SOLUTIONS TO BRIEF EXERCISES
BRIEF EXERCISE 6-1
1.
(a)
(b)
$70 = ($250 – $180)
28% ($70 ÷ $250)
2.
(c)
(d)
$200 = ($500 – $300)
60% ($300 ÷ $500)
3.
(e)
(f)
$1,100 = ($330 ÷ 30%)
$770 ($1,100 – $330)
BRIEF EXERCISE 6-2
HAMBY INC.
Income Statement
For the Quarter Ended March 31, 2014
Sales .......................................................................
Variable expenses
Cost of goods sold .........................................
Selling expenses ............................................
Administrative expenses ...............................
Total variable expenses .........................
Contribution margin ..............................................
Fixed expenses
Cost of goods sold .........................................
Selling expenses ............................................
Administrative expenses ...............................
Total fixed expenses ..............................
Net income .............................................................
$2,000,000
$760,000
95,000
79,000
934,000
1,066,000
600,000
60,000
66,000
726,000
$ 340,000
BRIEF EXERCISE 6-3
Contribution margin ratio = [($250,000 – $175,000) ÷ $250,000] = 30%
Required sales in dollars = $120,000 ÷ 30% = $400,000
BRIEF EXERCISE 6-4
(a)
$400Q = $250Q + $210,000 + $0
$150Q = $210,000
Q = 1,400 units
(b) Contribution margin per unit $150, or ($400 – $250)
X = $210,000 ÷ $150
X = 1,400 units
BRIEF EXERCISE 6-5
X = .60X + $210,000 + $60,000
.40X = $270,000
X = $675,000
BRIEF EXERCISE 6-6
Margin of safety = $1,200,000 – $960,000 = $240,000
Margin of safety ratio = $240,000 ÷ $1,200,000 = 20%
BRIEF EXERCISE 6-7
Model
A12
B22
C124
Sales Mix
Percentage
60%
15%
25%
Unit Contribution
Margin
$10 ($50 – $40)
$30 ($100 – $70)
$100 ($400 – $300)
Weighted-Average Unit
Contribution Margin
$ 6.00
4.50
25.00
$35.50
BRIEF EXERCISE 6-8
Total break-even = ($213,000 ÷ $35.50*) = 6,000 units
*Computed in BE 6-7
Sales Units
Units of A12 = .60 X 6,000 = 3,600
Units of B22 = .15 X 6,000 = 900
Units of C124 = .25 X 6,000 = 1,500
6,000
BRIEF EXERCISE 6-9
(a)
(b)
Weighted-average
contribution
=
margin ratio
(.30 X .20) + (.50 X .20) + ( .20 X .45) = .25
Total break-even
point
= ($440,000 ÷ .25) = $1,760,000
in dollars
Birthday
$1,760,000 X .30 = $ 528,000
Standard tapered $1,760,000 X .50 =
880,000
Large scented
$1,760,000 X .20 =
352,000
$1,760,000
BRIEF EXERCISE 6-10
(a)
Sales Mix
Bedroom Division
$500,000 ÷ $1,250,000 = .40
Dining Room Division $750,000 ÷ $1,250,000 = .60
(b)
Weight-average contribution = $575,000 = .46
margin ratio
$1,250,000
OR
Contribution Margin Ratio
Bedroom Division
($275,000 ÷ $500,000) = .55
Dining Room Division ($300,000 ÷ $750,000) = .40
Weighted-average contribution
margin ratio
= (.55 X .40) + (.40 X .60) = .46
BRIEF EXERCISE 6-11
Contribution margin per unit (a)
Machine hours required (b)
Contribution margin per unit of limited resource
[(a) ÷ (b)]
Product A
$12.0
2
$ 6
Product B
$15
3
$ 5
BRIEF EXERCISE 6-12
Degree of operating
leverage (old)
=
$200,000 ÷ $40,000 = 5
Degree of operating
leverage (new)
=
$240,000 ÷ $40,000 = 6
If Sam’s sales change, the resulting change in net income will be 1.2 times (6 ÷ 5)
higher with the new machine than under the old system.
BRIEF EXERCISE 6-13
Break-even point in dollars:
Logan Co.
$60,000 ÷ ($120,000 ÷ $200,000)
= $100,000
Morgan Co.
$90,000 ÷ ($150,000 ÷ $200,000)
= $120,000
Morgan Company’s cost structure relies much more heavily on fixed costs than
that of Logan Co. As result, Morgan has a higher contribution margin ratio of .75
($150,000 ÷ $200,000) versus .60 ($120,000 ÷ $200,000), for Logan Co. Morgan also
has much higher fixed costs to cover. Its break-even point is therefore higher
than that of Logan Co.
BRIEF EXERCISE 6-14
Degree of operating leverage = Contribution margin ÷ Net income
Montana Corp.
1.6 = Contribution margin ÷ $50,000
Contribution margin
= $50,000 X 1.6 = $80,000
APK Co.
5.4 = Contribution margin ÷ $50,000
Contribution margin
= $50,000 X 5.4 = $270,000
BRIEF EXERCISE 6-15
Contribution margin per unit (a)
Machine hours required (b)
Contribution margin per unit of limited resource
[(a) ÷ (b)]
Product 1
$ 42
.15
$280
Product 2
$ 35
.10
$350
Product 2 has a higher contribution margin per limited resource, even though it
has a lower contribution margin per unit. Given that machine hours are limited to
2,000 per month, Ger Corporation should produce Product 2.
PROBLEM 6-1A
(a) Sales were $2,000,000 and variable expenses were $1,100,000, which means
contribution margin was $900,000 and CM ratio was .45. Fixed expenses were
$1,035,000. Therefore, the break-even point in dollars is:
$1,035,000
= $2,300,000
.45
(b) 1.
The effect of this alternative is to increase the selling price per unit to
$31.25 ($25 X 125%). Total sales become $2,500,000 (80,000 X $31.25).
Thus, contribution margin ratio changes to 56% [($2,500,000 –
$1,100,000) ÷ $2,500,000]. The new break-even point is:
$1,035,000 = $1,848,214 (rounded)
.56
2.
The effects of this alternative are: (1) fixed costs decrease by $160,000,
(2) variable costs increase by $100,000 ($2,000,000 X 5%), (3) total fixed
costs become $875,000 ($1,035,000 – $160,000), and the contribution
margin ratio becomes .40 [($2,000,000 – $1,100,000 – $100,000) ÷
$2,000,000]. The new break-even point is:
$875,000
= $2,187,500
.40
3.
The effects of this alternative are: (1) variable and fixed cost of goods
sold become $734,000 each, (2) total variable costs become $884,000
($734,000 + $92,000 + $58,000), (3) total fixed costs are $1,251,000
($734,000 + $425,000 + $92,000) and the contribution margin ratio
becomes .558 [($2,000,000 – $884,000) ÷ $2,000,000]. The new breakeven point is:
$1,251,000
= $2,241,935 (rounded)
.558
Alternative 1 is the recommended course of action using break-even
analysis because it has the lowest break-even point.
PROBLEM 6-2A
(a) (1)
Current Year
$1,500,000
Sales
Variable costs
Direct materials
Direct labor
Manufacturing overhead ($350,000 X .70)
Selling expenses ($250,000 X .40)
Administrative expenses ($270,000 X .20)
Total variable costs
Contribution margin
Sales
Variable costs
Direct materials
Direct labor
Manufacturing overhead
Selling expenses
Administrative expenses
Total variable costs
Contribution margin
511,000
290,000
245,000
100,000
54,000
1,200,000
$ 300,000
Current Year
$1,500,000 X 1.1
511,000
290,000
245,000
100,000
54,000
1,200,000
$ 300,000
X 1.1
X 1.1
X 1.1
X 1.1
X 1.1
X 1.1
X 1.1
Projected Year
$1,650,000
562,100
319,000
269,500
110,000
59,400
1,320,000
$ 330,000
(2)
Fixed Costs
Current Year
Manufacturing overhead ($350,000 X .30)
$105,000
Selling expenses ($250,000 X .60)
150,000
Administrative expenses ($270,000 X .80)
216,000
Total fixed costs
$471,000
Projected year
$105,000
150,000
216,000
$471,000
PROBLEM 6-2A (Continued)
(b) Unit selling price = $1,500,000 ÷ 100,000 = $15
Unit variable cost = $1,200,000 ÷ 100,000 = $12
Unit contribution margin = $15 – $12 = $3
Contribution margin ratio = $3 ÷ $15 = .20
Break-even point in units
157,000 units
= Fixed costs
=
$471,000
Break-even point in dollars
$2,355,000
= Fixed costs
= $471,000
÷
÷
Unit contribution margin
$3.00
÷
÷
Contribution margin ratio
.20
(c) Sales dollars
required for
= (Fixed costs
target net income
+ Target net income) ÷ Contribution margin ratio
$3,355,000 =
+
($471,000
$200,000)
(d) Margin of safety = (Expected sales
ratio
29.8%
=
($3,355,000
÷
.20
– Break-even sales)
÷ Expected sales
–
÷
$2,355,000)
(e) (1)
Sales
Variable costs
Direct materials
Direct labor ($290,000 – $104,000)
Manufacturing overhead ($350,000 X .30)
Selling expenses ($250,000 X .90)
Administrative expenses ($270,000 X .20)
Total variable costs
Contribution margin
Current Year
$1,500,000
511,000
186,000
105,000
225,000
54,000
1,081,000
$ 419,000
$3,355,000
PROBLEM 6-2A (Continued)
Fixed cost
Manufacturing overhead ($350,000 X .70)
Selling expenses ($250,000 X .10)
Administrative expenses ($270,000 X .80)
Total fixed costs
$245,000
25,000
216,000
$486,000
(2) Contribution margin ratio = $419,000 ÷ $1,500,000 = .28 (rounded)
(3) Break-even point in dollars = $486,000 ÷ .28 = $1,735,714 (rounded)
The break-even point in dollars declined from $2,355,000 to $1,735,714. This
means that overall the company’s risk has declined because it doesn’t have
to generate as much in sales. The two changes actually had opposing
effects on the break-even point. By changing to a more commission-based
approach to compensate its sales staff the company reduced its fixed costs,
and therefore reduced its break-even point. In contrast, the purchase of the
new equipment increased the company’s fixed costs (by increasing its
equipment depreciation) which would increase the break-even point.
PROBLEM 6-3A
(a)
Selling price
Less: Variable costs
Contribution margin per unit
Economy
$30
14
$16
Product
Standard
$50
15
$35
Deluxe
$100
46
$ 54
Ignoring the machine time constraint, the Deluxe product should be produced
because it has the highest contribution margin per unit.
(b)
Contribution margin per unit (a)
Machine hours required (b)
Contribution margin
per limited resource (a)/(b)
Economy
$16
.5
$32
Product
Standard
$ 35
.8
$43.75
Deluxe
$ 54
1.6
$33.75
(c) If additional machine hours become available, the additional time should be
used to produce the Standard product since it has the highest contribution
margin per machine hour.
PROBLEM 6-4A
(a)
Appetizers
Main entrees
Desserts
Beverages
Sales Mix
Percentage
15%
50%
10%
25%
Total sales required
to achieve target net
income
=
Appetizers
Main entrees
Desserts
Beverages
X
X
X
X
X
Contribution
Margin Ratio
50%
25%
50%
80%
=
=
=
=
=
Weighted-Average
Contribution
Margin Ratio
.075
.125
.050
.200
.450
( $1,053,000 + $117,000 ) ÷ .45 = $2,600,000
Sales Mix
Percentage
15%
50%
10%
25%
X
X
X
X
X
Total Sales
Needed
$2,600,000
$2,600,000
$2,600,000
$2,600,000
=
=
=
=
=
Sales from
Each Product
$ 390,000
1,300,000
260,000
650,000
$2,600,000
(b)
Appetizers
Main entrees
Desserts
Beverages
Sales Mix
Percentage
25%
25%
10%
40%
Total sales required
to achieve target net
income
=
*$1,053,000 + $585,000
X
X
X
X
X
Contribution
Margin Ratio
50%
10%
50%
80%
=
=
=
=
=
Weighted-Average
Contribution
Margin Ratio
.125
.025
.050
.320
.520
( $1,638,000* + $117,000) ÷ .52 = $ 3,375,000
PROBLEM 6-4A (Continued)
Thus, sales would have to increase by $775,000 ($3,375,000 – $2,600,000) to
achieve the target net income. This increase in sales is driven by the increase in
fixed costs. The sales of each product line would be:
Appetizers
Main entrees
Desserts
Beverages
Sales Mix
Percentage
25%
25%
10%
40%
X
X
X
X
X
Total Sales
Needed
$3,375,000
$3,375,000
$3,375,000
$3,375,000
=
=
=
=
=
Sales from
Each Product
$ 843,750
843,750
337,500
1,350,000
$3,375,000
(c)
Appetizers
Main entrees
Desserts
Beverages
Sales Mix
Percentage
15%
50%
10%
25%
X
X
X
X
X
Contribution
Margin Ratio
50%
10%
50%
80%
=
=
=
=
=
Weighted-Average
Contribution
Margin Ratio
.075
.050
.050
.200
.375
The weighted-average contribution margin ratio computed in part (a) was 45%.
With the contribution margin ratio on entrees falling to 10%, that average will
now be 37.5% as shown previously. Applying this to the new fixed costs of
$1,638,000 and target net income of $117,000 we get:
Total sales required
to achieve target net
income
=
Appetizers
Main entrees
Desserts
Beverages
($1,638,000 + $117,000) ÷ .375 = $ 4,680,000
Sales Mix
Percentage
15%
50%
10%
25%
X
X
X
X
X
Total Sales
Needed
$4,680,000
$4,680,000
$4,680,000
$4,680,000
=
=
=
=
=
Sales from
Each Product
$ 702,000
2,340,000
468,000
1,170,000
$4,680,000
Relative to parts (a) and (b), the total required sales for (c) would increase. It
appears that the least risky approach would be for Phil to switch to the new
sales mix, but not to incur the additional fixed costs of expanding operations. If
the switch in sales mix appears to be successful, then it may be appropriate for
him to incur the additional fixed costs necessary for expansion of operations.
PROBLEM 6-5A
(a) To determine the break-even point in dollars we must first calculate the
contribution margin ratio for each company.
Viejo Company
Nuevo Company
Contribution
Margin
÷
$220,000
÷
$320,000
÷
Fixed
Costs
$180,000
$280,000
Viejo Company
Nuevo Company
Viejo Company
Nuevo Company
(Actual Sales
($500,000
($500,000
–
–
–
÷
÷
÷
Sales
$500,000
$500,000
Contribution Margin
=
Ratio
=
.44
=
.64
Contribution
Margin Ratio
.44
.64
Break-even Sales)
$409,091)
$437,500)
÷
÷
÷
Break-even Point
=
in Dollars
=
$409,091
=
$437,500
Actual Sales
$500,000
$500,000
=
=
=
Margin of Safety
Ratio
.182
.125
(b)
Viejo Company
Nuevo Company
Contribution
Margin
÷
$220,000
÷
$320,000
÷
Net
Income
$40,000
$40,000
Degree of Operating
=
Leverage
=
5.5
=
8.0
Because Nuevo Company relies more heavily on fixed costs, it has a higher
degree of operating leverage. This means that its net income will be more
sensitive to changes in sales. For a given change in sales, the change in net
income will be 1.45 (8.0 ÷ 5.5) times higher for Nuevo Company than for Viejo
Company.
(c)
Sales
Variable costs
Contribution margin
Fixed costs
Net income
*$500,000 X 1.2
**$280,000 X 1.2
***$180,000 X 1.2
Viejo Company
$600,000*
336,000**
264,000
180,000
$ 84,000
Nuevo Company
$600,000
216,000***
384,000
280,000
$104,000
PROBLEM 6-5A (Continued)
(d)
Viejo Company
$400,000*
224,000**
176,000
180,000
($ 4,000)
Sales
Variable costs
Contribution margin
Fixed costs
Net income (Loss)
Nuevo Company
$400,000
144,000***
256,000
280,000
($ 24,000)
*$500,000 X .80
**$280,000 X .80
***$180,000 X .80
(e) In part (b) the degree of operating leverage of Nuevo Company was higher
than that of Viejo Company, telling us that the net income of Nuevo Company
was more sensitive to changes in sales than that of Viejo Company. In part
(c) we see that a 20% increase in sales increased the net income of Nuevo
Company by $64,000 ($104,000 – $40,000), while the net income of Viejo
Company increased by only $44,000 ($84,000 – $40,000). However, in part (d)
we see that a 20% decrease in sales resulted in a $64,000 ($40,000 + $24,000)
decline in net income for Nuevo Company, while Viejo Company’s net income
only declined by $44,000 ($40,000 + $4,000). The increased risk caused by
higher operating leverage is also seen in part (a). Nuevo Company has a
higher break-even point, and a lower margin of safety ratio than Viejo
Company. Thus, while operating leverage can be very beneficial for a
company that expects its sales to increase, it can also significantly increase
a company’s risk.
CHAPTER REVIEW
Cost-Volume-Profit Income Statement
1.
(L.O. 1) The Cost-Volume-Profit (CVP) income statement classifies costs as variable or fixed and
computes a contribution margin. Contribution margin is the amount of revenue remaining after
deducting variable costs. It is often stated both as a total amount and on a per unit basis.
Desossa Music Player Company
CVP Income Statement
For the Month Ended June 30, 2014
Sales
Variable expenses
Cost of goods sold
Selling expenses
Administrative expenses
Total variable expenses
Total
$420,000
Per Unit
$120
$200,000
20,000
11,000
231,000
66
Contribution margin
Fixed expenses
Cost of goods sold
Selling expenses
Administrative expenses
Total fixed expenses
Net income
189,000
$ 54
50,000
30,000
19,900
99,900
$ 89,100
Basic Computations
2.
3.
4.
(L.O. 2) Desossa Music Player’s CVP income statement shows that total contribution margin (sales minus
variable expenses) is $175,000, and the company’s contribution margin per unit is $50. The contribution
margin ratio (contribution margin divided by sales) is 45% ($54 ÷ $120). Desossa’s break-even point in
units (using contribution margin per unit) or in dollars (using contribution margin ratio) are calculated as
follows:
Fixed cost
$99,900
÷
÷
Contribution margin per unit
$54
Fixed cost
$99,900
÷
÷
Contribution margin ratio
.45
=
=
Break-even point in units
1,850 units
= Break-even point in dollars
=
$222,000
Assuming Desossa’s management has a target net income of $108,000, the required sales in units and
dollars to achieve its target net income are calculated as follows:
(Fixed cost + Target net income) ÷ Contribution margin per unit
($99,900 + $108,000)
÷
$54
=
=
(Fixed cost + Target net income) ÷
($99,900 + $108,000)
÷
= Required sales in dollars
=
$462,000
Contribution margin ratio
.45
Required sales in units
3,850 units
Desossa’s margin of safety in dollars or as a ratio is calculated as follows:
Actual (expected) sales
$420,000
–
–
Break-even sales
$222,000
= Margin of safety in dollars
=
$198,000
Margin of safety in dollars ÷ Actual (expected) sales =
$198,000
÷
$420,000
=
Margin of safety ratio
47.1%
CVP and Changes in the Business Environment
5.
To better understand how CVP analysis works, let’s assume that shipping costs have increased
significantly causing the unit variable cost to increase by 10%, what effect will this have on Desossa’s
break-even point?
Answer: A 10% increase in variable costs increases the per unit variable cost to $72.60 [$66 +
($66 X 10%)]. The new contribution margin per unit is therefore $47.40 ($120 – $72.60). Thus the new
break-even point in units is calculated as follows:
Fixed cost
$99,900
Sales Mix
÷
÷
Contribution margin per unit
$47.40
=
=
Break-even point in units
2,108 units
6.
(L.O. 3) Sales mix is the relative percentage in which a company sells its multiple products. For example,
if 80% of Company A’s unit sales are shoes and the other 20% are jeans, its sales mix is 80% shoes to
20% jeans.
7.
Break-even sales can be computed for a mix of two or more products by determining the weightedaverage unit contribution margin of all the products. Assume that Seth Inc. sells tables and chairs in
a ratio of four chairs for every one table. The sales mix in percentages is 20% (1/5) for tables and 80%
(4/5) for chairs. The following is the per unit data for Seth Inc.:
Unit Data
Tables
Selling price
$100
Variable costs
60
Contribution margin
$ 40
Sales mix-units
20%
Fixed costs = $192,000
Chairs
$20
10
$10
80%
To compute break-even for Seth Inc., we use the weighted-average unit contribution margin as follows:
Tables
Chairs
 Unit
Sales
  Unit
Sales

 Contribution X Mix
 +  Contribution X Mix
=

 

 Margin
Percentage  Margin
Percentage 
($40
X
.20)
+
($10
X
.80)
=
Weighted – Average
Unit Contribution
Margin
$16
Fixed Costs
÷
$192,000
÷
Weighted – Average
Unit
Contribution Margin
$16
=
Break – even Point
in Units
12,000 units
To break even, Seth must sell 2,400 (12,000 X 20%) tables and 9,600 (12,000 X 80%) chairs.
8.
At any level of units sold, net income will be greater if more high contribution margin units are sold than
low contribution margin units. An analysis of these relationships generally shows that a shift from lowmargin sales to high-margin sales may increase net income, even though there is a decline in total units
sold.
9.
The calculation of the break-even point computed in units works well if a company has only a small
number of products. When a company has a large number of products, it’s more useful to compute the
break-even point in terms of sales dollars. The formula for computing the break-even point in dollars is
fixed costs divided by the weighted-average contribution margin ratio. To compute a company’s
weighted-average contribution ratio, multiply each division’s contribution margin ratio by its percentage of
total sales and then sum these amounts.
Seth Inc’s contribution margin ratio for sales of tables is .40 ($40/$100) and for chairs is .50 ($10/$20).
The weighted-average contribution margin ratio is calculated as follows:
Tables
Chairs
 Contribution Sales Mix 
 MarginRatio X Percentage
(.40
X
.20)
Weighted - Average
 Contribution Sales Mix 
X
+ 
=

 MarginRatio Percentage  ContributionMarginRatio
+
(.50
X
.80)
=
.48
The break-even point in dollars is calculated as follows:
Fixed Costs
÷
$192,000
÷
Weighted – Average
Contribution Margin Ratio
.48
=
=
Break – even Point
in Dollars
$400,000
Sales Mix with Limited Resources
10.
(L.O. 4) When a company has limited resources (e.g., floor space, raw materials, direct labor hours),
management must decide which products to make and sell in order to maximize net income. Assume that
Seth Inc. has limited machine capacity which is 2,600 hours per month. Relevant data consist of the
following:
Contribution margin per unit
Machine hours required per unit
Tables
$40
.8
Chairs
$10
.16
The contribution margin per unit of limited resource is calculated as follows:
Tables
Chairs
Contribution margin per unit (a)
$40
$10
Machine hours required (b)
.8
.16
Contribution margin per unit of
limited resource [(a)  (b)]
$50
$62.50
If Seth Inc. increases machine capacity hours by 400 hours per month, it would be better to use the hours
to produce more chairs.
Machine hours (a)
Contribution margin per unit of
limited resource (b)
Contribution margin [(a) X (b)]
Tables
400
Chairs
400
$
50
$20,000
$ 62.50
$25,000
Cost Structure and Operating Leverage
11. (L.O. 5) Cost structure refers to the relative proportion of fixed versus variable costs that a company
incurs. In most cases, increased reliance on fixed costs increases a company’s risk. When sales are
increasing, profits can increase at a high rate, but when sales decline, losses can also increase at a high
rate. Companies can change their cost structure by using more sophisticated robotic equipment and
reducing it later, or vice versa. The equipment would increase the fixed costs whereas labor increases
variable costs.
12. Operating Leverage refers to the extent to which a company’s net income reacts to a given change in
sales. The degree of operating leverage provides a measure of a company’s earnings volatility and can
be used to compare companies. The formula is:
Contribution Margin
÷
Net Income
=
Degree of Operating Leverage