Solution manual cost accounting by LauderbachPROFIT PLANNING
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CHAPTER 2
PROFIT PLANNING
21 Assumptions and Misconceptions about CVP Analysis
General Note to the Instructor: This question can prove difficult
because it requires not only considerable understanding of the concepts
introduced in Chapter 2 but also some anticipation of concepts introduced in
Chapter 3. The purposes of the questions are to stimulate discussion of the
uses and limitations of CVP analysis and to counter the natural student
skepticism regarding the applicability of basic concepts in light of the
factors that make it impossible to portray the practicalities of business
operations in the simple forms offered by theoretical analysis.
The points to be made are that, the uncertainties of the real world
notwithstanding, managers must plan and take actions and that any actions
managers take implicitly reflect some assumptions about the future. For
example, a store owner must set some prices, and the action of setting a
price reflects some expectations about volume and costs. Similarly, a manager
must decide not only whether or not to advertise but also, if some
advertising is to be done, how much is reasonable. A manager must also
decide how many employees to have as well as a host of other matters. CVP
analysis, though far from a cureall, provides a reasonable basis for
planning.
1. CVP analysis answers "what if" and "what must we do to achieve"
questions. It is a planning tool and helps managers see what should occur
given certain estimates of the values of important variables. All of the
classmate's statements are true; but they relate to facts that can only be
known after the manager is required to decide what to do. A manager must
decide what to do on the basis of estimates because the future is not known.
The emphasis in CVP analysis is not on past costs nor on current costs,
but rather on the costs that can be expected in the future. A manager must
make some estimates of the expected pattern of increases of costs and prices,
and it is those estimates of expected patterns that form the basis for
successful use of CVP analysis. Plans can be made by month, or for the
entire year, or for some period of time in between those two extremes. The
point is that planning relates to the future. It is probably impossible to
overemphasize this point.
2. Note to the Instructor: The depth of the answer to be expected on this
question depends on the depth of the students' knowledge and understanding of
microeconomics. In any case it is important to emphasize that basic study in
microeconomic theory assumes that managers of a firm have information that is
not, in fact, automatically available to them.
21
The typical demand curve for a particular product has a negative slope.
But CVP analysis is not concerned so much with the relationship between price
and quantity demanded as it is with the likely results of a particular price
and, implicitly, a set of other variables such as advertising expenditures.
CVP analysis does not purport to answer the question, "How many will we sell
at this price?" Rather it answers questions about profits at given levels of
volume and price. CVP analysis is a planning tool.
Note also that the idea of relevant range is important here. A cost
structure (mix of variable and fixed costs) holds over a range of volume
levels for a single firm regardless of the sales price of the product. (To
emphasize the points of difference between microeconomic theory and break
even analysis, note also that the longrun cost curves used for the former do
not assume the same cost structures at each level of volume.)
3. Again, CVP analysis is a planning tool and utilizes the best information
available at a given point in time when planning must take place. If a
manager knows (or considers it probable) that certain costs will change, his
CVP analysis should take such knowledge into consideration, for that analysis
is, by virtue of its being a planning tool, future oriented.
4. The possibility of reduced prices does not reduce the usefulness of CVP
analysis but only changes the manner in which the analysis is carried out.
There are several ways to handle the problem proposed by some sales at
reduced prices. One way is to integrate into the calculation of contribution
margin percentage the effects of sales at reduced prices. Another is to
estimate separately the contribution margins from sales at regular prices and
sales at reduced prices. In either case, the critical concern is the
quantity of merchandise that the manager believes will have to be sold at
reduced prices.
22 Effects of Events
1. The slope of the revenue line will increase.
2. The slope of the total cost line will increase, but the intercept will
remain the same.
3. The graph will not change, but the expected volume will be higher.
23 Effects of Keeping Up With Technology
The statement describes a typical situation in a retailing company
dependant upon technology. Amazon.com will face large and continued fixed
costs expenditures to support its marketing and promotion, product
development and technology, and operating infrastructure development.
Amazon.com’s variable costs are primarily the cost of the merchandise (books,
audio, and video) sold. To achieve profitability, Amazon.com must emphasize
revenue growth.
22
24 Income Statement and CVP Analysis (1015 minutes)
1.
Sales $480,000
Variable costs 360,000
Contribution margin 120,000
Fixed costs 80,000
Income $ 40,000
2. (a) 40,000 units $80,000/($8 $6)
(b) $320,000, $8 x 40,000, or $80,000/[($8 $6)/$8]
Note to the Instructor: We can calculate required volumes incrementally,
either in units or dollars, by dividing the existing income or loss by the
contribution margin (per unit or percentage) and subtracting that from
existing sales. For breakeven units, the calculations are as follows:
Income $ 40,000
Divided by contribution margin per unit ($8 $6) $2
Equals decrease in unit sales to reach breakeven point 20,000
Subtracted from current unit volume 60,000
Equals breakeven unit sales 40,000
3. (a) 100,000 units $80,000/[($8 $6) (15% x $8)]
= $80,000/($2 $1.20)
(b) $800,000 100,000 x $8, or $80,000/(25% 15%).
The contribution margin percentage of 25% is ($8 $6)/$8.
An income statement shows,
Sales $800,000
Variable costs 600,000
Contribution margin 200,000
Fixed costs 80,000
Income $120,000 15% x $800,000
4. $8.67 rounded
Desired profit ($40,000 x 2) $ 80,000
Plus fixed costs 80,000
Equals required contribution margin $160,000
Divided by volume 60,000 units
Equals required perunit contribution margin $ 2.67
Plus perunit variable cost 6.00
Equals required selling price $ 8.67
25 Income Statement and CVP Analysis (1015 minutes)
1. Sales $800,000
Variable costs at 40% 320,000
Contribution margin 480,000
Fixed costs 450,000
Income $ 30,000
2. $750,000 $450,000/(100% 40%)
23
3. $850,000 [$450,000 + (2 x $30,000)]/(100% 40%) = $510,000/60%
You might wish to show that this part can also be solved by finding the
increase in sales required to increase profit by $30,000. That is $50,000
($30,000/60%). Adding $50,000 to existing sales of $800,000 gives $850,000.
26 Income Statement and CVP Analysis with Taxes (1520 minutes)
1. Sales $480,000
Variable costs 360,000
Contribution margin 120,000
Fixed costs 80,000
Income before taxes 40,000
Income taxes at 30% 12,000
Income $ 28,000
2.
Desired income (2 x $28,000) $ 56,000
Divided by 70% = required pretax income $ 80,000
Plus fixed costs 80,000
Equals required contribution margin $160,000
Divided by unit contribution margin $2
(a) Equals unit sales required 80,000
Times unit price $8
(b) Equals sales dollars required $640,000
Note to the Instructor: An alternative calculation is to divide the
required contribution margin by the contribution margin percentage.
Required contribution margin $160,000
Divided by contribution margin percentage 25%
Equals sales dollars required $640,000
3. $8.67 rounded This is the same question and answer as requirement 4 of
24. Income taxes do not affect pretax profit calculations or breakeven
calculations.
Desired pretax profit ($40,000 x 2) $ 80,000
Plus fixed costs 80,000
Equals required contribution margin $160,000
Divided by volume 60,000
Equals required perunit contribution margin $ 2.67
Plus variable cost 6.00
Equals required price $ 8.67
Note to the Instructor: The $8.67 price also doubles the aftertax
profit. We asked the assignment in this way to highlight that doubling
pretax profit is equivalent to doubling aftertax profit.
24
27 Income Statement and CVP Analysis with Taxes (1520 minutes)
1.
Sales $800,000
Variable costs 320,000
Contribution margin 480,000
Fixed costs 450,000
Income before taxes 30,000
Income taxes at 40% 12,000
Income $ 18,000
2.
Desired income (2 x $18,000 above) $ 36,000
Divided by (100% 40%) 60%
Equals required pretax income 60,000
Plus fixed costs 450,000
Equals required contribution margin $510,000
Divided by contribution margin percentage 60%
Equals sales required $850,000
28 Basic CVP Analysis (2025 minutes)
1. (a) 33,334 units (rounded) $600,000/($30 $12) = $600,000/$18
(b) $1,000,000 $600,000/($18/$30) = $600,000/60%, or 33,334 x $30
2. (a) 40,000 units ($600,000 + $120,000)/$18
(b) $1,200,000 ($600,000 + $120,000)/60%, or 40,000 x $30
3. (a) 41,667 (rounded) $600,000/($18 [12% x $30]) = $600,000/$14.40
(b) $1,250,00 $600,000/(60% 12%) = $600,000/48%, or 41,667 x $30
4. $35.33 rounded
Sales variable costs fixed costs = profit
S (30,000 x $12) $600,000 = $100,000
S $360,000 $600,000 = $100,000
S = $1,060,000
Price = $1,060,000/30,000 = $35.33
5. $35.93 rounded
Sales variable costs fixed costs = profit
S 30,000 x $9 10%S $600,000 = $100,000
S $270,000 10%S $600,000 = $100,000
90%S = $970,000
S = $1,077,778
Price = $1,077,078/30,000 = $35.93 (rounded)
Note to the Instructor: This basic exercise makes the point that CVP
analysis and other techniques can yield impossible answers, here fractions of
units or pennies. Some students believe that if their answer is not a whole
number, they must have done something wrong. (This feeling is especially
prevalent during examinations.)
29 Basic CVP Relationships, with Income Taxes (1520 minutes)
25
1. (a) 266,667 units ($3,000,000 + [$600,000/60%])/($40 $25) =
$4,000,000/$15
(b) $10,666,667
Total required contribution margin (part a) $4,000,000
Divided by contribution margin percentage ($40 $25)/$40 37.5%
Or, 266,667 x $40
2. $38.333
Required contribution margin (part 1) $4,000,000
Divided by units 300,000
Required contribution margin per unit $ 13.333
Plus variable cost 25.000
Required price $ 38.333
3. $38.15 rounded
Sales variable costs fixed costs = pretax profit
S (300,000 x $21) 10%S $3,000,000 = $1,000,000
90%S = $10,300,000
S = $11,444,444
Price = $11,444,444/300,000 = $38.15 rounded
210 Relationships Among Variables (2030 minutes)
1. To work this part it is necessary to start with the second blank.
(d) $78,000, $28,000 + $50,000
(c) 2,600 units ($78,000/$30 contribution margin per unit)
Contribution margin per unit ($50 x 60%) $30
Contribution margin in total, from part (d) $78,000
2. (b) 75% (100% contribution margin of 25%)
Contribution margin per unit ($60,000/3,000) $20
Contribution margin percentage ($20/$80) 25%
(e) $80,000, (loss of $20,000 after deducting fixed costs from a
contribution margin of $60,000)
3. Again, it is necessary to start with the second blank.
(d) $75,000, $25,000 + $50,000
(b) 80% (100% contribution margin percentage of 20%)
Contribution margin per unit ($75,000/15,000) $5
Contribution margin percentage ($5/$25) 20%
26
211 Relationships Among Variables (1520 minutes)
1. $8 selling price $6 + ($2,000/1,000)
$800 fixed costs $2,000 $1,200
2. 2,000 units sold $4,000/($5 $3)
$2,500 income $4,000 $1,500
3. $10 selling price $6 + ($16,000/4,000)
$8,000 income $16,000 $8,000
212 CVP Graph (1015 minutes)
1. $6,000
2. $2,000, which is the answer at all levels of sales.
3. $4,000, the difference between $6,000 total costs at the 4,000unit
(breakeven) level minus $2,000 fixed costs. You do not need variable cost
per unit to solve this part.
4. $1.00, $4,000/4,000 from the previous part. Or, read the value of total
cost at any level above zero sales, subtract fixed costs of $2,000, and
divide by unit sales.
5. $1.00, same as in part 4. This question emphasizes the point that
variable cost per unit remains constant throughout the relevant range.
6. $1.50, $6,000 sales divided by 4,000 units at the breakeven point.
7. $1,500, $0.50 contribution margin ($1.50 $1.00) times 3,000 units.
8. $500 loss, $1,500 contribution margin (part 7) minus $2,000 fixed costs.
9. $500 profit, which is contribution margin of $2,500 (500 x $0.50) less
fixed costs of $2,000.
10. 5,000 units. This is $2,500 fixed costs divided by $0.50 contribution
margin per unit.
213 Basic Sales Mix (10 minutes)
1. 34% 12% + 7% + 15%
Produce Meat/Dairy Canned Goods
Contribution margin percentage 40% 35% 30%
Sales mix percentage 30% 20% 50%
Weightedaverage contribution margin 12% 7% 15%
2. $2,000,000 $680,000/34%
3. $2,617,647 ($680,000 + $210,000)/34%
27
214 Improving Sales Mix (1520 minutes)
1. 62% 20% + 18% + 24%
Termites Lawn Pests Interior Pests
Contribution margin percentage 50% 60% 80%
Sales mix percentage * 40% 30% 30%
Weightedaverage 20% 18% 24%
* $160,000/$400,000; $120,000/$400,000, $120,000/$400,000
Alternatively, some students will solve for total contribution margin by
carrying out the multiplication of CM% by budgeted sales, then adding the
sales and contribution margins. This part tests to see whether students
understand the concept of sales mix by presenting the information in a
different form from that in the text.
2. $98,000
Contribution margin, $400,000 x 62% $248,000
Fixed costs 150,000
Profit $ 98,000
3. (a) 68% 10% + 18% + 40%
Termites Lawn pests Interior pests
Contribution margin percentage 50% 60% 80%
Sales mix percentage 20% 30% 50%
Weightedaverage 10% 18% 40%
(b) $122,000
Contribution margin ($400,000 x 68%) $272,000
Fixed costs 150,000
Profit $122,000
Note to the Instructor: This exercise demonstrates that sales mix
affects profit (through its effect on the contribution margin percentage).
Thus, even though selling prices, the percentages of variable cost to price,
total fixed costs, and total sales dollars remained constant, the shift in
sales mix resulted in a six percentage point increase in the weightedaverage
contribution margin percentage and a corresponding six percentage point
increase in return on sales, an additional $24,000 profit.
215 Margin of Safety (510 minutes)
2,250 units, or $202,500 (2,250 x $90), as computed below.
Expected sales, in units 16,000
Fixed costs $275,000
Contribution margin, $90 $52 (20% x $90) $ 20
Breakeven point 13,750
Margin of safety, in units 2,250
216 Alternative CVP Graph (continuation of 215) (1015 minutes)
28
Perunit contribution margin under the alternative is $26.50 [$90 $41
(25% x $90)] and the breakeven point is 12,264 units ($325,000 fixed costs/
$26.50), which is 1,486 less than before.
300,000
200,000
100,000
0
-100,000
-
5,000
10,000
15,000
20,000
-200,000
-300,000
-400,000
The graph highlights the desirability of the change. Profit is higher under
the alternative once volume reaches 7,692 units ($50,000 difference in fixed
costs divided by $6.50 difference in contribution margin). Because the
company expects sales of 16,000 units, unless the new production/marketing
strategies will reduce volume, the alternative dominates the existing case.
217 CVP Graph, Analysis of Changes (510 minutes)
Revenue Line Total
Cost Line Breakeven Point
1. Decrease slope No effect Increase
(shallower revenue line)
2. No effect Decrease slope Lower (decrease)
(shallower angle on
cost line)
3. No effect Higher intercept of Not determinable (the
cost line, but re answer depends on the
duction of slope of specific numbers)
that line
4. No effect No effect No effect
5. Increase slope Increase slope Not determinable
(depends on relationship
between price and cost
changes)
Note to the Instructor: This exercise should help students understand
29
how changes in the basic facts of a situation will change its graphical
analysis. To emphasize that both the graphic and the contributionmargin
approaches allow conceptual analysis of breakeven situations, you might wish
to review each of the above changes using the contributionmargin approach,
as follows:
1. A price decrease decreases perunit contribution margin, which raises
the breakeven point.
2. A decrease in perunit variable cost increases perunit contribution
margin, which lowers the breakeven point.
3. A decrease in perunit variable cost increases perunit contribution
margin and therefore reduces the breakeven point. An increase in
fixed costs increases the breakeven point, so the effect of the two
events cannot be determined without knowing the numerical amounts.
4. Since price, perunit variable costs, and total fixed costs do not
change, the breakeven point remains the same. The company's profit
will be lower than expected, but breakeven remains the same.
5. An increase in selling price increases contribution margin, thus
lowering the breakeven point; but an increase in perunit variable
cost decreases contribution margin, thus raising the breakeven
point.
The ultimate effect on the breakeven point depends on the relative
magnitudes of the changes in the two factors.
218 Converting an Income Statement (20 minutes)
1. Sales $400,000
Variable costs:
Cost of goods sold $240,000
Commissions ($400,000 x 10%) 40,000
Total variable costs 280,000
Contribution margin 120,000
Fixed costs:
Salaries ($71,000 $40,000) 31,000
Utilities 10,000
Rent 15,000
Other 25,000
Total fixed costs 81,000
Income $ 39,000
2. (a) 10,800 units $81,000/$7.50 Volume is $400,000/$25 = 16,000, so
contribution margin is $120,000/16,000 = $7.50
(b) $270,000 10,800 x $25 or $81,000/30% (30% = $120,000/$400,000)
210
3. $26 Cost of goods sold is $15 per unit ($240,000/16,000). Adding the
commission of 10% of price gives
sales variable costs fixed costs = profit
S (15,000 x $15) 10%S $81,000 = $45,000
90%S = $351,000
S = $390,000
Price = $390,000/15,000 = $26
219 Target Costing (10 minutes)
1. $14,000,000
Revenue (200,000 x $100) $20,000,000
Target profit 6,000,000
Total allowable cost $14,000,000
2. $25, $5,000,000 allowable variable cost divided by 200,000 units
Total allowable cost $14,000,000
Estimated fixed cost 9,000,000
Allowable total variable cost $ 5,000,000
220 Profit Planning (2025 minutes)
The following preliminary calculations will be helpful.
Selling price $35.00
Cost of goods sold:
Cost of sales $800,000
Divided by number of units sold 40,000
Equals unit cost of sales $20.00
Plus increase expected 1.50
Equals new unit cost of sales in 21.50
Selling costs:
Selling costs, per unit $2.00
Plus expected increase 0.10
Equals new unit selling cost 2.10
Total variable cost per unit 23.60
Contribution margin per unit $11.40
1. Zaldec Company
Income Statement
Sales, 48,000 (40,000 units x 120%) x $35 $1,680,000
Variable costs:
Cost of goods sold (48,000 x $21.50) $1,032,000
Selling costs (48,000 x $2.10) 100,800 1,132,800
Contribution margin (48,000 x $11.40) 547,200
Fixed costs:
Selling* $310,000
Administrative ($190,000 + $30,000) 220,000 530,000
Income $ 17,200
*Fixed costs $350,000 (40,000 x $2) $270,000
211
Expected increase 40,000
Fixed costs, new $310,000
2. 51,754 units rounded ($60,000 + $530,000)/$11.40 = $590,000/$11.40
3. $35.89 rounded, $1,722,800 total revenue divided by 48,000 units
sales = variable costs + fixed costs + profit
S = (48,000 x $23.60) + $530,000 + $60,000
S = $1,722,800
221 Basic Income Taxes (1520 minutes)
1. $109,200
Sales (12,000 x $120) $1,440,000
Variable costs:
Manufacturing (12,000 x $72) $864,000
Commission ($1,440,000 x 10%) 144,000 1,008,000
Contribution margin 432,000
Fixed costs 250,000
Income before taxes 182,000
Income taxes (40%) 72,800
Net income $ 109,200
2. 12,500 units
Desired aftertax profit $120,000
Divided by (1 tax rate of 40%) .60
Required pretax profit 200,000
Plus, fixed costs 250,000
Equals required contribution margin for target profit 450,000
Divided by contribution margin per unit:
Selling price $120
Variable manufacturing cost ( 72)
Commission (10% of selling price) (12) $36
Equals volume required for target profit 12,500
units
3. About $123.43
Sales variable costs fixed costs = profit
S [(11,000 x $72) 10%S] $250,000 = $180,000
90%S = $1,222,000
S = $1,357,778
Price = $1,357,778/11,000 = $123.43 (rounded)
212
222 Basic Sales Mix (20 minutes)
1. 60% weightedaverage contribution margin, $400,000 monthly sales.
Allergyfree Cleansaway
Selling price $18 $24
Variable cost 9 6
Contribution margin $ 9 $18
Contribution margin percentage 50% 75%
Sales mix, in dollars 60% 40%
Weighted contribution margin 30% + 30% = 60%
Required sales = ($180,000 + $60,000)/60% = $400,000
Allergyfree Cleansaway
Sales, 60%, 40% $240,000 $160,000
Divided by selling price $18 $24
Units sold (rounded) 13,333 6,667 20,000
Thus, the company could also express the mix percentage in units as 2/3
Allergyfree, 1/3 Cleansaway. Again, we have a fractional answer, indicating
that the company cannot really earn $60,000 under the stated conditions.
2. $13.50 weightedaverage unit contribution margin, 17,778 units
Allergyfree Cleansaway
Contribution margin $9 $ 18
Sales mix, in units 50% 50%
Weightedaverage contribution margin $4.50 + $9.00 = $13.5
Required sales = $240,000/$13.50 = 17,778, 8,889 of each
Dollar sales = 8,889 x $18, 8,889 x $24 = $160,002 + $213,336 = $373,338
The reason that unit sales here are much lower than the unit sales required
in requirement 1, where the mix was expressed in dollars is that the implied
unit mix of 2/3, 1/3 in requirement 1 is leaner than the 50/50 given here.
Therefore, the company needs to sell less total product to earn the same
profit. The same reasoning applies to the dollar sales differences.
Some students do not understand that the way you express mix, units or
dollars, depends on circumstances. A department store manager would never
try to express mix in units because units range from handkerchiefs to
refrigerators. An auto dealer would be very comfortable using units to
express mix.
213
3. Profit rises by $12,000, to $72,000.
Allergyfree Cleansaway
Contribution margin percentage 50% 75%
Sales mix, in dollars 40% 60%
Weighted contribution margin 20% + 45% = 65%
Contribution margin, $400,000 x 65% $260,000
Fixed costs, $180,000 + $8,000 188,000
Profit $ 72,000
An alternative calculation that emphasizes the change in total
contribution margin accompanying a change in the weightedaverage
contribution margin percentage is:
Monthly volume $400,000
times increase in weighted average contribution margin
(65% 60%) 5%
Increase in total contribution margin 20,000
Less increased fixed costs 8,000
Increase in profit $ 12,000
223 WeightedAverage Contribution Margin (20 minutes)
1. Luxury, because its perunit contribution margin is highest.
2. Necessary, because its contribution margin percentage is highest.
Necessary Frill Luxury
Selling price $10.00 $20.00 $25.00
Variable cost 4.00 12.00 12.50
Contribution margin $ 6.00 $ 8.00 $12.50
Contribution margin percentage 60% 40% 50%
3. (a) 52% 24% + 8% + 20%
Contribution margin percentage 60% 40% 50%
Sales mix, in dollars 40% 20% 40%
Weighted contribution margin 24% 8% 20%
(b) $550,000 $286,000/52%
(c) 8,800 units
Sales at the breakeven point, part 3b $550,000
Times sales mix % for Luxury 40%
Sales of Luxury $220,000
Divided by selling price per unit of Luxury $25
Equals sales of Luxury at breakeven 8,800
4. (a) $9 $2.40 + $1.60 + $5.00
Necessary Frill Luxury Total
Contribution margin per unit $6.00 $8.00 $12.50
Sales mix, in units 40% 20% 40%
Weighted contribution margin $2.40 $1.60 $ 5.00 $9.00
(b) 31,778 units, rounded $286,000/$9
214
(c) 12,711 units, rounded 31,778 x 40%
224 Indifference Point (1015 minutes)
1. Alternative #1 Alternative #2
Fixed costs $60,000 $104,000
Divided by contribution margin:
Selling price $60 $60
Variable cost 34 28
Contribution margin $26 $32
Equals breakeven point, in units 2,308 rounded 3,250
2. 7,333 units We can solve this using either total costs or total
profit. Let Q = volume. Using total costs,
Alternative #1, Total Costs = Alternative #2, Total Costs
Fixed costs + variable costs = Fixed costs + variable costs
$60,000 + $34Q = $104,000 + $28Q
$ 6Q = $44,000
Q = 7,333
Using profit,
($60 $34)Q $60,000 = ($60 $28)Q $104,000
$26Q $60,000 = $32Q $104,000
$6Q = $44,000
Q = 7,333
Thus, if managers expect volume to exceed 7,333 units, they should prefer
alternative 2 because it will give higher profits than alternative 1 above
that volume. The reverse is true for volumes below 7,333 units.
Note to the Instructor: It is necessary to work with profit if total
costs are not the same at the volume where profits are the same. This occurs
if the selling price differs between the alternatives. Here, the selling
price is the same, but we show the technique for completeness.
225 Cost Structure (15 minutes)
1. $300,000 and $308,000
HandFed Machine Automatic Machine
Total annual fixed costs $124,000 $168,000
Total annual variable costs:
4,000 x $44 176,000
4,000 x $35 ________ 140,000
Total annual cost $300,000 $308,000
215
2. 4,889 tables, Let Q = volume
Total cost with handfed machine = total cost with automatic machine
$44Q + $124,000 = $35Q + $168,000
$9Q = $44,000
Q = 4,889
226 Changes in Contribution Margin (20 minutes)
General Note to the Instructor: This assignment looks at relationships
of contribution margin per unit and contribution margin percentage. It
highlights some important points about volume, in units and in dollars,
required to achieve target profits.
1. 25,000 units ($50,000 + $50,000)/($10 $6)
2. (a) $11
Profit $50,000
Fixed costs 50,000
Required contribution margin 100,000
Divided by volume 20,000
Required unit contribution margin $5
Plus variable cost 6
Required price $11
(b) $220,000 20,000 units x $11
3. (a) $12
Unit variable cost $ 6
Divided by variable cost percentage 50% $5/$10 from last year
Selling price $12
(b) $200,000 ($50,000 + $50,000)/50%
(c) 16,667 units, $200,000/$12
Note to the Instructor: This part could be troublesome. The key is that
the variable cost ratio is one minus the contribution margin ratio, so that
you must divide the per unit variable cost by the variable cost ratio. The
point of (b) and (c) is that maintaining the contribution margin ratio
results in needing the same dollar volume but a lower unit volume, to earn
the same profit.
227 Pricing and Return on Sales (2530 minutes)
1. (a) $25,000,000 $5,000,000/20% The 20% is ($30 $18)/$30 20% =
(40% 20%)
(b) 833,333 square feet $5,000,000/[$30 $18 (20% x $30)] =
$5,000,000/$6, or $25,000,000 (part a)/$30
2. $27
Required contribution margin ($5,000,000 + $400,000) $5,400,000
Divided by expected volume 600,000
Required contribution margin/sq. ft $ 9
Plus variable cost 18
Required price $27
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3. $21.20
Selling price
$30.00
Required contribution margin ($5,000,000 + $280,000) $5,280,000
Divided by volume 600,000
Required contribution margin/sq. ft.
8.80
Allowable variable cost
$21.20
4. $32.56
Required contribution margin $5,280,000
Divided by volume 500,000
Required contribution margin/sq. ft $10.56
Plus variable cost 22.00
Required price $32.56
Note to the Instructor: This assignment uses square feet as the measure
of volume, allowing you to remind students that volume can be expressed in
different ways. It also can be used to discuss the assumption of a constant
sales mix, which the chapter describes. The appendix covers the use of
weightedaverage contribution margin in multiproduct cases. Here, the point
is that so long as the mix remains reasonably constant, it is possible to use
CVP analysis.
228 CVP Analysis for a Service Firm (510 minutes)
1. 1,838 hours ($97,000 + $50,000)/$80
2. $20 per hour, as follows
Salary, 300 x $8 $2,400
Profit 3,000
Total revenue required $5,400
divided by chargeable hours (300 30) 270
Required hourly rate $20
229 Pricing Decision—Nursery School (2530 minutes)
1. $108 per child per month.
Fixed costs ($34,000 + $1,200 + $800) $36,000
Divided by number of children 40
Contribution margin per child per year $900
Divided by nine months 9
Contribution margin per child per month $100
Variable cost per child per month ($3 + $5) 8
Required monthly price $108
An alternative calculation, where P = price
Revenue variable costs fixed costs = profit
(40 x 9 x P) [40 x 9 x ($3 + $5)] ($34,000 + $1,200 + $800) = $0
360P $2,880 $36,000 = $0
360P = $38,880
P = $108
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2. Approximately 43 children. (Exactly 43 children will actually yield a
small loss if all estimates are correct.) One way to make the calculation is
to determine the total annual contribution margin per child at a fee of $100
per month.
Contribution margin per month per child
($100 variable cost of $8) $92
Number of months 9
Annual contribution margin per child $828
Breakeven point ($36,000/$828) 43.48 children
230 Sensitivity of Variables (2535 minutes)
1. Item (a) reduces profit the most (yielding a loss, in fact). Profits
are computed below using two approaches. The first shows an answer resulting
from the simple equation sales variable costs fixed costs = profit. The
second approach uses contribution margin and compares total contribution
margin with fixed costs.
(a) ($75,000) (50,000 x $25 x 90%) ($18 x 50,000) $300,000 or
[50,000 x ($22.50 $18)] $300,000
(b) ($40,000) (50,000 x $25) (50,000 x $18 x 110%) $300,000 or
[50,000 x ($25 $19.80)] $300,000
(c) $20,000 (50,000 x $25) (50,000 x $18) ($300,000 x 110%) or
[50,000 x ($25 $18)] $330,000
(d) $15,000 (50,000 x 90% x $25) (50,000 x 90% x $18) $300,000 or
[45,000 x ($25 $18)] $300,000
2. Item (a) produces the largest profit.
(a) $175,000 (50,000 x $25 x 110%) (50,000 x $18) $300,000 or
50,000 x ($27.50 $18) $300,000
(b) $140,000 (50,000 x $25) (50,000 x $18 x 90%) $300,000 or
[50,000 x ($25 $16.20)] $300,000
(c) $85,000 (50,000 x 110% x $25) (50,000 x 110% x $18) $300,000 or
[55,000 x ($25 $18)] $300,000
(d) $80,000 (50,000 x $25) (50,000 x $18) ($300,000 x 90%) or
[50,000 x ($25 $18)] $270,000
3. 77,778 units, rounded, an increase of 55.6%
Profit at planned volume and original price
[50,000 x ($25 $18)] $300,000 $50,000
Required volume at reduced price:
($300,000 + $50,000)/($22.50 $18) 77,778
4. $5, the same as the increase in selling price ($25 x 20% = $5).
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Note to the Instructor: This problem illustrates the sequence and
degree of sensitivity in a particular case. However, some of the
relationships will usually hold in other cases. So long as price exceeds
variable cost, profit will be more sensitive to changes in price than to
equal percentage changes in variable cost. Also, changes in price will have
greater effects on income than will equal percentage changes in volume. (In
both cases revenue increases by the given percentage, but with the price
change total variable costs remain the same, unless all variable costs are a
constant percentage of sales.) The effects of changes in fixed costs are
probably less than those of the others. Only if fixed costs are extremely
high will changes in them have greater effects on profit than will equal
percentage changes in other variables.
231 CVP AnalysisChanges in Variables (20 minutes)
March April
Sales $200,000 $222,000
Total variable costs $130,000 $154,200
Less commission at 10% of sales 20,000 22,200
Purchase cost of goods sold $110,000 $132,000
Divided by purchase cost per unit $11 $11
Equals unit sales 10,000 12,000
Divided into sales (above) equals price per unit $20 $18.50
Total variable cost, from above $130,000 $154,200
Divided by units of sales, as above 10,000 12,000
Equals variable cost per unit $13 $12.85
Note to the Instructor: This rather difficult problem makes an
important point. The key is to recognize that the two components of variable
cost (purchase price and sales commission) do not both vary with the same
factor. It is necessary to separate the two components of variable cost.
Some instructors might prefer to assign this problem with Chapter 3, rather
than attack it as a complication of Chapter 2. Note also that the company
sold 20% more units in April than in March, but earned less profit because of
the reduced selling price. Some students believe that increasing sales
automatically increases income, failing to realize that variable costs
increase as sales increase.
232 Changes in Cost Structure (20 minutes)
1. 40,000 units $48,000/$1.20
2. $24,000 increase
Reduced variable costs ($1.20 x 60,000) $72,000
Increase in fixed costs 48,000
Increase in income $24,000
3. More likely, because the cost would then be avoidable at any time. If
volume fell, the machine could be returned and production performed as
before, assuming no changeover cost in returning to the old method.
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233 CVP Analysis on New Business (15 minutes)
1. 208,333 ($650,000 + $450,000 + $150,000)/($12 $6), or $1,250,000/$6
2. $12.25 $1,250,000/200,000 + $6, or $6.25 + $6
3. $0.25 reduction to $5.75. The $6.25 from requirement 2 is still the
required contribution margin. The $6.25 is $0.25 over the original $6 ($12
$6) so variable cost must be reduced by $0.25.
This reasoning illustrates the point that contribution margin is the
critical figure, not price or variable cost alone. The assignment also shows
the use of CVP analysis for a single product, rather than for an entire one
product company.
Alternatively,
$150,000 = [($12 V) x 200,000] $1,100,000
$1,250,000 = $2,400,000 200,000V
200,000V = $1,150,000
V = $5.75
234 CVP Analysis for a Hospital (1520 minutes)
1. An increase of $5,200 per month.
Sales (200 per month x $65) $13,000
Variable costs (200 x $10) 2,000
Contribution margin 11,000
Fixed costs ($2,200 + $3,600) 5,800
Additional income $ 5,200
2. $39
Sales variable costs fixed costs = profit
S $2,000 $5,800 = $0
S = $7,800
Price = $7,800/200
As proof:
Sales (200 x $39) $7,800
Variable costs (200 x $10) 2,000
Contribution margin 5,800
Fixed costs 5,800
Additional income $ 0
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235 CVP in a Service Business (1015 minutes)
1. $200,000
Hours generated internally, 15 x 2,000 30,000
Hours from freelancers, 80,000 30,000 50,000
Total hours 80,000
Revenues at $40 per hour $3,200,000
Variable cost, 50,000 x $25 1,250,000
Contribution margin 1,950,000
Fixed costs 1,750,000
Profit $ 200,000
2. 56,667
Fixed costs plus desired profit ($1,750,000 + $300,000)
$2,050,000 Revenue from internal billing, 30,000 x $40 (no variable cost)
1,200,000 Contribution needed from freelancers
850,000 Required hours, $850,000/($40 $25)
56,667
Or, to increase profit by $100,000 from $200,000 to $300,000 requires 6,667
additional hours, which is $100,000/$15 contribution per hour.
236 Developing CVP Information (2530 minutes)
April May
Sales $100,000 $80,000
Variable costs:
Cost of sales (40% of sales) $40,000 $32,000
Commissions (20% of sales) 20,000 16,000
Supplies (2% of sales) 2,000 1,600
Total variable costs (62% of sales) 62,000 49,600
Contribution margin (38% of sales) 38,000 30,400
Fixed costs:
Rent $ 1,200 $ 1,200
Salaries* 14,500 14,500
Insurance 1,100 1,100
Utilities 1,500 1,500
Miscellaneous 6,000 6,000
Total fixed costs 24,300 24,300
Income $13,700 $ 6,100
*Calculation of fixed cost of salaries:
Salaries, wages commissions for April $34,500
Less variable cost of commissions:
April sales $100,000
Commission percentage 20%
Commissions for April 20,000
Fixed portion of payroll $14,500
Note to the Instructor: This assignment offers the opportunity to
illustrate the greater usefulness of contribution margin format income
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statements, as well as to discuss the notion of fixed and variable costs
being in the same account (salaries, wages, and commissions).
237 Margin of Safety (25 minutes)
1. Margins of safety in dollars
Model 440 Model 1200
Expected sales $200,000 $250,000
Sales at breakeven point:
$59,000/40% 147,500
$120,000/60% 200,000
Margins of safety $ 52,500 $ 50,000
Margins of safety as percentages
Model 440, 26.25%, $52,500/$200,000
Model 1200, 20%, $50,000/$250,000
2. With a higher margin of safety on Model 440, most students will conclude
that it should be introduced despite its lower expected profitability. There
is no correct answer because there are no reasonably objective data regarding
the probabilities of the expected sales not materializing.
The decision should hinge on whether the expected difference in profits
of $9,000 ($30,000 $21,000) is significant enough to offset the greater
risk that attends Model 1200.
Some factors that bear on the decision follow.
(a). The current state of the company and its expected state without
considering the new possibilities. If the company expects high profitability
from its other lines, it might be more willing to take the greater risk
involved with the Model 1200. A company experiencing low profitability and
expecting it to continue, might be more likely to take the apparently surer
thing, the Model 440. It could go the other way, as well. A company with
relatively low expected profitability might be more willing to take some
risks to get back into a more favorable situation.
(b). The extent to which the fixed costs are avoidable. If virtually
all fixed costs could be avoided if the wallet turned out to be a poor
seller, there might be more willingness to bring out the Model 1200. The
less the avoidability of fixed costs, the more likely that a conservative
management would select the safer product.
(c). The confidence in the forecasts. At this point students have not
been exposed to expected value calculations and other techniques that could
be applied, but some will see that investigation into the reliability of the
forecasts would be helpful.
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238 Changes in Operations (2530 minutes)
1. Extending the hours of operations appears wise. Packard can expect an
additional profit of $460 per week, computed as follows:
Revenues (2,000 x $.80 per hour) $1,600
Costs to achieve additional revenue:
Variable costs:
Additional rent on lease (10% of
additional revenue) $160
Additional city tax (5% of
additional revenue) 80
Total additional variable cost (15%) $ 240
Fixed costs:
Additional salaries for attendants $800
Additional utilities and insurance 100
Total additional fixed cost 900
Total additional costs 1,140
Increase in profit $ 460
2. About 1,324 hours
Fixed costs to be covered, from requirement 1 $ 900
Contribution margin from additional revenue
$0.80 15% of $0.80 (from requirement 1) $0.68
Hours required to offset additional costs ($900/$0.68) 1,323.5
Note to the Instructor: The $12,000 paid to the owner of the lot is, of
course, irrelevant because it will not change regardless of the number of
hours the parking lot remains open. Even at this early stage in the course,
most students are likely to recognize this fact and deal only with
incremental costs in their solutions, but it may be worthwhile to point out
this fact specifically in reviewing the solution.
239 CVP AnalysisProduct Mix (35 minutes)
1. About 319,000 cases (rounded) ($600,000 + $375,000)/$3.057
Premium Regular Total
Selling price $10.50 $7.40
Variable brewing costs 5.10 4.25
Commissions, 10% of price 1.05 0.74
Total variable costs 6.15 4.99
Unit contribution margin $4.35 $2.41
Percentage in mix 1/3 2/3
Weightedaverage contribution margin $1.45 + $1.607 = $3.057
2. 106,333 premium and 212,667 regular (1/3 and 2/3 of 319,000)
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3. Monthly profit decreases about $7,000, so the campaign is not worthwhile.
The totals below are rounded.
Profit without campaign
Contribution margin 350,000 x $3.057 $1,069,950
Fixed costs 975,000
Profit $ 94,950
Profit with campaign
Premium Regular Total
Cases, 350,000/3 x 120%; 140,000
350,000 x 2/3 x 95% 221,700
361,700
Per case contribution margin $ 4.35 $ 2.41
Total contribution margin $609,000 $534,300 $1,143,300
Fixed costs $975,000 + $80,000 1,055,000
Profit $ 88,300
4. $3.161 (rounded) $1,143,300/361,700 It is possible to redo the analysis
from requirement 1, but unnecessary if the students understand the weighted
average contribution margin.
5. 333,755 $1,055,000/$3.161
You might want to note that the increase in the breakeven point indicates
that the increase in fixed costs overwhelmed the increase in WACM per case.
Of course, the opposite could have happened. Moreover, we have no assurance
that the new mix would prevail at different levels of total volume. For
example, the increased advertising might get nearly all of the new and
existing customers who would to switch to premium to do so. So the company
might have to rely on increases in regular sales beyond the 361,700 case
level.
240 Unit Costs (2025 minutes)
Anderson Shoe Store
Income Statement for Month
Sales (5,000 x $25) $125,000
Cost of sales (50% of sales) 62,500
Gross profit 62,500
Commissions (15% of sales) 18,750
Contribution margin 43,750
Fixed costs:
Salaries and wages $30,000
Utilities, insurance, rent 3,500 33,500
Profit $ 10,250
An alternative way to determine what would happen to income if sales
increase by 1,000 pairs is to use contribution margin of $8.75 per pair ($25
$12.50 $3.75 commission). Profit should rise by $8,750 if volume rises
by 1,000 pairs, and the income statement shows that.
The fallacy in Anderson's reasoning is the unit cost problem. He
224
assumed that the unit costs would be constant, not decline as sales
increased. Despite the great deal of attention paid to this point, it
remains a serious difficulty for many students.
241 CVP Analysis and Breakeven PricingMunicipal Operation (1520
minutes)
1. A loss of $8,000
Revenues, (200 x $50) + (1,000 x $15) $25,000
Costs:
Fixed $25,000
Variable, businesses, 200 x 12 x $1.25 3,000
residences, 1,000 x 4 x $1.25 5,000 33,000
Loss $( 8,000)
2. $61.87 for businesses, $20.63 for residences, both rounded
Total revenue required, equals total cost, above $33,000
Total pickups (200 x 12) + (1,000 x 4) 6,400
Price per pickup $5.156
Business charge = perpickup price x 12 $61.87
Residence charge = perpickup price x 4 $20.63
Alternatively, solving for the monthly prices, let R = residence price, then
3R = business price
1,000R + (3 x 200 x R) = $33,000
1,600R = $33,000
R = $20.63
242 Product Profitability (35 minutes)
1. Gold is the most profitable per unit sold, because its contribution
margin per unit is highest.
2. Silver is the most profitable per dollar of sales because its
contribution margin percentage is highest.
Regular Silver Gold
Contribution margin $ 4 $12 $15
Divided by selling price $10 $20 $30
Contribution margin percentage 40% 60% 50%
3. (a) 48%
Regular Silver Gold
Contribution margin percentages 40% 60% 50%
Sales mix percentage, in dollars 40% 20% 40%
Weightedaverage contribution margin 16% + 12% + 20% = 48%
(b) The breakeven point is $416,667 ($200,000/48%)
(c) Volume required for a profit of $30,000 is $479,167
($200,000 + $30,000)/48%
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