12–11
E12.13.
a.
Use the model, enter the known data, and solve for the unknown.
Per Unit
*
Volume
=
Total
%
Revenue
$ ?
100%
Variable Expense
7.80
65%
Contribution Margin
$ ?
$
35%
b.
Per Unit
*
Volume
=
Total
%
Revenue
$12.00
100%
Variable Expense
7.80
65%
Contribution Margin
$ 4.20
*
?
=
$ ?
35%
Fixed Expense
(15,000)
Operating Income
$ 6,000
product that would have to be sold to increase operating income by $6,000.
E12.14.
a.
Per Unit
*
Volume
=
Total
%
Revenue
$ ?
100%
Variable Expense
8.25
66%
Contribution Margin
$ ?
*
?
=
$ ?
34%
b.
Note: The requirement is to determine the number of units of the new product
that must be sold to break even on the new product.
Per Unit
*
Volume
=
Total
%
Revenue
$12.50
100%
Variable Expense
8.25
66%
Contribution Margin
$ 4.25
*
?
=
$ 30,600
34%
Fixed Expense
(30,600)
Operating Income
$ 0
Chapter 12 Managerial Accounting and Cost-Volume-Profit Relationships
E12.14.
(continued)
New Product
Existing Products
Total
c.
Revenue
$13.75 * 20,000 = $275,000
$275,000
$550,000
Variable Expense
8.25
Contribution Margin
$ 5.50 * 20,000 = $ 110,000
$ 93,500 = 34%
203,500
Fixed Expense
(100,000)
Operating Income (loss)
$ (6,500)
d.
The specific data for existing products, not known in this example, would have to be
adjusted for the reduction due to volume “stolen” by the new product. This could result
E12.15.
a.
Per Unit
*
Volume
=
Total
%
Revenue
$1.25
100%
Variable Expense
0.35
28%
Contribution Margin
$0.90
Fixed Expense
Operating income from increased volume
Variable expenses of 600 cones given away, @ $0.35
beverages) on which additional contribution margin will be earned.
E12.16.
a.
Per Unit
*
Volume
=
Total
Revenue
$9.99
Variable Expense
3.00
Contribution Margin
$6.99
=
b.
Revenue#
$5.00
Variable Expense
3.00
Contribution Margin
$2.00
*
?
=
$2,796
12–13
E12.16.
(continued)
c.
Will customers buy other products such as drinks, salads, etc.? Will this
promotion “steal” volume from large and small pizzas? If so, normal
P12.17.
a.
Solution approach: First, calculate variable cost per unit in September and use
the same per unit cost for October. Second, fixed cost will be the same for each
month. Third, with knowledge of total costs for August, and variable and fixed
costs for October, solve for mixed costs for October.
September
October
Activity ………………………………………
5,000 units
8,000 units
Costs:
Variable ($10,000 / 5,000 units = $2 per unit)
$10,000
Fixed (same total amount each month) ………
Total …………………………………………
$60,000
b.
Variable rate
=
(High $ – Low $) / (High units – Low units)
=
($24,500 – $20,000) / (8,000 – 5,000)
=
$4,500 / 3,000 = $1.50 per unit
Total mixed cost
=
Fixed cost + Variable cost
$24,500
=
? + ($1.50 * 8,000 units)
$12,500
Fixed cost + (Variable rate * Volume)
P12.18.
February
August
a.
Production level (units) …………………………
12,000 units
18,000 units
Costs:
Variable ($21,000 / 12,000 units = $1.75 per unit)
$21,000
$ 31,500
Fixed (same total amount each month) …………
Mixed (Total costs – (Variable + Fixed)) ………
Total ……………………………………………
$70,000
$88,000
b.
Total mixed cost
=
(Fixed cost + Variable cost)
Variable cost
=
(Variable rate * Volume)
Variable rate
=
(High $ – Low $) / (High units – Low units)
=
($25,500 – $18,000) / (18,000 – 12,000)
=
$7,500 / 6,000 = $1.25 per unit
Chapter 12 Managerial Accounting and Cost-Volume-Profit Relationships
P12.18.
(continued)
b.
At 12,000 units:
Variable cost
=
($1.25 * 12,000 units) = $15,000
Total mixed cost
=
Fixed cost + Variable cost
$18,000
=
Fixed + $15,000
Fixed
=
$3,000
At 10,000 units:
Variable cost
=
($1.25 * 18,000 units) = $22,500
=
Fixed cost + Variable cost
$25,500
=
Fixed + $22,500
Fixed
=
$3,000
Fixed cost + (Variable rate * Volume)
=
$3,000 + $1.25 per unit
c.
At 20,000 units:
Variable (20,000 units * $1.75 per unit) …………
$ 35,000
Fixed (same total amount each month)……………
31,000
Mixed ($3,000 + (20,000 units * $1.25 per unit))…
d.
Cost behavior pattern is linear. Relevant range does not change.
P12.19.
a.
Revenues (8,000 units * $4 per unit) …………………
$32,000
Variable expenses:
Cost of goods sold (8,000 units * $2.10 per unit) ……
$16,800
Selling expenses (8,000 unit * $0.10 per unit) ………
800
Administrative expenses (8,000 units * $0.20 per unit)
1,600
Total variable expenses ………………………………
Contribution margin …………………………………
$12,800
Fixed expenses:
Cost of goods sold ……………………………………
Selling expenses ………………………………………
Administrative expenses………………………………
Total fixed expenses …………………………………
Operating income ……………………………………
b.
Contribution margin per unit = Total CM / Volume = $12,800 / 8,000 units = $1.60
Contribution margin ratio = CM / Revenues = $12,800 / $32,000 = 40%
CM ratio = CM per unit / Selling price per unit = $1.60 / $4.00 = 40%
Alternative approach:
CM per unit = Selling price per unit – Variable expense per unit
P12.19.
(continued)
c.
1. Volume of 12,000 units:
Per Unit
*
Volume
=
Total
%
Revenue
$4.00
100%
Variable Expense
2.40
60%
Contribution Margin
$1.60
=
Fixed Expense
Operating Income
new operating income will be $8,000.
2. Volume of 4,000 units:
Per Unit
*
Volume
=
Total
%
Revenue
$4.00
100%
Variable Expense
2.40
60%
Contribution Margin
$1.60
4,000
=
Fixed Expense (no change)
Operating Loss
an operating loss of $4,800.
d.
1. Use the contribution margin ratio of 40%. Revenue increase of $12,000 causes a
2. Revenue decrease of $7,000 causes a $2,800 decrease (40% * $7,000) in
P12.20.
a.
Revenues (15,000 units * $7.00 per unit) ………………
$105,000
Variable expenses:
Cost of goods sold (15,000 units * $ 3.60 per unit)……
$54,000
Selling expenses (15,000 units * $0.80 per unit)………
12,000
Administrative expenses (15,000 units * $0.50 per unit)
7,500
Total variable expenses ………..……..………………
Contribution margin……………………..……………
Fixed expenses:
Cost of goods sold ………………….…………………
Selling expenses ………………………………………
Administrative expenses………………………………
Total fixed expenses …………………………………
Operating income………………………………………
Chapter 12 Managerial Accounting and Cost-Volume-Profit Relationships
P12.20.
(continued)
b.
Contribution margin per unit = Total contribution margin / Volume = $31,500 /
15,000 units = $2.10 per unit
Alternative approach:
Contribution margin per unit = Selling price per unit – Variable expense per unit
CM ratio = CM per unit / Selling price per unit = $2.10 / $7.00 = 30%
c.
1. Volume of 20,000 units:
Per Unit
*
Volume
=
Total
Revenue
$7.00
Variable Expense
4.90
Contribution Margin
$2.10
=
Fixed Expense
Operating Income
2. Volume of 10,000 units:
Per Unit
*
Volume
=
Total
Revenue
$7.00
Variable Expense
4.90
Contribution Margin
$2.10
=
Fixed Expense
to $7,500.
d.
1. Use the contribution margin ratio of 30%. Revenue increase of $15,000
2. Revenue decrease of $10,000 causes a $3,000 decrease (30% * $10,000) in
12–17
P12.21.
a.
Sales ……………………………………………………………………
$65,000
Variable expenses (80% * $65,000) ……………………………………
(52,000)
Contribution margin (20% * $65,000) …………………………………
$13,000
Fixed expenses …………………………………………………………
(18,000)
Operating loss …………………………………………………………
$(5,000)
Contribution margin + $5,000 Operating loss).
b.
Increase in sales (30% * $65,000) ………………………………………
$19,500
Contribution margin ratio ………………………………………………
20%
Increase in contribution margin …………………………………………
$ 3,900
Previous operating loss …………………………………………………
Adjusted operating loss …………………………………………………
is also a decrease in the operating loss, because fixed expenses do not change.
c.
At break-even, contribution margin = fixed expenses = $18,000
Contribution margin = (20% contribution margin ratio * ??? sales) = $18,000
P12.22.
a.
Sales ……………………………………………………………………
$80,000
Variable expenses (70% * $80,000) ……………………………………
(56,000)
Contribution margin (30% * $80,000) …………………………………
$24,000
Fixed expenses …………………………………………………………
(18,000)
Operating income ………………………………………………………
b.
Increase in sales (8% * $80,000) ………………………………………
$6,400
Contribution margin ratio …………………………………….…………
30%
Increase in contribution margin……………………………….…………
$1,920
Previous operating income………………………………………………
Adjusted operating income………………………………………………
c.
At break-even, contribution margin = fixed expenses = $18,000
Contribution margin = (30% contribution margin ratio * ??? sales) = $18,000
Chapter 12 Managerial Accounting and Cost-Volume-Profit Relationships
P12.23.
a.
Per Unit
*
Volume
=
Total
Revenue
$15
Variable Expense
9
Contribution Margin
$ 6
*
?
=
$ 27,000
Fixed Expense
(27,000)
Operating Income
$ 0
At the break-even point, total contribution margin must equal total fixed expenses.
Break-even volume = ($6 contribution margin per unit * ??? volume) = $27,000
b.
= 10%
Margin of safety = Total sales – Break-even sales
= $75,000 – $67,500
= $7,500
c.
Per Unit
*
Volume
=
Total
Revenue
$15
Variable Expense
9
Contribution Margin
$ 6
*
5,400
=
$32,400
Fixed Expense
(27,000)
Operating Income
$ 5,400
Per Unit
*
Volume
=
Total
Revenue
$13
Variable Expense
9
Contribution Margin
$ 4
*
8,400
=
Fixed Expense
Operating Income
$ 6,600
e.
Does the increase in volume move fixed expenses into a new relevant range?
Are variable expenses really linear?
f.
Per Unit
*
Volume
=
Total
Revenue
$16
Variable Expense
9
Contribution Margin
$ 7
*
5,400
=
Fixed Expense
Operating Income
$ 4,800
12–19
P12.23.
(continued)
g.
1. Volume of 5,400 units per month:
Per Unit
*
Volume
=
Total
Revenue
$15.00
Variable Expense
9.80
Contribution Margin
$ 5.20
*
=
Operating Income
Decrease in fixed expenses (2 salespersons @ $2,500) ………………
Increase in fixed expenses (2 salespersons @ $400) …………………
Adjusted fixed expenses ………………………………………………
2. Volume of 6,000 units per month:
Per Unit
*
Volume
=
Total
Revenue
$15.00
Variable Expense
9.80
Contribution Margin
$ 5.20
*
=
Fixed Expense
Operating Income
Per Unit
*
Volume
=
Total
h.
Revenue
$15
Variable Expense
9
Contribution Margin
*
=
Fixed Expense ($27,000 + $1,000)
Operating Income
income than does the plan to increase advertising.
P12.24.
a.
Per Unit
*
Volume
=
Total
Revenue
$32.00
Variable Expense
20.80
Contribution Margin
$11.20
*
4,250
=
$47,600
Fixed Expense
Operating Income
$ 0
b.
= 15%
Margin of safety = Total sales – Break-even sales
= $160,000 – $136,000 ($32 * 4,250 = $136,000)
P12.24.
(continued)
Chapter 12 Managerial Accounting and Cost-Volume-Profit Relationships
12–20
c.
Per Unit
*
Volume
=
Total
Revenue
$32.00
Variable Expense
20.80
Contribution Margin
$11.20
=
$56,000
Fixed Expense
Operating Income
d.
Per Unit
*
Volume
=
Total
Revenue
$33.00
Variable Expense
20.80
Contribution Margin
$12.20
=
$65,880
Fixed Expense
Operating Income
Original
New Product
Total
e.
Revenue
$32.00
$20
Variable Expense
20.80
14
Contribution Margin
$11.20 * 5,000 = $56,000
$ 6 * 4,000 = $24,000
Fixed Expense
Operating Income
Original
New Product
Total
f.
Revenue
$32.00
$20
Variable Expense
20.80
14
Contribution Margin
$11.20 * 4,000 = $44,800
$ 6 * 5,000 = $30,000
Fixed Expense
Operating Income
g.
The contribution margin ratio for each product is different, so that changes in the sales mix
result in a change in total contribution margin. Specifically, in this case, a shift occurred
such that a larger proportion of the mix consisted of the newer, lower margin product.
P12.25.
a. & b.
Current
Operation:
Luxury
Economy
Total
Revenue
$20 * 10,000 = $200,000
$12 * 20,000 = $240,000
$440,000
Variable Expense
8
7
________
Fixed Expense
Operating Income