Exercise 6-3 (30 minutes)
1.
Sales
$90Q
$27Q
Q
Q
= Variable expenses + Fixed expenses + Profits
= $63Q + $135,000 + $0
= $135,000
= $135,000 ÷ $27 per lantern
= 5,000 lanterns, or at $90 per lantern, $450,000 in sales
Alternative solution:
Fixed expenses
Break-even point =
in unit sales
Unit contribution margin
=
$135,000
= 5,000 lanterns,
$27 per lantern
or at $90 per lantern, $450,000 in sales
2. An increase in the variable expenses as a percentage of the selling
price would result in a higher break-even point. The reason is that
if variable expenses increase as a percentage of sales, then the
contribution margin will decrease as a percentage of sales. A lower
CM ratio would mean that more lanterns would have to be sold to
generate enough contribution margin to cover the fixed costs.
Exercise 6-3 (continued)
Present:
8,000 Lanterns
Total
Per Unit
3.
Sales................................. $720,000
Less variable expenses ....... 504,000
Contribution margin ........... 216,000
Less fixed expenses ........... 135,000
Net operating income ......... $ 81,000
$90
63
$27
Proposed:
10,000 Lanterns*
Total
Per Unit
$810,000
630,000
180,000
135,000
$ 45,000
$81 **
63
$18
* 8,000 lanterns × 1.25 = 10,000 lanterns
** $90 per lantern × 0.9 = $81 per lantern
As shown above, a 25% increase in volume is not enough to offset
a 10% reduction in the selling price; thus, net operating income
decreases.
4.
Sales
$81Q
$18Q
Q
Q
= Variable expenses + Fixed expenses + Profits
= $63Q + $135,000 + $72,000
= $207,000
= $207,000 ÷ $18 per lantern
= 11,500 lanterns
Alternative solution:
Unit sales to attain = Fixed expenses + Target profit
target profit
Unit contribution margin
=
$135,000 + $72,000
= 11,500 lanterns
$18 per lantern
Problem 6-19 (75 minutes)
1. a. Selling price.......................
Less variable expenses .......
Contribution margin ...........
Sales
$37.50Q
$15.00Q
Q
Q
$37.50
22.50
$15.00
100%
60
40%
= Variable expenses + Fixed expenses + Profits
= $22.50Q + $480,000 + $0
= $480,000
= $480,000 ÷ $15.00 per skateboard
= 32,000 skateboards
Alternative solution:
Break-even point = Fixed expenses
in unit sales
CM per unit
=
$480,000
$15 per skateboard
= 32,000 skateboards
b. The degree of operating leverage would be:
Degree of operating leverage =
=
Contribution margin
Net opearating income
$600,000
= 5.0
$120,000
2. The new CM ratio will be:
Selling price .............................
Less variable expenses .............
Contribution margin..................
$37.50
25.50
$12.00
100%
68
32%
Problem 6-19 (continued)
The new break-even point will be:
Sales
$37.50Q
$12.00Q
Q
Q
= Variable expenses + Fixed expenses + Profits
= $25.50Q + $480,000 + $0
= $480,000
= $480,000 ÷ $12.00 per skateboard
= 40,000 skateboards
Alternative solution:
Break-even point = Fixed expenses
in unit sales
CM per unit
=
$480,000
$12 per skateboard
= 40,000 skateboards
3.
Sales
$37.50Q
$12.00Q
Q
Q
= Variable expenses + Fixed expenses + Profits
= $25.50Q + $480,000 + $120,000
= $600,000
= $600,000 ÷ $12.00 per skateboard
= 50,000 skateboards
Alternative solution:
Unit sales to attain = Fixed expenses + Target profit
target profit
CM per unit
=
$480,000 + $120,000
$12 per skateboard
= 50,000 skateboards
Problem 6-19 (continued)
Thus, sales will have to increase by 10,000 skateboards (50,000
skateboards, less 40,000 skateboards currently being sold) to earn
the same amount of net operating income as earned last year.
The computations above and in part (2) show quite clearly the
dramatic effect that increases in variable costs can have on an
organization. These effects from a $3 per unit increase in labour
costs for Tyrene Company are summarized below:
Present
Break-even point (in skateboards) ............... 32,000
Sales (in skateboards) needed to earn net
operating income of $120,000 .................. 40,000
Expected
40,000
50,000
Note particularly that if variable costs do increase next year, then
the company will just break even if it sells the same number of
skateboards (40,000) as it did last year.
4. The contribution margin ratio last year was 40%. If we let P equal
the new selling price, then:
P
0.60P
P
P
= $25.50 + 0.40P
= $25.50
= $25.50 ÷ 0.60
= $42.50
To verify: Selling price............................... $42.50
Less variable expenses ............... 25.50
Contribution margin ................... $17.00
100%
60
40%
Therefore, to maintain a 40% CM ratio, a $3 increase in variable
costs would require a $5 increase in the selling price.
Problem 6-19 (continued)
5. The new CM ratio would be:
Selling price .......................... $37.50
Less variable expenses .......... 13.50 *
Contribution margin............... $24.00
100%
36
64%
*$22.50 – ($22.50 × 40%) = $13.50
The new break-even point would be:
Sales
$37.50Q
$24.00Q
Q
Q
= Variable expenses + Fixed expenses + Profits
= $13.50Q + $912,000* + $0
= $912,000
= $912,000 ÷ $24.00 per skateboard
= 38,000 skateboards
*$480,000 × 1.9 = $912,000
Alternative solution:
Break-even point = Fixed expenses
in unit sales
CM per unit
=
$912,000
$24 per skateboard
= 38,000 skateboards
Although this break-even figure is greater than the company’s
present break-even figure of 32,000 skateboards [see part (1)
above], it is less than the break-even point will be if the company
does not automate and variable labour costs rise next year [see
part (2) above].
Problem 6-19 (continued)
6. a.
Sales
$37.50Q
$24.00Q
Q
Q
= Variable expenses + Fixed expenses + Profits
= $13.50Q + $912,000* + $120,000
= $1,032,000
= $1,032,000 ÷ $24.00 per skateboard
= 43,000 skateboards
*480,000 × 1.9 = $912,000
Alternative solution:
Unit sales to attain = Fixed expenses + Target profit
target profit
CM per unit
=
$912,000 + $120,000
$24 per skateboard
= 43,000 skateboards
Thus, the company will have to sell 3,000 more skateboards
(43,000 – 40,000 = 3,000) than now being sold to earn a profit
of $120,000 each year. However, this is still far less than the
50,000 skateboards that would have to be sold to earn a
$120,000 profit if the plant is not automated and variable
labour costs rise next year [see part (3) above].
Problem 6-19 (continued)
b. The contribution income statement would be:
Sales
(40,000 skateboards × $37.50 per skateboard) .....
Less variable expenses
(40,000 skateboards × $13.50 per skateboard) .....
Contribution margin...............................................
Less fixed expenses...............................................
Net operating income ............................................
$1,500,000
540,000
960,000
912,000
$ 48,000
Degree of operating = Contribution margin
leverage
Net operating income
=
$960,000
= 20
$48,000
c. This problem shows the difficulty faced by many firms today.
Variable costs for labour are rising, yet because of competitive
pressures it is often difficult to pass these cost increases along
in the form of a higher price for products. Thus, firms are
forced to automate (to some degree) resulting in higher
operating leverage, often a higher break-even point, and
greater risk for the company.
There is no clear answer as to whether one should have been in
favour of constructing the new plant. However, this question
provides an opportunity to bring out points such as in the
preceding paragraph and it forces students to think about the
issues.
Problem 6-23 (40 minutes)
a. Target net income for this year:
Contribution margin per unit: $23 – ($12 + $5) = $6
Fixed costs: $600,000 + $300,000 = $900,000
Target net income: (185,000 x $6) – ($900,000) = $210,000
This year:
Fixed costs ($900,000 – $59,000)
Plus: target net income
Total contribution margin needed
Less: earned so far on units sold (30,000 x $6)
Remaining contribution margin
$ 841,000
210,000
1,051,000
(180,000)
$ 871,000
Contribution margin per unit required on remaining (160,000 30,000) = 130,000 units
$871,000/130,000 = $6.70 per unit
b)
Current
Cost Structure
Sales (185,000 x $23)
$ 4,255,000
Variable costs
(185,000 x $17)
3,145,000
(185,000 x ($3.35 + $5))
Contribution margin
1,110,000
Fixed costs
900,000
Net operating income
$ 210,000
Problem 6-23 (continued)
Degree of operating leverage (DOL)
$1,110,000 ÷ $210,000
= 5.28
New
Cost Structure
$ 4,255,000
1,544,750
2,710,250
2,500,000
$ 210,250
$2,710,250 ÷ 210,250
= 12.89
If sales increase by 19%
Sales
$ 5,063,450
$ 5,063,450
Variable costs
Contribution margin
Fixed costs
Net operating income
3,742,550
1,838,252
1,320,900
3,225,198
2,500,000
900,000
1
$ 420,990 $ 725,1982
If sales decrease by 19%
Sales
$ 3,446,550
$ 3,446,550
1,251,247
Variable costs
2,547,450
Contribution margin
899,100
2,195,303
2,500,000
Fixed costs
900,000
1
Net operating income (loss)
$ (900) $ (304,697)2
1 Using DOL: NI = 210,000 ± (210,000 x 0.19 x 5.28) = $210,000 ±
$210,672
2 Using DOL: NI = 210,250 ± (210,250 x 0.19 x 12.89) = $210,250 ±
$514,923
Problem 6-23 (continued)
MEMO
To:
President
From:
Cost analyst
Subject: Proposed Cost Structure
As you can see from the above analysis, a move to the new cost
structure has potential benefits, but it is also considerably more risky.
Should sales volume increase by approximately 20% over this year,
the new cost structure will generate an increase in net operating
income of over 3 times the present net operating income, compared
to approximately 2 times the present net income under the current
cost structure. However, should sales volume decrease by about 20%
from this year’s, under the old structure we will be in essentially a
break-even position, while under the proposed structure we will incur
a significant loss. In general, a move to a structure with high fixed
costs and low variable costs is much more sensitive to upswings and
downswings in sales volume. If there is a high probability of sales
volume increases in the future, the changes are probably a good
idea; if there is some uncertainty about future sales volumes, the
changes may not be such a good idea.
Problem 6-25 (20 minutes)
1. Decision tree:
Net
Profits
Strategy A
Small
(.3)
-$50,000
Moderate
(.5)
$100,000
Large
(.2)
$400,000
Small
(.3)
$ 10,000
Moderate
(.5)
$ 75,000
Large
(.2)
$250,000
1
Strategy B
2. Strategy A
Expected net profits:
Strategy B:
Expected net profits:
= -$50,000 (.3) + $100,000 (.5)
+$400,000 (.2)
= -$15,000 + $50,000 + $80,000
= $115,000
= $10,000 (.3) + $75,000 (.5)
+$250,000 (.2)
= $3,000 + $37,500 + $50,000
= $90,500
The manager should choose strategy A.
(CGA-Canada Solution Adapted)