and shortterm decision making. The key is to use a classification of costs that is appropriate for the time horizon. For longerterm decisions, newer cost control technologies such as activitybased costing can be used to determine which costs are likely to vary with decision alternatives being considered. By relating the cost drivers to the decision at hand, managers can determine which costs are likely to be affected, and by how much, by the decision being made.
31. a. Each “bag” contains one unit of liquid and two units of spray. Thus, each bag generates contribution margin of: (1 × $10) + (2 × $5) = $20. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
The breakeven point would be: $100,000 ÷ $20 = 5,000 bags. Since each bag contains two units of spray, at the breakeven point 5,000 × 2 or 10,000 units of spray must be sold. b.
At the breakeven point, Total CM = Total FC; and the CM per unit would be $1,600 ÷ 4,000 = $0.40. If one unit is sold beyond the breakeven point, net income would rise by $0.40.
c. $10X 0.40($10X) $216,000 = 0.25($10X) $3.50X = $216,000 X = 61,715 units (rounded) d.
In units: 3,200 – 2,800 = 400 units In dollars: 400 units × $65 per unit = $26,000 Percentage: $26,000 ÷ ($65 × 3,200) = 12.5%
32. a. Fixed costs that would increase include the additional equipment costs and salaries for testing, treating, storage, and disposal of treated waste. Increased variable costs would include labor wages, the treatment supplies, and energy costs of performing the treatment and disposing of the neutralized waste. The increases in these variable costs would lower the product contribution margin unless prices are raised to compensate. b.
After determining that the substance is toxic, the president has to consider business as usual versus the costs of treatment and/or proper disposal that may make product prices uncompetitive, preserving the health of humans downriver, the effects on fish, wildlife and the environment, maintaining the good name and reputation of the company, the impact on the stakeholders should the dumping be discovered, the legality of falsifying the reports, the impact on the employees should the plant be closed from lack of profitability, the economic stability of the town, and its dependence on the plant for survival.
c.
The employees are implying that (1) not addressing the problem is the lesser of evils because there is no proof that the waste causes cancer; (2) to clean up the problem may cause the company to become uncompetitive; (3) 10,000 employees could lose their jobs; and (4) the town’s economy could collapse. The fault with the above rationalizations about the waste not being toxic to humans lies partially in the fact that the company failed to recognize the damage to other nonhuman environmental participants. The waste may be potentially harmful to the fish and other organisms in the river, and the polluted water is absorbed by the surrounding land (thus polluting the land). Furthermore, the fishermen sell their polluted catches to outside markets, thus spreading the effects of the pollution even further. Fault is also seen in the rationalization because the company falsified the levels of suspected cancercausing materials in its reports to authorities. If the company truly believed that no harm was being done to either the people downstream or the environment, why were the reports falsified? Doing so instilled a false sense of security in the members of its society (both © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
20
Chapter 9
employees and townspeople) regarding their general welfare. If the company had provided accurate disclosure of toxicity levels, the public would have had the opportunity to decide whether to remain on their jobs or in the vicinity of the polluters, look for work elsewhere or relocate to an area where better conditions exist, or to seek the necessary assistance in requiring the company to take corrective action. These rationalizations seem to indicate that unhealthy and unethical acts can be permitted and tolerated if a large number of directly affected people benefit without regard for the effects on people or entities that are indirectly affected. While utilitarianism does look at the greatest good for the greatest number, it considers all parties—directly and indirectly affected—in making that cost benefit analysis. The company in this case is not considering the indirect effects of its actions. d.
The president must take some action to deal with the problem. First, the dumping should be discontinued altogether until the waste is tested to determine if it is cancer causing. If it is not, obtain information on the environmental effects of the dumping and, if not harmful, continue to dump. The company should then report its findings to the authorities and discontinue falsifying its reports. If the waste is cancer causing or causes significant environmental damage, the company should immediately issue a policy statement that no additional dumping shall take place. Then the costs of treating the waste to neutralize it should be compared to other alternatives that might exist or could be created such as using it as a raw material in another product or introducing alternative processing methods. The company could solicit the employees’ and townspeople’s assistance since all have a large vested interest in finding a solution to the problem. Investigation of how other companies producing the same waste handle the problem would be helpful; some of this type of information should be available from the EPA or state environmental agencies. If other companies are handling the waste in a similar manner, all companies could be liable for the costs of cleanup, which would disallow any economic advantage to the other companies. In addition, the company should investigate the costs of cleaning up the waste (if possible) that has already been dumped. Since all of these options take time, however, the company will most likely have to incur additional shortrun costs so that the longrun effects can be minimized.
33. a. Revenue is constant per unit within the relevant range. b. Variable costs are constant per unit within the relevant range. Labor productivity will not change. c.
The sales mix remains constant as volume changes within the relevant range.
d.
Mixed costs can be accurately separated into their fixed and variable components. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
e.
All variable costs are constant per unit within the relevant range and total fixed cost is constant within the relevant range.
f.
Sales and production are equal.
g.
No capacity additions will be made within a period.
34. Joanna’s calculations assume that the current cost and revenue structure will be maintained in future periods. Over time productivity can be improved and revenues can be increased. Closing the business is a longterm decision and CVP is shortterm analysis. The CVP analysis is based on the assumption that cost and revenue structures will not change. Over the long term, prices may be increased, volume may be increased, and cost structures can be improved. Hence, Joanna’s recommendation should be taken with skepticism, and Aire should examine her longterm prospects to enhance revenues and reduce costs.
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
22
Chapter 9
PROBLEMS 35. a. CM% = ($5,000 $2,800 $200) ÷ $5,000 = 40% Breakeven = $280,000 ÷ 0.40 = $700,000 b. Fixed costs in CGS = $400,000 – (100 × $2,800) = $120,000 Only $120,000 of fixed overhead was assigned to CGS, therefore units sold = $120,000 ÷ $200,000 of units produced = 100 ÷ 0.6 = 167 units (rounded) c. Because the company manufactured more units than it sold, $80,000 of fixed overhead was assigned to ending inventories rather than the Cost of Goods Sold. Accordingly, the company reported breakeven results even though sales fell far short of the breakeven level. d.
Sales Variable costs Production Selling Contribution margin Fixed costs Production Selling & admin. Operating income (loss)
$ 500,000 $280,000 20,000 (300,000) $ 200,000 $200,000 80,000 (280,000) $ (80,000)
e. No, it would not be unethical to present the absorption costing income format. In fact, that is the most accepted format for reporting outside of the firm. The lending institution, with adequate information regarding the inventories, can adjust the income statement to a variable costing format if it desires to do so.
Sales Variable costs Contribution margin b.
e.
Dollars per Unit Percent $ 60.00 100% (45.00) (75) $ 15.00 25%
Breakeven point = $975,000 ÷ $15.00 per unit = 65,000 carts
c.
Target pretax profit of $900,000 ($975,000 + $900,000) ÷ $15.00 per cart = 125,000 carts
d.
Target aftertax profit of $750,000 Before tax profit = $750,000 ÷ (1 0.40) = $1,250,000 ($975,000 + $1,250,000) ÷ $15 per cart = 148,333 carts (rounded) Selling price Variable costs Manufacturing ($35 × 0.40) Manufacturing labor (0.60 × $35 × 0.90) Selling Contribution margin
$60.00 14.00 18.90 10.00 $17.10
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
Fixed costs: Manufacturing ($975,000 × 0.40 × 0.90) Selling ($975,000 × 0.60) Total fixed costs
$351,000 585,000 $936,000
Breakeven point = $936,000 ÷ 17.10 = 54,737 carts (rounded up) The breakeven point will decrease by 10,263 carts f.
Target unit sales 600,000 × 0.25 = 150,000 carts Sales – VC – FC = $1,350,000 Let X = variable cost per unit ($60 × 150,000) 150,000X $975,000 = $1,350,000 $9,000,000 – 150,000X = $2,325,000 $6,675,000 = 150,000X X = $44.50 Variable costs will need to be reduced by $0.50 ($45.00 $44.50). Student answers will vary. No solution provided.
Sales Variable costs Contribution margin b.
Breakeven point in units = $1,250,000 ÷ $2.50 per unit = 500,000 baseballs
c.
Breakeven point in dollars = $1,250,000 ÷ 0.3846 = $3,250,130
d.
e.
Dollars per Unit Percent $ 6.50 100.00% (4.00) (61.54) $ 2.50 38.46%
MS, in units = 960,000 – 500,000 = 460,000 baseballs MS, in dollars = ($6.50 × 460,000) = $2,990,000 MS, percentage = $2,990,000 ÷ $6,240,000 = 47.9% Current sales (960,000 × $6.50) Variable costs (960,000 × $4) Contribution margin Fixed costs Income before taxes
$ 6,240,000 (3,840,000) $ 2,400,000 (1,250,000) $ 1,150,000
Degree of operating leverage = $2,400,000 ÷ $1,150,000 = 2.087 Percentage increase in income = 30% × 2.087 = 62.6% f. Required sales = ($1,250,000 + $1,096,000) ÷ $2.50 per baseball = 938,400 baseballs g. Pretax equivalent of $750,000 = $750,000 ÷ (1 0.40) = $1,250,000 Required sales = ($1,250,000 + $1,250,000) ÷ $2.50 per baseball = 1,000,000 baseballs © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
24
Chapter 9
h. Breakeven point = ($1,250,000 + $50,000) ÷ $2.50 per baseball = 520,000 baseballs e.
Additional sales ($4.40 × 20,000) Additional variable costs ($4.20 × 20,000) Additional contribution margin Additional fixed costs Additional pretax income (loss)
$ 88,000 (84,000) $ 4,000 (6,000) $ (2,000)
No, the order should not be accepted as profits will decrease by $2,000. Even though normal sales would not be affected, regular customers may find out about the special deal and become upset because their prices have been undercut. Alternatively, by making this onetime sale at a loss to this customer, goodwill and future business from this customer could follow. 38. a. Total variable cost = $28 + $12 + $8 = $48 Contribution margin per unit = $70 $48 = $22 per unit Contribution margin ratio = $22 ÷ $70 = 31.4% (rounded) Total fixed costs = $10,000 + $24,000 = $34,000 Breakeven point in units = $34,000 ÷ $22 per unit = 1,545 units (rounded) Breakeven point in dollars = $34,000 ÷ 0.314 = $108,280 (rounded) b.
($40,000 + $34,000) ÷ 0.314 = $235,669 (rounded) ($235,669 ÷ $70) = 3,367 units (rounded)
c. Convert aftertax earnings to pretax earnings: $40,000 ÷ (1 0.40) = $66,667 Required sales = ($66,667 + $34,000) ÷ 0.314 = $320,596 (rounded) $320,596 ÷ $70 = 4,580 units (rounded) d.
Convert the aftertax rate of earnings to a pretax rate of earnings: [20% ÷ (1 0.40)] = 33.33% Because the CM% is only 31.4%, no level of sales would generate net income equal to, on a pretax basis, 33.33% of sales.
e.
Variable cost savings (5,000 × $6.00) Additional fixed costs Decrease in profit
$ 30,000 (40,000) $(10,000)
The company should not buy the new sewing machine. f.
Existing CM per unit = $22 CM under proposal = ($70 × 0.90) $48 = $15 Total CM under proposal (3,000 × 1.30 × $15) Existing CM (3,000 × $22) Change in CM Change in fixed costs Change in net earnings before taxes
$ 58,500 (66,000) $ (7,500) (10,000) $ (17,500)
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
No, these two changes should not be made because they would lower pretax profits by $17,500 relative to existing levels. 39. a. Revenues: Game tickets ($60,000 × 0.08 Airline tickets ($9,000 × 0.10) Hotel bookings ($14,000 × 0.20) Costs: Advertising Rent Utilities Other Net loss b.
$4,800 900 2,800
$ 8,500
$2,200 1,800 500 4,400 (8,900) (400)
Increase in revenue ($9,000 × 0.40 × 0.10) Increase in cost Increase in profit
$ 360 (1,200) $ (840)
No, Weatherby should not incur the $1,200 of advertising expense because it would cause profit to drop by $840. c.
Increase in revenues: Game ticket ($8,000 × 0.08) Airline ticket ($1,500 × 0.10) Hotel booking ($6,000 × 0.20) Increase in costs: Rusty’s commission ($1,990 × 0.50) Rusty’s wage Increase in profits
$ 640 150 1,200 $ 995 400
$ 1,990 (1,395) $ 595
Yes, Weatherby should hire Rusty because it would increase his profits by $595. d.
Increase in revenues: Airline tickets ($13,000 × 0.10) Increase in costs: Rusty’s commission ($1,300 × 0.50) Increase in fixed costs Increase (decrease)
$ 1,300 $650 600 (1,250) $ 50
Because there was at least a slight increase in profits, Weatherby did make a good decision. 40. a. Total Revenue
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
26
Chapter 9
b.
c. The breakeven chart would probably be more helpful. The point could be made that the club has only 20 members in excess of the breakeven level of 100 members. Additional information should be provided indicating the contribution margin and contribution margin ratio. Armed with the chart and the additional information, a very good point could be made for a membership recruiting project. 41. a. Total sales price per bag: Commercial ($5,600 × 1) Residential ($1,800 × 3) Total variable costs per bag: Commercial ($3,800 × 1) Residential ($1,000 × 3) Total contribution margin
$5,600 5,400 $3,800 3,000
$11,000 (6,800) $ 4,200
Breakeven point in units = $8,400,000 ÷ $4,200 = 2,000 bags Commercial: 2,000 × 1 = 2,000 mowers Residential: 2,000 × 3 = 6,000 mowers b. ($8,400,000 + $1,260,000) ÷ $4,200 = 2,300 bags Commercial: 2,300 × 1 = 2,300 mowers Residential: 2,300 × 3 = 6,900 mowers c.
Pretax equivalent of $1,008,000 aftertax = $1,008,000 ÷ (1 0.40) = $1,680,000 ($8,400,000 + $1,680,000) ÷ $4,200 = 2,400 bags Commercial: 2,400 × 1 = 2,400 mowers © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
Residential: 2,400 × 3 = 7,200 mowers d. Let X = number of bags that must be sold to produce pretax earnings equaling 12 percent of sales revenue, then: $4,200X $8,400,000 = 0.12($11,000X) X = 2,917 bags (rounded) Commercial: 2,917 × 1= 2,917 mowers Residential: 2,917 × 3 = 8,751 mowers e. Convert the aftertax return to a pretax rate of return: 0.08 ÷ (1 0.40) = 13% (rounded) $4,200X $8,400,000 = 0.13($11,000X) X = 3,032 bags (rounded) Commercial: 3,032 × 1= 3,032 mowers Residential: 3,032 × 3 = 9,096 mowers 42. a.
Ducks Ducklings Sales $ 24.00 $12.00 Variable costs (12.00) (8.00) Contribution margin $ 12.00 $ 4.00 Mix × 1 × 5 Total contribution margin $ 12.00 $20.00 The average contribution margin ratio is $32 ÷ $84 = 38.1% (rounded) b. Breakeven point = $288,000 ÷ $32 = 9,000 bags per year or 750 bags a month Ducks: 750 × 1 = 750 per month Ducklings: 750 × 5 = 3,750 per month c. Target profit is $96,000 × 12 = $1,152,000 ($288,000 + $1,152,000) ÷ $32 = 45,000 bags per year or 3,750 bags a month. Ducks: 3,750 × 1 = 3,750 per month Ducklings: 3,750 × 5 = 18,750 per month
d. Sales Variable costs Contribution margin Mix Total contribution margin
Ducks Ducklings $ 24.00 $12.00 (12.00) (8.00) $ 12.00 $ 4.00 × 1 × 9 $ 12.00 $36.00
Target profit after tax is $31,680. Pretax profit is $31,680 ÷ (1 0.40) = $52,800 monthly or $633,600 per year. Breakeven = ($633,600 + $288,000) ÷ $48 = 19,200 bags per year, or 1,600 per month Ducks (19,200 × $24) Ducklings (19,200 × 9 × $12) Total
Units 19,200 172,800
Revenue $ 460,800 2,073,600 $2,534,400
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
28
Chapter 9
e. [$288,000 + ($8,500 × 12)] ÷ [$12 + ($8 × 5)] ($288,000 + $102,000) ÷ $52 = 7,500 Yes, the company would want to make the change because the breakeven point is reduced from 9,000 mix units to 7,500 mix units. 43.
a. and b. Total variable costs: Variable product cost Variable selling expenses Variable administrative exp. Total
Sales Variable costs Contribution margin Mix Total contribution margin
Reindeer $12.00 6.00 3.00 $21.00
Snowmen $15.00 4.50 5.50 $25.00
Flamingos $25.00 8.00 6.00 $39.00
Reindeer $ 40.00 (21.00) $ 19.00 × 1 $ 19.00
Snowmen $ 35.00 (25.00) $ 10.00 × 2 $ 20.00
Flamingos $ 60.00 (39.00) $ 21.00 × 4 $ 84.00
Contribution margin per “bag” = $19 + 20 + $84 = $123 Breakeven point in units = ($420,000 + $150,000 + $80,178) ÷ $123 = 5,286 “bags” Reindeer (5,286 × $40.00) Snowmen (5,286 × 2 × $35.00) Flamingos (5,286 × 4 × $60.00) Total
Units Sold 5,286 10,572 21,144
Revenues $ 211,440 370,020 1,268,640 $1,850,100
c. Units = ($650,178 + $250,428) ÷ $123 = 7,322 bags Reindeer (7,322 × $40.00) Snowmen (7,322 × 2 × $35.00) Flamingos (7,322 × 4 × $60.00) Total
Units Sold 7,322 14,644 29,288
Revenues $ 292,880 512,540 1,757,280 $2,562,700
d. Pretax profit = $155,718 ÷ (1 0.40) = $259,530 Breakeven in units = ($650,178 + $259,530) ÷ $123 = 7,396 bags Reindeer (7,396 × $40.00) Snowmen (7,396 × 2 × $35.00) Flamingos (7,396 × 4 × $60.00)
Units Sold 7,396 14,792 29,584
Revenues $ 295,840 517,720 1,775,040
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
Total
$2,588,600
e. MS bags = 7,396 bags 5,286 bags = 2,110 bags MS $ = 2,110 × [$40 + ($35 × 2) + ($60 × 4)] = $738,500 MS % = 2,110 ÷ 7,396 = 28.5% 44.
a. and b. Total variable costs: Direct material Direct labor Variable overhead Variable selling Variable administrative Total
Oak $10.40 3.60 2.00 1.00 0.40 $17.40
Hickory $6.50 0.80 0.30 0.50 0.20 $8.30
Determination of sales ratio: Sales in Yards % of Sales Oak 9,000 10.34 Hickory 72,000 82.76 Cherry 6,000 6.90 Total 87,000 100.00
Cherry $17.60 12.80 3.50 4.00 0.60 $38.50
Per “Bag”* 3 24 2 29
*The content per bag is determined by dividing the sales in yards by 3,000. Sales Variable costs Contribution margin Oak Hickory Cherry Total
Oak Hickory Cherry $ 32.80 $16.00 $ 50.00 (17.40) (8.30) (38.50) $ 15.40 $ 7.70 $ 11.50
Contribution Margin $15.40 × 3 = $ 46.20 $7.70 × 24 = 184.80 $11.50 × 2 = 23.00 $254.00
Sales $32.80 × 3 = $ 98.40 $16.00 × 24 = 384.00 $50.00 × 2 = 100.00 $582.40
Total fixed costs = $760,000 + $240,000 + $200,000 = $1,200,000 Breakeven point in units = $1,200,000 ÷ $254 = 4,724.409 or 4,725 bags Oak: 4,725 × 3 = 14,175 square yards Hickory: 4,725 × 24 = 113,400 square yards Cherry: 4,725 × 2 = 9,450 square yards Contribution margin ratio per bag = $254 ÷ $582.40 = 0.4 (rounded) Breakeven point in dollars = $1,200,000 ÷ 0.4 = $3,000,000 c. ($1,200,000 + $800,000) ÷ $254 = 7,875 bags (rounded) © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
30
Chapter 9
Oak: Hickory: Cherry: Total d.
Yards 7,875 × 3 = 23,625 × $32.80 = 7,875 × 24 = 189,000 × 16.00 = 7,875 × 2 = 15,750 × 50.00 =
Revenue $ 774,900 3,024,000 787,500 $4,586,400
Revenue per bag: Oak ($32.80 × 3) Hickory ($16.00 × 24) Cherry ($50.00 × 2) Total
$ 98.40 384.00 100.00 $ 582.40
Contribution margin ratio = $254 ÷ $582.40 = 43.6% {$1,200,000 + [$680,000 ÷ (1 0.40)]} ÷ 0.436 = $5,351,681 e. Breakeven point in dollars = $1,200,000 ÷ 0.436 = $2,752,294 Margin of safety in dollars = $5,351,681 $2,752,294 = $2,599,387 Margin of safety percentage = $2,599,387 ÷ $5,351,681 = 48.6%
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
45. a.
Fixed costs: Depreciation Labor Utilities Miscellaneous Total Variable costs: Labor Utilities Miscellaneous Food Total
$160,000 320,000 158,000 100,000 $738,000 Coaches $ 5.00 1.00 6.00 40.00 $52.00
Players $ 5.00 1.00 6.00 15.00 $27.00
Total fixed costs $ 738,000 Total variable costs Coaches: (10 × $52.00 × 360 × 80%) $149,760 Players: (50 × $27.00 × 360 × 80%) 388,800 538,560 Desired profit 240,000 Total required revenue $1,516,560 Guest days: Coaches: 10 × 360 × 80% = 2,880 Players: 50 × 360 × 80% = 14,400 Total 17,280 Required charge per guest day: $1,516,560 ÷ 17,280 = $87.76 (rounded) b. (1) Sales price per day Variable costs Contribution margin
Coaches
Players
$240.00 52.00 $188.00
$200.00 27.00 $173.00
CM per “bag” of guest days = $188.00 + ($173.00 × 4) = $880 Breakeven in bags = $738,000 ÷ $880 per bag = 839 (rounded) bags, which represents 839 coachdays and 3,356 playerdays. (2) ($738,000 + $400,000) ÷ $880 per bag = 1,293 (rounded) bags, which represents 1,293 coachdays and 5,172 playerdays. (3) {$738,000 + [$400,000 ÷ (1 0.35)]} ÷ $880 per bag = 1,538 (rounded) bags, which represents 1,538 coachdays and 6,152 playerdays. c. $500,000 ÷ (839 + 3,356) = $119.19 per guest day (rounded) 46. a. Contribution margin = $140 $60 = $80 per passenger Contribution margin ratio = $80 ÷ $140 = 57.1% © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
32
Chapter 9
Breakeven point in passengers = Fixed costs ÷ Contribution margin = $2,400,000 ÷ $80 per passenger = 30,000 passengers Breakeven point in dollars = Fixed costs ÷ Contribution margin ratio = $2,400,000 ÷ 0.571 = $4,203,152 b. 60 × 0.75 = 45 seats per train car 30,000 ÷ 45 = 667 train cars (rounded) c. CM = $170 $60 = $110 per passenger 60 × 0.60 = 36 filled seats Breakeven point in passengers = Fixed costs ÷ Contribution margin = $2,400,000 ÷ $110 per passenger = 21,818 passengers (rounded) 21,818 ÷ 36 = 606 train cars (rounded) d. Contribution margin = $140 $80 = $60 per passenger Breakeven point in passengers = Fixed costs ÷ Contribution margin = $2,400,000 ÷ $60 per passenger = 40,000 passengers 40,000 ÷ 4 = 889 train cars (rounded) e. Aftertax income
= $800,000 ÷ (1 Tax rate) = $800,000 ÷ (1 0.40) = $800,000 ÷ 0.60 = $1,333,333
$160X $3,000,000 $70X = $1,333,333 $90X = $4,333,333 X = 48,148 (rounded) f. Number of discounted seats = 60 × 0.05 = 3 seats Contribution margin for discounted fares = $100 $60 = $40 × 3 discounted seats = $120 each train × 40 train cars per day × 30 days per month = $144,000 – $160,000 additional fixed costs = $16,000 pretax loss. g.(1) No. Contribution margin = $150 $60 = $90 per passenger 60 × 0.60 = 36 seats × $90 × 15 train cars = $ 48,600 Increased fixed costs (200,000) Pretax loss on new route $ (151,400) (2) $150X $60X $200,000 = $101,000 $90X = $301,000 X = 3,345 passengers (rounded) 3,345 ÷ 36 = 93 train cars (rounded) (3) 60 × 0.75 = 45 seats filled 3,345 ÷ 45 = 74 train cars (rounded) (4) Fairbanks should consider such things as: connections to other Fairbanks trains that might be made by these passengers © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
longrange potential for increased load factors increased customer goodwill in this new market increased employment opportunities for labor in the area competition in the market
47. a. Breakeven point in units = Fixed costs ÷ Contribution margin Contribution margin = $94.00 – ($18.40 + $13.00 + $8.60 + $4.60 + $3.00) = $46.40 Breakeven point in units = ($1,200,000 + $960,000 + $480,000) ÷ $46.40 = $2,640,000 ÷ $46.40 = 56,897 units or $5,348,318 b. Margin of safety Dollars = Total sales – Breakeven sales = (150,000 × $94) $5,343,318 = $14,100,000 $5,343,318 = $8,756,682 Units = 150,000 56,897 = 93,103 Percentage = 93,103 ÷ 150,000 = 62%
Sales Variable cost Contribution margin Fixed expenses Net income
Original $14,100,000 (7,140,000)
1 $ 16,920,000 (11,160,000)
2 3 $ 16,215,000 $14,734,500 (8,211,000) (7,854,000)
$ 6,960,000
$ 5,760,000
$ 8,004,000
(2,640,000) $ 4,320,000
(2,640,000) $ 3,120,000
(3,160,000) (2,640,000) $ 4,844,000 $ 4,240,500
$ 6,880,500
The best alternative is idea number 2; this is the plan management should implement. Olson 48. a. Income Statements 2013 2014 Sales $ 600,000 $ 960,000 a Less variable expense (420,000) (672,000) Contribution marginb $ 180,000 $ 288,000 Less fixed expenses (60,000) (60,000) Net income before taxc $ 120,000 $ 228,000 Tax expense (48,000) (91,200) Net income $ 72,000 $ 136,800 Variable expense = Sales Contribution margin 2013 = $600,000 $180,000 = $420,000 2014 = $960,000 $288,000 = $672,000
a
Contribution margin = Net income before tax + Fixed costs 2013 = $120,000 + $60,000 = $180,000
b
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
34
Chapter 9
2014 = $228,000 + $60,000 = $288,000 Net income before tax 2013 = $ 72,000 ÷ (1 0.40) = $120,000 2014 = $136,800 ÷ (1 0.40) = $228,000
c
Sales Less variable expensea Contribution marginb Less fixed expenses Net income before taxc Tax expense Net income
Miami Income Statements 2013 2014 $ 600,000 $ 840,000 (180,000) (252,000) $ 420,000 $ 588,000 (300,000) (300,000) $ 120,000 $ 288,000 (48,000) (115,200) $ 72,000 $ 172,800
Variable expense = Sales less contribution margin 2013 = $600,000 $420,000 = $180,000 2014 = $840,000 $588,000 = $252,000
a
Contribution margin = Net income before tax + Fixed costs 2013 = $120,000 + $300,000 = $420,000 2014 = $288,000 + $300,000 = $588,000
b
Net income before tax = 2013 = $ 72,000 ÷ (1 0.40) = $120,000 2014 = $172,800 ÷ (1 0.40) = $288,000
c
b. Breakeven sales
2013
Olson $60,000 ÷ ($180,000 ÷ $600,000) $60,000 ÷ ($288,000 ÷ $960,000)
$200,000
Miami $300,000 ÷ ($420,000 ÷ $600,000) $300,000 ÷ ($588,000 ÷ $840,000)
428,572
2014 $200,000
428,572
c. Olson Profit before taxes = 0.12(of investment); tax rate = 40% = 0.12($1,200,000) = $144,000 Profit after taxes = $144,000 ÷ (1 0.4) = $240,000 ($60,000 + $240,000) ÷ 0.30 = $1,000,000 Miami © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
Profit before taxes = 0.12(of investment); tax rate = 40% = 0.12($1,200,000) = $144,000 Profit after taxes = $144,000 ÷ (1 0.4) = $240,000 ($300,000 + $240,000) ÷ 0.70 = $771,429 d. Margin of safety = Actual sales – Breakeven sales Olson 2013 $600,000 $200,000 = $400,000 2014 $960,000 $200,000 = $760,000 Miami 2013 $600,000 $428,572 = $171,428 2014 $840,000 $428,572 = $411,428 Operating leverage = Contribution margin ÷ Profit before tax Olson 2013 2014 Miami 2013 2014
$180,000 ÷ $120,000 = 1.50 $288,000 ÷ $228,000 = 1.26 $420,000 ÷ $120,000 = 3.50 $588,000 ÷ $288,000 = 2.04
e.
f.
Contribution margin
Olson $ 288,000
Miami $ 588,000
Increase (1.15 × CM) Less fixed costs Net income before taxes Taxes (40%) Net income
$ 331,200 (60,000) $ 271,200 (108,480) $ 162,720
$ 676,200 (300,000) $ 376,200 (150,480) $ 225,720
Contribution margin
Olson $288,000
Miami $ 588,000
Decrease (0.80 × CM) Less fixed costs Net income before taxes Taxes (40%) Net income
$230,400 $ 470,400 (60,000) (300,000) $170,400 $ 170,400 (68,160) (68,160) $102,240 $ 102,240
g. Olson
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
36
Chapter 9
Miami
49. a. Dayton Company Income Statement (Variable Costing) Sales Cost of goods sold Beginning FG CGM Variable production Available goods Ending FG Other variable costs Contribution margin Fixed costs Production Operating Pretax income Income taxes Net income
First Qtr. of 2013 $ 4,500,000 $ 0
Second Qtr. of 2013 $ 5,250,000 $ 588,000
4,116,000 3,528,000 $4,116,000 $4,116,000 (588,000) (0) 342,000 (3,870,000) 399,000 (4,515,000) $ 630,000 $ 735,000 $ 195,000 42,800
(237,800) $ 392,200 (137,270) $ 254,930
$ 195,000 42,800
(237,800) $ 497,200 (174,020) $ 323,180
b. 1. $75.00 ($58.80 + $5.70) = $10.50
4.
2.
$10.50 ÷ $75.00 = 14%
3.
260,000 × $ 10.50 = $2,730,000 Contribution margin
$2,730,000
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 9
Fixed costs [($195,000 + $42,800) × 4] Pretax income Income taxes (35%) Net income
951,200 $1,778,800 622,580 $1,156,220
5.
$2,730,000 ÷ $1,778,800 = 1.5 (rounded)
6.
$951,200 ÷ $10.50 per unit = 90,590 units (rounded)
7.
$951,200 ÷ 0.14 = $6,794,286 (rounded)
8. 9.
260,000 – 90,590 = 169,410 169,410 ÷ 260,000 = 65% (rounded) 260,000 – 90,590 = 169,410 units
50. Accountants don’t believe that their assumptions are perfectly descriptive, nor do they believe that they are reasonable for any possible level of activity. Rather, accountants only believe their assumptions are “reasonably valid” within a relevant range of activity. The simplifying assumptions are justified because they allow the accountant to work with linear cost and revenue functions, which are much more manageable than nonlinear functions. Significant time and effort would be required to model nonlinear functions and the improvement in predictability would likely be small. Thus, the effort would largely be wasted. 51. a. Atlantic Fish Company Contribution Income Statement For the Year Ended December 31, 2013 Sales $ 3,600,000 Variable costs: Cost of cod $2,240,000 Shipping 160,000 Commissions 360,000 (2,760,000) Contribution margin $ 840,000 Fixed costs: Selling and administrative (650,000) Income before tax $ 190,000 Income tax expense (76,000) Net income $ 114,000 b.
Selling price Variable costs per unit: Cost of cod Shipping Sales commissions Contribution margin
$ 9.00 $5.60 0.40 0.90
(6.90) $ 2.10
Contribution margin ratio: $2.10 ÷ $9.00 = 23.3% © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
38
Chapter 9
c. BEPu = FC ÷ CM per unit BEPu = $650,000 ÷ $2.10 = 309,524 pounds (rounded) BEP$ = 309,524 × $9.00 = $2,785,716 Or BEPu = FC ÷ CM% BEPu = $650,000 ÷ 0.233 = $2,789,700 (off due to rounding) d.
Degree of operating leverage: DOL = CM ÷ Income before tax DOL = $840,000 ÷ $190,000 = 4.4 Margin of safety: Projected 2013 sales Breakeven sales Margin of safety
$ 3,600,000 (2,785,716) $ 814,284
e. Sales increase × Degree of operating leverage = Projected increase in profit before income taxes 20% × 4.4 = 88% expected increase in operating profit Projected profit before taxes (a) $190,000 Expected increase in profit ($190,000 × 0.88) 167,200 Expected profit before taxes after 20% increase $357,200
f. Convert desired aftertax income to before tax income: After tax income ÷ (1 – Tax rate) $900,000 ÷ (1 – 0.4) = $900,000 ÷ 0.6 = $1,500,000 Pounds required: (Total fixed costs + Desired beforetax profit) ÷ CM per pound ($650,000 + $1,500,000) ÷ $2.10 = $2,150,000 ÷ $2.10 = 1,023,810 pounds (rounded)
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.
View more...
Comments
