CHAPTER 6
SOLUTIONS TO PROBLEMS: SET B
(a) Sales were $2,400,000 and variable expenses were $1,536,000, which
means contribution margin was $864,000 and CM ratio was .36. Fixed
expenses were $936,000. Therefore, the break-even point in dollars is:
(b) 1. The effect of this alternative is to increase the selling price per unit to
$15 ($12 X 125%). Total sales become $3,000,000 (200,000 X $15).
Thus, contribution margin changes to 48.8% [($3,000,000 –
$1,536,000) ÷ $3,000,000]. The new break-even point is:
2. The effects of this alternative are: (1) fixed costs decrease by
$120,000, (2) variable costs increase by $144,000 ($2,400,000 X 6%),
(3) total fixed costs become $816,000 ($936,000 – $120,000), and the
3. The effects of this alternative are: (1) variable and fixed cost of
goods sold become $594,400 and $891,600, (2) total variable costs
become $1,060,400 ($594,400 + $356,000 + $110,000), (3) total fixed
Alternative 1 is the recommended course of action using break-even
analysis because it has the lowest break-even point.
PROBLEM 6-1B
PROBLEM 6-2B
(a)
(1)
Current Year
Sales
Variable costs
Direct materials
$1,000,000
327,000
Current Year
Projected Year
Contribution margin
Sales
Variable costs
Direct materials
Direct labor
$1,000,000
327,000
190,000
X 1.2
X 1.2
X 1.2
$1,200,000
392,400
228,000
(2)
Fixed Costs
Current Year
Projected year
Total fixed costs
Manufacturing overhead ($240,000 X .80)
Selling expenses ($200,000 X .70)
$192,000
140,000
$192,000
140,000
Contribution margin
PROBLEM 6-2B (Continued)
(b) Unit selling price = $1,000,000 ÷ 40,000 = $25.00
Unit variable cost = $700,000 ÷ 40,000 = $17.50
Break-even point in units
=
Fixed costs
÷
Unit contribution margin
67,600 units
=
$507,000
÷
$7.50
Break-even point in dollars
=
Fixed costs
÷
Contribution margin ratio
=
÷
(c) Sales dollars
required for
=
(Fixed costs
+
Target net income)
÷
Contribution margin ratio
target net income
=
+
÷
ratio
=
÷
(e)
(1)
Current Year
Contribution margin
Fixed cost
Total fixed costs
Sales
Variable costs
Direct materials
Direct labor ($190,000 – $90,000)
Manufacturing overhead ($240,000 X .10)
$1,000,000
327,000
100,000
24,000
PROBLEM 6-2B (Continued)
(2) Contribution margin ratio = $314,000 ÷ $1,000,000 = .314
(3) Break-even point in dollars = $431,000 ÷ .314 = $1,372,611 (rounded)
The break-even point in dollars declined from $1,690,000 to $1,372,611. This
means that overall the company’s risk has declined because it doesn’t have to
PROBLEM 6-3B
(a)
Sales Mix
Percentage
X
Contribution
Margin Ratio
=
Weighted-Average
Contribution
Margin Ratio
Appetizers
Main entrees
15%
60%
X
X
60%
25%
=
=
.09
.15
Sales Mix
Percentage
X
Total Sales
=
Sales from
Each Product
Appetizers
Main entrees
15%
60%
X
X
$1,320,000
$1,320,000
=
=
$ 198,000
792,000
(b)
Sales Mix
Percentage
X
Contribution
Margin Ratio
=
Weighted-Average
Contribution
Margin Ratio
Desserts
Beverages
X
X
=
=
Appetizers
Main entrees
25%
40%
X
X
60%
10%
=
=
.15
.04
Desserts
Beverages
X
X
=
=
PROBLEM 6-3B (Continued)
Thus, sales would have to increase by $280,000 ($1,600,000 – $1,320,000) 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:
Sales Mix
Percentage
X
Total Sales
Needed
=
Sales Dollars
Per Product
Appetizers
Main entrees
25%
40%
X
X
$1,600,000
$1,600,000
=
=
$ 400,000
640,000
(c)
Sales Mix
Percentage
X
Contribution
Margin Ratio
=
Weighted-Average
Contribution
Margin Ratio
Main entrees
Desserts
Beverages
60%
X
X
X
=
=
=
Appetizers
15%
X
60%
=
.09
The weighted-average contribution margin ratio computed in part (a) was 40%.
With the contribution margin ratio on entrees falling to 10%, that average will
now be 32% as shown above. Applying this to the new fixed costs of $528,000
and target net income of $176,000 we get:
Total sales required
to achieve target net
income = ($528,000 + $176,000) ÷ .32 = $2,200,000
Sales Mix
Percentage
X
Total Sales
Needed
=
Sales from
Each Product
Appetizers
15%
X
$2,200,000
=
$ 330,000
Desserts
Beverages
X
X
=
=
PROBLEM 6-3B (Continued)
Relative to parts (a) and (b), the total required sales for (c) would increase. It
appears that the least risky approach would be for Michael to switch to the
PROBLEM 6-4B
(a)
Product
Economy
Standard
Deluxe
Selling price
$270
$450
$650
(b)
Product
Economy
Standard
Deluxe
Unit contribution margin (a)
$126
$ 190
$ 220
Machine hours required (b)
(c) If additional machine hours become available, the additional time should be
Less: Variable costs
Unit contribution margin
$126
$190
$220
PROBLEM 6-5B
(a) To determine the break-even point in dollars we must first calculate the
contribution margin ratio for each company.
Contribution
Margin
÷
Sales
=
Contribution
Margin Ratio
Lyte Company
$400,000
÷
$1,000,000
=
.40
(Actual Sales
–
Break-even Sales)
÷
Actual Sales
=
Margin of Safety
Ratio
Darke Company
–
$750,000)
÷
=
Lyte Company
($1,000,000
–
$500,000)
÷
$1,000,000
=
.50
(b)
Contribution
Margin
÷
Net
Income
=
Degree of Operating
Leverage
Lyte Company
$400,000
÷
$200,000
=
2.00
Darke Company
÷
=
PROBLEM 6-5B (Continued)
(c)
Lyte Company Darke Company
Sales $1,300,000* $1,300,000
Variable costs 780,000** 260,000***
Contribution margin 520,000 1,040,000
(d)
Lyte Company Darke Company
Sales $700,000* $700,000
Variable costs 420,000** 140,000***
Contribution margin 280,000 560,000
(e) In part (b) the degree of operating leverage of Darke Company was higher
than that of Lyte Company, telling us that the net income of Darke
Company was more sensitive to changes in sales than that of Lyte
Company. In part (c) we see that a 30% increase in sales increased the net
income of Darke Company by $240,000 ($440,000 – $200,000), while the
PROBLEM 6-6B
(a) Reformat the income statement to CVP format.
All amount are in $000s.
Sales ………………………………………………………… $120,000
Variable costs ($58,500 + $19,500) ……………… 78,000
Contribution margin ………………………………….. 42,000
(b) If a hired workforce replaces sales agents, commissions will be reduced to
10% of sales, or $12,000; but fixed costs will increase by $12,000.
Sales ………………………………………………………… $120,000
Variable costs ($58,500 + $12,000) ……………… 70,500
(c) Operating leverage = contribution margin ÷ operating income
PROBLEM 6-6B (Continued)
The calculations indicate that at a sales level of $120 million, a percentage
change in sales and contribution margin will result in 2.00 times that
percentage change in operating income if Peaches continues to use sales
agents. If they choose to employ their own, the change in operating income
will be 3.00 times the percentage change in sales.
(d) The sales level at which operating incomes will be identical is called the
point of indifference. This would be when the cost of the network of
agents (16.25% of sales) is exactly equal to the cost of paying employees
10% commission along with additional fixed costs of $12.0 million. None
of the other costs is relevant, because they will not change between
alternatives.
*PROBLEM 6-7B
(a) FAB COMPANY
Income Statement
For the Year Ended December 31, 2016
Variable Costing
Sales (400,000 yards X $2.50) ………………….
Variable cost of goods sold
Inventory, January 1 ………………………..
Variable cost of goods manufactured
[500,000 yards X $2.50 X 30%] ………
Variable cost of goods available
$ –0–
375,000
$1,000,000
*PROBLEM 6-7B (Continued)
FAB COMPANY
Income Statement
For the Year Ended December 31, 2017
Variable Costing
Sales (500,000 yards X $2.50) ……………………..
Variable cost of goods sold
Inventory, January 1 …………………………...
$ 75,000
$1,250,000
(b) FAB COMPANY
Income Statement
For the Year Ended December 31, 2016
Absorption Costing
Sales (400,000 yards X $2.50) ……………………
Cost of goods sold
Inventory, January 1 ………………………….
Cost of goods manufactured ……………..
$ –0–
775,000
(1)
$1,000,000
Variable cost of goods manufactured
FAB COMPANY
Income Statement
For the Year Ended December 31, 2017
Absorption Costing
Sales (500,000 yards X $2.50) ……………
Cost of goods sold
Inventory, January 1 ………………….
$ 155,000
$1,250,000
(c) The variable costing and the absorption costing income from operations
can be reconciled as follows:
2016
2017
Variable costing net income
Fixed manufacturing overhead
expensed with variable costing
$400,000
$100,000
$400,000
$250,000
*PROBLEM 6-7B (Continued)
*PROBLEM 6-8B
(a)
ELECTRICOIL DIVISION
Income Statement
For the Year Ended December 31, 2017
Absorption Costing
200,000 250,000
Produced Produced
Sales (200,000 units X $9) $1,800,000 $1,800,000
Cost of goods sold
(b)
ELECTRICOIL DIVISION
Income Statement
For the Year Ended December 31, 2017
Variable Costing
_______________________________________________________________
200,000 250,000
Produced Produced
Sales (200,000 units X $9) $1,800,000 $1,800,000
(c) If the company produces 250,000 units, but only sells 200,000 units, then
50,000 units will remain in ending inventory. Under absorption costing
these 50,000 units will each include $2.00 of fixed manufacturing cost—a
total of $100,000. However, under variable costing, fixed manufacturing
cost is expensed when incurred. This accounts for the $100,000 difference
($705,000 – $605,000) in net income. This is summarized as:
(d) Variable costing has a number of advantages over absorption costing for
decision making and evaluation purposes. (1) The use of variable costing
is consistent with cost-volume-profit and incremental analysis: (2) Net
income computed under variable costing is unaffected by changes in
production levels. Note that, under variable costing the company’s net