3-11
1. Breakeven point revenues =
percentagemargin on Contributi
costs Fixed
$660,000
$1,100,000
2. Contribution margin percentage =
price Selling
unit per cost Variable price Selling −
SP $16
SP
−
0.60 SP = SP – $16
3. Breakeven sales in units = Revenues ÷ Selling price = $1,100,000 ÷ $40 = 27,500 units
Margin of safety in units = Sales in units – Breakeven sales in units
3-25 (25 min.) Operating leverage.
1a. Let Q denote the quantity of carpets sold
Breakeven point under Option 1
2. Operating income under Option 1 = $150Q − $5,000
Operating income under Option 2 = $100Q
3-12
For Q > 100, say, 101 carpets,
Option 1 gives operating income = ($150 101) − $5,000 = $10,150
Option 2 gives operating income = $100 101 = $10,100
3. Degree of operating leverage =
Contribution margin
Operating income
Contribution margin per unit Quantity of carpets sold
Operating income
=
$10,000
$10,000
4. The calculations in requirement 3 indicate that when sales are 100 units, a percentage
2. The degree of operating leverage at a given level of sales helps managers calculate the effect
of fluctuations in sales on operating incomes.
3-13
3-26 (15 min.) CVP analysis, international cost structure differences.
Variable
Variable
Sales Price
Annual
Manufacturing
Marketing and
Contribution
Operating Income
to Retail
Fixed
Cost per
Distribution Cost
Margin
Breakeven
Breakeven
for Budgeted Sales
Country
Outlets
Costs
Rug
per Rug
Per Rug
Units
Revenues
of 75,000 Rugs
(1)
(2)
(3)
(4)
(5)=(1)–(3)–(4)
(6)=(2)
(5)
(6)
(1)
(7)=[75,000
(5)]–(2)
Singapore
$250.00
$ 9,000,000
$75.00
$25.00
$150.00
60,000
$15,000,000
$2,250,000
Brazil
$250.00
8,400,000
60.00
15.00
175.00
48,000
12,000,000
4,725,000
United States
$250.00
12,400,000
82.50
12.50
155.00
80,000
20,000,000
(775,000)
Requirement 1
Requirement 2
3-14
1.
New
Customers
Upgrade
Customers
SP
VCU
CMU
$275
100
175
$100
50
50
The 60%/40% sales mix implies that, in each bundle, 3 units are sold to new customers and 2
units are sold to upgrade customers.
1.5S = Number of units sold to new customers
$512.5S – $200S – $15,000,000 = OI
Breakeven point is 120,000 units when OI = $0 because
1.5S = 72,000 units sold to new customers
BEP = 120,000 units
2. When 220,000 units are sold, mix is:
Units sold to new customers (60% 220,000) 132,000
Units sold to upgrade customers (40% 220,000) 88,000
Revenues ($275 132,000) + ($100 88,000) $45,100,000
Variable costs ($100 132,000) + ($50 88,000) 17,600,000
1.5S = 90,000 units sold to upgrade customers
BEP = 150,000 units
Check
Revenues ($275 60,000) + ($100 90,000) $25,500,000
Alternatively,
Let S = Number of units sold to upgrade customers
then 4S = Number of units sold to new customers
[$275 (4S) + $100S] – [$100 (4S) + $50S] – $15,000,000 = OI
1,200S – 450S = $15,000,000
3-17
3-28 (30 min.) Sales mix, three products.
1.
Coffee
Bagels
SP
VCU
CMU
$2.50
1.25
$1.25
$3.75
1.75
$2.00
The sales mix implies that each bundle consists of 4 cups of coffee and 1 bagel.
Contribution margin of the bundle = 4 $1.25 + 1 $2 = $5.00 + $2.00 = $7.00
Breakeven point in bundles =
Fixed costs $7,000 1,000 bundles
Contribution margin per bundle $7.00
==
2.
Coffee
Bagels
SP
VCU
CMU
$2.50
1.25
$1.25
$3.75
1.75
$2.00
3-18
=
Fixed costs + Target operating income $7,000 $28,000 5,000 bundles
Contribution margin per bundle $7.00
+
==
Breakeven point is:
Coffee: 5,000 bundles 4 cups per bundle = 20,000 cups
Bagels: 5,000 bundles 1 bagel per bundle = 5,000 bagels
3.
Coffee
Bagels
Muffins
SP
VCU
CMU
$2.50
1.25
$1.25
$3.75
1.75
$2.00
$3.00
0.75
$2.25
The sales mix implies that each bundle consists of 3 cups of coffee, 2 bagels and 1 muffin
Contribution margin of the bundle = 3 $1.25 + 2 $2 + 1 $2.25
3-19
Alternatively,
Let S = Number of muffins sold
2S = Number of bagels sold
3S = Number of cups of coffee sold
Revenues – Variable costs – Fixed costs = Operating income
3-20
1. Ticket sales per concert
$ 2,500
Variable costs per concert:
Guest performers
$ 1,000
Marketing and advertising
500
Total variable costs per concert
1,500
Contribution margin per concert
$ 1,000
Fixed costs
Salaries
$50,000
Mortgage payments ($2,000 × 12)
24,000
Total fixed costs
$74,000
Less donations
40,000
Net fixed costs
$34,000
Breakeven point in units =
Net fixed costs
Contribution margin per concert
=
$1,000
$34,000
= 34 concerts
Check
Donations
$ 40,000
Revenue ($2,500 × 34)
85,000
Total revenue
125,000
Less variable costs
Guest performers ($1,000 × 34)
$34,000
Marketing and advertising ($500 × 34)
17,000
Total variable costs
51,000
Less fixed costs
Salaries
$50,000
Mortgage payments
24,000
Total fixed costs
74,000
Operating income
$ 0
2. Ticket sales per concert
$ 2,500
Variable costs per concert:
Guest performers
$1,000
Marketing and advertising
500
Total variable costs per concert
1,500
Contribution margin per concert
$ 1,000
Fixed costs
Salaries ($50,000 + $40,000)
$90,000
Mortgage payments ($2,000 × 12)
24,000
Total fixed costs
$114,000
Less donations
40,000
Net fixed costs
$ 74,000