Solution manual cost accounting by LauderbachCOST ANALYSIS
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CHAPTER 3
COST ANALYSIS
31 Cost Classification
(a) Committed
(b) Committed
(c) Discretionary, but in some companies could be committed (Intel,
Microsoft, et. al.)
(d) Committed
(e) Discretionary
(f) Committed
(g) Discretionary
32 Limitations of HighLow Method
The procedure would not work well because the two points used to
determine the pattern of cost behavior are outside the relevant range. The
results will probably understate the fixed component and overstate the
variable component. Total costs at shutdown (all fixed costs) are almost
certainly less than fixed costs in the relevant range and total costs at 100%
of capacity will reflect inefficiencies from sacrificing efficiency to
increase output. The company will hire inexperienced workers, expedite
deliveries of materials, and take other actions that will increase costs. If
they can sell all that they can make, the company will be very profitable,
and cost control is not likely to be a high priority.
33 Methods of Cost Behavior Analysis
The highlow method is quick and easy, but uses only two observations
and so is seriously deficient. It assumes that the two selected points are
representative. It gives no indication of how accurate predictions are
likely to be.
The scatterdiagram method is better than the highlow method. It uses
more observations, it allows a visual, informal analysis of goodness of fit,
and it allows users to spot outliers or problematic patterns of cost (such as
curvilinear behavior or kinks that indicate two or more cost functions).
Regression analysis gives more precise results than scatterdiagrams,
gives formal measures of goodness of fit, and permits the use of more than
one independent variable. By itself, it does not allow the user to spot
outliers or problematic cost patterns.
31
34 Cost Classification
It needs to be made clear with respect to what decision a cost is
avoidable. You might wish to ask for other decisions or types of decisions
for which each cost might be avoided.
(a) Avoidable and direct
(b) Unavoidable, but direct
(c) Avoidable and direct
(d) Unavoidable and indirect
(e) Unavoidable and indirect The cost is avoidable, but not with
respect to decisions about the SouthCentral region.
(f) Avoidable and direct
The pattern that emerges is that avoidable costs are typically direct,
indirect costs usually unavoidable, but not necessarily vice versa. Chapter
5 discusses situations in which indirect, common costs might be avoided,
essentially when dropping a segment so greatly reduces workload that a
service department might be reduced.
35 Cost Classification
BDirectness and Avoidability
(a) Avoidable and direct
(b) Unavoidable and indirect
(c) Unavoidable, but direct
(d) Unavoidable and indirect
(e) Avoidable and direct
(f) Unavoidable and indirect
36 Accuracy of Predictions (5 minutes)
Indirect labor is much easier. The observations lie along a line while
supplies cost is widely dispersed. If a cost line were fitted visually in
each graph and costs predicted based on the formula for that line, the actual
costs of supplies will be farther from that line than the actual costs of
indirect labor.
37 Mixed Costs (10 minutes)
1. $64,230 fixed, $0.57 per hour variable
$90,450 $85,890 = $4,560/8,000 = $0.57 per hour variable
component
46,000 38,000
Fixed cost = total cost total variable cost
Using the high volume,
Fixed cost = total cost total variable cost
= $90,450 (46,000 x $0.57)
= $90,450 $26,220
= $64,230
32
Using the low volume,
= $85,890 (38,000 x $0.57)
= $85,890 $21,660
= $64,230
2. $89,880 $64,230 + ($0.57 x 45,000 hours)
3. The controller wants to be able to predict costs, and also must take part
in decisions about pricing, whether to accept particular types of business,
and others.
38 Cost Behavior (10 minutes)
1. Variable component = cost at high volume cost at low volume
high volume low volume
= $29,840 $21,150 = $8,690/$220,000 = 0.0395, or 3.95%
$560,000 $340,000
Fixed component = Total cost variable cost, using the high volume,
F = $29,840 (0.0395 x $560,000)
F = $29,840 $22,120
F = $7,720
2. Excel output follows.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.783200
R Square
0.613403
Adjusted R Square
0.558175
Standard Error
1,829.53
Observations
9
Intercept
Monthly Service
Revenues
Standard
Coefficients
Error
t Stat Pvalue Lower 95%
Upper 95%
11,928.34 3,946.01 3.023 0.019 2,597.52 21,259.17
0.02902 0.00871 3.333 0.013 0.00843 0.04960
The results are quite different. The regression line is $11,928 + 0.029 x
sales as opposed to $7,720 + 0.0395 x sales. The fixed component is higher
and the variable component lower than the highlow method gives. The high
and low observations appear to be nonrepresentative of the entire set. Of
course, its reliance on two observations is a major weakness of the highlow
method.
3. The equation is reasonably good. An r2 of .613 and a standard error of
$1,830 are decent measures of goodness of fit. The 95% confidence interval
for the variable cost does not include zero. Given that service revenues
average nearly $450,000, the average predicted cost will be about $25,000, so
68% of observations should be within $1,830, or about 7.4%.
33
39 Cost Analysis, HighLow Method (20 minutes)
1.
Cost of
Goods Sold Selling Administrative
Cost at high volume $54,000 $ 8,800 $9,400
Cost at low volume 48,000 8,500 9,200
Change in cost $ 6,000 $ 300 $ 200
Divided by change in volume $10,000 $10,000 $10,000
Equals variable cost percentage 60% 3% 2%
Total cost at sales of $90,000 $54,000 $ 8,800 $ 9,400
Variable cost portion ($90,000 x
variable cost percentage) 54,000 2,700 1,800
Fixed portion of cost $ $ 6,100 $ 7,600
2. Income Statement
Sales $100,000
Variable costs:
Cost of goods sold at 60% $60,000
Selling expenses at 3% 3,000
Administrative expenses at 2% 2,000
Total variable costs at 65% 65,000
Contribution margin at 35% 35,000
Fixed costs:
Selling $6,100
Administrative 7,600
Total fixed costs 13,700
Income $ 21,300
Note to the Instructor: Students will use different formats in
requirement 2. Some might find only the total for each component and place
only that total on the statement. Alternatives offer the opportunity to
discuss the idea of preparing statements and internal reports in a form most
likely to be understood and useful to their readers. The point to be made is
that information provided by accountants does not fulfill its function if the
managers receiving it cannot use it to fulfill their functions. A useful
analogy of "different reports for different people" is found in financial
accounting, where the formats change for reports to stockholders, the many
governmental units, regulatory agencies, trade associations, etc.
You might wish to make the point that, for a nonmanufacturing company,
cost of goods sold should be wholly variable (not mixed, as it can be for a
manufacturer). Of course, cost of sales might not be exactly the same
percentage of sales from period to period even if selling prices are
constant. Changes in the percentage of cost of sales to sales between two
periods could result from a change in purchase prices or sales mix (covered
in Chapter 4).
310 Understanding Regression Results (1015 minutes)
The memorandum should contain the following major points.
The equation tells us that parttime consultants cost has a fixed
component of $101,187 per month and a variable component of $0.0898 per
34
dollar of consulting revenue. Therefore, to predict the cost, we multiply
expected revenue by $0.0898 and add $101,187. For example, at $900,000,
Y = $101,187 + ($0.0898 x $900,000) = $182,007
The slope tells us the variable component of the cost, so we can use it
to determine the probable increase (or decrease) in costs that would
accompany an increase (or decrease) in business.
The coefficient of determination, r2 of 0.6266, or 62.66%, is the
percentage of the variation in parttime consultants cost that is associated
with changes in revenue. The value is relatively high for such data and so
indicates that the fit is good.
The standard error of the estimate, tells us how close our predictions
are likely to be to the actual results. In this case, we expect predictions
to be within $9,329 about 68% of the time, and within $18,658 (2 x $9,329)
about 95% of the time. (This is a bit rough and does not tell us the
confidence interval for a single prediction but for the average. This point
is probably not important to most classes.)
It is also helpful to understand what the results do not tell you. The
equation is not necessarily the best available. Some other factor might
predict better. Multiple regression with some other factors might give
better results in the form of a higher rsquared and a lower standard error.
The intercept, $101,187, is not the estimate of total cost at zero
revenue. The data were collected in the range of $800,000 to $1,200,000, and
it is unsafe to extrapolate outside that range.
Note to the Instructor: Students often ask what a good value is for r2.
The best answer, that it depends on the data, is not too satisfying. Anything
above .50 is probably quite good for cost data in a complicated environment.
Evaluating the standard error requires examining the relationship of the
error to the total cost. For instance, at $1,000,000 hours (midpoint of
range) predicted cost is $190,987. The standard error of $9,329 is about 5%
of predicted cost, which is a pretty good fit.
311 Interpreting Behavior Patterns (1015 minutes)
1. The first step is to determine just what the behavior is. The first set
of observations shows a relatively low fixed cost and a rapidly increasing
total cost. This indicates that variable cost is relatively high. The
second segment shows a jump above the level of the first segment, with a
flattening of the total cost line, indicating a decline in variable cost per
unit of activity. The third segment shows much the same: a jump in the
level of costs, with a further flattering of the slope of the cost line.
One possible explanation for the observed behavior is that "variable"
costs per unit drop as volume increases, with increases in stepvariable
costs accounting for the jumps. If the cost were total manufacturing cost, a
possible explanation is that materials were subject to quantity discounts and
were a large proportion of total costs, with jumps in cost occurring because
of stepvariable costs such as supervision.
Another possible explanation is that the company has three alternative
methods of production, with increasing amounts of machinery causing the jumps
in cost and increased efficiency in the use of labor and materials causing
35
the flattenings of the cost lines. It is unlikely that the firm could
actually operate from near zero to near full capacity in this manner at short
notice, unless the machinery could be rented at short notice. Hence, the
cost behavior under this explanation should be viewed as relatively long
term.
2. Planning for the costs should be relatively simple if the range within
which the company expects to operate was relatively certain. Three different
lines would be drawn and used in prediction, depending on the range in which
volume was expected to occur. A single line could not be a good predictor.
312 HighLow Method for Manufacturing Company (20 minutes)
1. Cost of sales: 30% of sales $$ variable, $340.0 fixed
S&A expenses: 20% of sales $$ variable, $150.0 fixed
Cost of Sales S&A Expenses
Cost at high volume $688.0 $382.0
Cost at low volume 670.0 370.0
Differences $ 18.0 $ 12.0
Divided by difference in sales $ 60.0 $ 60.0
Variable components 30% 20%
Cost at high volume $688.0 $382.0
Less variable cost:
$1,160.0 x 30% 348.0
$1,160.0 x 20% ______ 232.0
Fixed components $340.0 $150.0
2. April May
Sales $1,100.0 $1,160.0
Variable costs:
Manufacturing at 30% $330.0 $348.0
S&A at 20% 220.0 550.0 232.0 580.0
Contribution margin 550.0 580.0
Fixed costs:
Manufacturing 340.0 340.0
S&A 150.0 490.0 150.0 490.0
Income $ 60.0 $ 90.0
Several comments apply here. First, some students do not understand that
recasting income statements does not change profit, only the form of the
statement. Second, the contribution margin format allows us to do CVP
analysis, which we could not with the functional income statements. We can,
for example, determine the breakeven point because we know that contribution
margin is 50% (100% 30% 20%) and total fixed costs are $490.0:
$490.0/50% = $980.0
We can also calculate sales volumes required for target profits and do other
planning that is impossible without knowledge of cost behavior.
313 Relationships (15 minutes)
36
1. (b) $600,000 $400,000 + $200,000
(a) $2.00 $8 selling price less $6 contribution margin per
unit ($600,000/100,000)
(c) $230,000 $200,000 current income + additional contribution
margin of $30,000 (5,000 x $6), or 105,000 x $6 =
$630,000 total contribution margin less $400,000 fixed
costs = $230,000
2. (d) $250,000 $50,000/20%
(c) 25,000 units $250,000/$10
(b) $6 $10 x (100% 40%)
(a) $50,000 ($250,000 x 40%) $50,000 profit
3. (c) $60,000 $400,000 x 15%
(a) 10,000
Sales $400,000
Total contribution margin ($60,000 + $90,000) 150,000
Variable costs $250,000
Variable cost per unit $25
Number of units sold ($250,000/$25) 10,000
(b) $15 $150,000 CM/10,000 units
314 PerUnit Analysis (1015 minutes)
1. $432,000, $5.40 x 80,000. You might want to reemphasize that fixed costs
come in total, not perunit, and that this multiplication is necessary
because you must work backwards.
2. 85,000 units
Total fixed costs $432,000
Desired profit 180,000
Total required contribution margin $612,000
Divided by contribution margin per unit ($12 $4.80) $7.20
Units required 85,000
3. $13.54 per unit
Desired income $180,000
Fixed costs from requirement 1 432,000
Required total contribution margin $612,000
Divided by expected unit volume 70,000 units
Equals required perunit contribution margin $8.74
rounded
Plus expected variable cost per unit 4.80
Required price $13.54
4. $9,600 increase in profit. Either the total or incremental approaches
could be used here. Using the total approach,
Expected total contribution margin ($7.20 x 83,000) $597,600
Expected fixed costs ($432,000 + $12,000) 444,000
Expected total profit 153,600
Profit expected without additional expenditure (80,000 x $1.80) 144,000
Increase in profit $ 9,600
Using the incremental approach,
37
Additional contribution margin ($7.20 x 3,000 units) $ 21,600
Added fixed costs 12,000
Increase in profit $ 9,600
Note to the Instructor: You might wish to ask the class how many additional
units the company must sell to make the advertising campaign just pay for
itself. The calculation is similar to that of an indifference point, or even
of a breakeven point.
$12,000/$7.20 = 1,667 units
Because 1,667 is well below the expected 3,000 units, the company is probably
welladvised to go ahead. Had the indifference point been, say, 2,800 units,
a reasonable manager might believe that the risk is too great because a
relatively small shortfall would wipe out the additional profit.
315 Percentage Income Statement (1520 minutes)
1. $80,000 $800,000 x 10%
2. $160,000 fixed costs, $533,333 breakeven point, ($160,000/30%) and
$266,667 margin of safety ($800,000 $533,333)
Variable costs are 70% of salescost of sales of 60% plus 10% commissionso
contribution margin is 30%. To find fixed costs,
Total costs at $800,000 sales $800,000 $80,000 profit $720,000
Total variable costs ($800,000 x 70%) 560,000
Total fixed costs $160,000
3. $50,000
Contribution margin ($700,000 x 30%) $210,000
Fixed costs 160,000
Profit $ 50,000
Or, the decreased sales of $100,000 decrease profit by $30,000 ($100,000 x
30% CM%), from $80,000 to $50,000.
4. 5.55% The easiest way to approach this requirement is to use the basic
profit equation. Cost of sales remains at $480,000, ($800,000 x 60%).
S $480,000 .1S $160,000 = $120,000
.9S = $760,000
S = $844,444
Percentage increase = 5.55% ($44,444/$800,000)
As proof,
Sales $844,444
Cost of sales, as before 480,000
Gross margin 364,444
Commission ($844,444 x 10%) 84,444
Contribution margin 280,000
Fixed costs 160,000
Profit $120,000
316 Cost Behavior Graphs (15 minutes)
38
Unofficial answers to this CPA problem are as follows:
1. C 2. F 3. K 4. B 5. A 6. D 7. J 8. E or H
9. L (Item 9 is different from the original CPA problem.) 10. G
Many of the answers assume that the use of the cost element is at least
partly variable with production. Item 3 is an example. The cost of water as
the use of water increases is described by graph K. It is assumed that
increases in production cause proportional increases in the amount of water
consumed. It is possible, but unlikely, that the use of water is relatively
constant whatever production is. It is also possible that 1,000,000 gallons
or more is the base amount, with additional water being related to
production.
Note to the Instructor: Although we did not show the vertical segments
of stepvariable costs in the text, students have had little difficulty with
cost graphs such as item 7. You might wish to point out that graph J is
technically incorrect because the cost is discontinuous, jumping from one
level to another. This poses no real problem in a practical situation
because the portions of discontinuity are quite small. In this case, a
single machinehour at the breaking point gives the jumps, and it is unlikely
that any company could be so precise in its hiring practices.
Some students will wonder why the second segment of the line in graph H
(item 8) tilts upward instead of being parallel to the horizontal axis. The
reason seems to be that although the labor force is "constant in number," it
could be changing in composition because of turnover. It is also possible
that some workers earn annual wages of less than $8,500. Graph E is a good
answer if (a) there is no turnover and all workers earning more than $8,500.
317 CVP Review (20 minutes)
1. 183 sweaters, rounded ($5,000 + $6,000)/($100 $40) = $11,000/$60
Use the highlow method to determine fixed and variable costs:
At 150 units, costs are (150 x $100) $4,000 = $11,000
At 200 units, costs are (200 x $100) $7,000 = $13,000
Variable costs = ($13,000 $11,000)/(200 – 150) = $40
Fixed costs = $13,000 – ($40 x 200) = $5,000
2. $113.33 rounded
Sales variable costs fixed costs = profit
(S x 150) ($40 x 150) $5,000 = $6,000
(S $40) = $11,000/150
S = $40 + 73.33
3. 150 sweaters, same as now Some alert students will see that the
supplier receives $40 either way at the $100 price. Some will go through
calculations such as the following.
$100 $30 (10% x $100) = $60 new contribution margin, same as now
($5,000 + $4,000)/$60 = 150
The proposed agreement gives the supplier the same total compensation at the
$100 selling price. At higher selling prices the supplier will take a larger
share. In all likelihood, Mia will raise prices in the future, making the
proposed arrangement more attractive to the supplier, less attractive to Mia.
39
318 Profit Improvement Alternatives (15 to 25 minutes)
To: Leslie Meriwether
From: Student
Date: Today
Subj: Profit improvement
We can achieve our target profit by (a) increasing selling price, (b)
decreasing variable cost,(c) decreasing fixed costs, and (d) increasing sales
volume. The required changes in these items appear below:
(a) Increase selling price to $10.60, an increase of $0.60 per unit.
With no change in fixed or variable costs, a $60,000 increase in profit
($100,000 desired vs. $40,000 earned last year) requires a $60,000 increase
in contribution margin at a volume (current level) of 100,000. Hence, an
increase of $0.60 ($60,000/100,000) is necessary.
Competition will determine whether we can achieve the expected volume with
the higher price.
(b) Reduce variable cost per unit to $5.40, a decrease of $0.60 per unit.
The logic here is the same as in requirement (a). Contribution margin
must increase by $0.60 per unit, and with a constant selling price of $10
the perunit variable cost must decline $0.60 from $6.
We might change suppliers to reduce variable costs, but such a step could
reduce the quality of the product. We should look for activities/costs
that do not add value to the product.
(c) Fixed costs must decrease by $60,000, to $300,000.
If profit is to increase $50,000 and contribution margin is to remain the
same, fixed costs must be reduced by an amount equal to the desired
increase in profit.
We can easily reduce some fixed costs, but again the question is whether we
might run into other difficulties. We can always reduce discretionary costs
such as advertising, but perhaps at the cost of reduced sales. We could cut
other costs that might harm us in the long run. Such costs include employee
training and maintenance.
(d) Increase sales to 115,000, an increase of 15%.
Here again, if profit is to increase $60,000 without a change in fixed costs,
total contribution margin must also increase by that amount. If selling
price ($10) and variable cost per unit ($6) remain constant, contribution
margin remains at $4, and it will require 15,000 more units ($60,000/$4) to
produce the desired increase in profit.
Increasing unit sales without increasing costs could be difficult. An
expanding market would help, as would better service to our customers and a
higherquality product. Achieving these improvements without increasing
costs might not be possible.
310
319 Interpreting Data (1015 minutes)
The assistant merely connected the high and low points with his line, not
considering the intervening observations. Moreover, the high and low points
are at volumes far removed from the other observations, so we should question
whether they are within the relevant range. Because the cost is maintenance,
we might even expect a relatively higherthannormal cost at low activity
because there is then more time for performing the work. Similarly, at the
high point we might expect lowerthannormal costs because of the inability
to perform work then, as well as managers' unwillingness to take limos in for
service during a peak period.
The assistant's line shows observations in almost equal numbers above and
below, but the line would fit the majority (all but the high and low) of the
observations better if it were tilted up and pushed down on the vertical
axis. A line hitting the vertical axis at $100 and with a slope of $1.55 fits
nicely. At 500 hours, the cost is about $875. This line ignores the extreme
points. If the extreme points are to be considered, the line would tilt less
and the fixedcost component would be higher than $100. Putting a couple of
alternatives on the board will help students see the differences that would
arise from differing interpretations of the particular observations.
320 Delta Airlines CVP Relationships (20 minutes)
1. The key is to find revenues and costs at breakeven to be able to use the
highlow method.
Revenue and cost at breakeven = $14,881 ($16,741/.729) x .648
So, $15,003 $14,881 = $ 122 = 6.56% variable component
$16,741 $14,881 $1,860
2. The fixed component is $13,905 million, $14,881 ($14,881 x $0.0656)
3. $1,953 million
Revenue, $16,741/.729 x .739 $16,971
Operating expenses
Variable at 6.56% $ 1,113
Fixed 13,905
Total operating expenses 15,018
Operating income $ 1,953
4. The lesson is that an airline, or any other company with very high fixed
costs and low variable costs, lives and dies by volume. The calculation in
requirement 3 shows that each percentage point adds over $215 million ($1,953
$1,738 = $215) to operating income. Of course, each drop reduces operating
income by the same amount.
311
321 Using Multiple Regression (20 minutes)
1. $75,992 $49,272 + ($1.78 x 12,000) + ($2.68 x 2,000)
2. $30.90, calculated as follows:
Materials $ 6.00
Labor, 2 hours x $10 20.00
Variable manufacturing overhead (2.0 x $1.78) + (.50 x $2.68) 4.90
Total variable cost $30.90
3. $5.89
Reduced labor, $10 x .50 $5.00
Reduced variable overhead $1.78 x .50 0.89
Total reduction $5.89
Note to the Instructor: You might expand on the important idea that, as
item 3 shows, when a company reduces labor time, it reduces not only labor
cost but also any variable manufacturing overhead driven by direct labor
time.
322 Understanding Regression Results (15 minutes)
1. $209,345, $118,645 + ($0.907 x 100,000)
2. No, because zero hours is outside the relevant range. This point is very
important, yet often overlooked. It is not safe to predict costs below
75,000 nor above 140,000 hours.
3. $40.815 (45 x $0.907) per batch of 100, or $0.40815 per unit
4. This question refers to measures of goodness of fit. The r 2 of 79.25%
indicates quite a good fit because 79.25% of the variation in power cost is
associated with changes in machine hours. The specific requirement of the
question gets at the meaning of the standard error. Actual cost should be
within $9,497 of predicted cost about 68% of the time and within $18,994 (2 x
$9,497) about 95% of the time. At 100,000 hours, $18,994 is only 9.1% of
predicted cost of over $209,345 (part 1).
5. No. There could be another simple regression equation or a multiple
regression equation that predicts better. Only if the correlation is
perfect, r2= 1, Standard error = zero, can you say that there is none better.
323 Review Problem, Including Income Taxes (3540 minutes)
1. $10 ($500,000 sales/50,000 units)
2. $2.50 ($10 selling price $7.50 variable cost)
variable cost = $375,000/50,000 units = $7.50
3. 24,000 units ($60,000 fixed costs/$2.50 contribution margin
4. $7,500 (3,000 units x $2.50 contribution margin per unit)
5. 48,000 units ($60,000 target profit + $60,000 fixed costs)/$2.50
6. $400,000 $60,000 fixed costs/(25% contribution margin 10% ROS)
312
7. 54,000 units
Desired aftertax profit $ 45,000
Divided by 60% = pretax profit $ 75,000
Fixed costs 60,000
Required contribution margin $135,000
Divided by $2.50 unit CM = 54,000 units
8. 60,000 units
Desired aftertax return 9%
Divided by 60% = pretax return 15%
Sales = $60,000/(25% 15%)
= $600,000
$600,000/$10 selling price = 60,000 units
9. $10.20 per unit
Desired aftertax profit $ 45,000
Divided by 1 tax rate 0.60
Required pretax profit $ 75,000
Fixed costs 60,000
Required contribution margin $135,000
Divided by unit volume 50,000
Equals required unit contribution margin $ 2.70
Plus variable cost 7.50
Selling price $ 10.20
10. $10.36 per unit, let P = selling price
50,000P – (50,000 x $7.50) $60,000 = 0.16P x 50,000
P = $10.357
11. $625,000
Contribution margin, $10.00 ($7.50 + $0.50) $2.00
Contribution margin percentage, $2/$10 20%
Required contribution margin, $60,000 + $65,000 $125,000
Divided by 20% equals required sales $625,000
324 Cost Formula, HighLow Method (5 minutes)
The variable cost rate is about 5.2% of sales, and fixed costs are about
$412.
Sales Wages
High $18,100 $1,350
Low 5,050 675
Difference $13,050 $ 675
Change in cost divided by change in volume ($675/$13,050) = 5.2% rounded
Substituting 5.2% in the total cost formula at the low volume level:
Fixed costs + Variable costs = Total costs
F + (5.2% x $5,050) = $675
F = $412 rounded
Note to the Instructor: This relatively simple problem emphasizes three
important points. First, the observations used in calculating the variable
and fixed components of a mixed cost are the high and low points for the
313
independent variable, not for the dependent variable. (Students
misunderstanding this point will use sales volumes of $1,950 and $15,040.)
Second, the points to be used must be within the relevant range. (Students
misunderstanding this point will use sales volumes of $1,950 and $18,100.)
The third, and more general, point demonstrated by this problem is the
need to understand the facts of the situation. A grasp of the facts is
necessary if the student is to question whether the observations for sales
volumes of $2,000, $17,000, and $18,000 are outside the relevant range, given
that the low and high cost observations occur at $1,950 and $18,100. In this
case, the owner calls in parttime help based on the estimate of sales for
the coming week, and it is to be expected that the owner's estimates are
sometimes off by a wide margin. Errors in estimates result in wages being
higher or lower than predicted using a formula based on actual sales. Thus,
when actual sales were $15,040, the owner might have expected much larger
volume in one or more weeks and committed to more parttime help (who had to
be paid!). Similarly, the facts given about the period with $1,950 sales
suggest that that level of volume is below the relevant range and should be
disregarded.
325 Fixed Costs and Decisions (25 Minutes)
This is a straightforward problem that allows you to discuss several
important points at an early stage in the course. The idea of opportunity
cost and loss of sales are treated in Chapter 5, but the introduction here of
these points is relatively simple. Moreover, you need not even use the term
opportunity cost in connection with this problem.
Considering only quantitative issues, Keith is better off staying open.
An income statement assuming that he closes shows the following.
Rent on building $1,550
Depreciation on fixtures 600
Utilities, minimum 450
Net loss $2,600
Adding the $2,600 loss to the $350 profit that he could earn staying
open, Keith is $2,950 better off remaining open.
The final recommendation depends on what Keith means by "net at least
$2,500 for the month." If he means that he wants to be at least $2,500
better off staying open, he should stay open, but if he means that he wants
to show a profit of $2,500, he should close.
Whatever the intention of Keith's stated decision criterion, he should be
advised to recognize the effect of a onemonth closing on the profit for a
full year. That is, the cost to him of closing is $2,950, not just the $350
profit given up. Moreover, Keith might have reason to believe that closing
could affect future sales. Some semiregular customers might find another
restaurant they like better. Some might be put off by the closing and stay
away longer than their normal intervals.
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326 Alternative Cost Structures
A Movie Company (30 minutes)
Note to the Instructor: This problem can be answered either by computing
profits at each level of admissions or by using the breakeven points from
problem 243.
1. (a) Blockbusters:
Normal contract
$180 million
$200 million
Revenues (40%)
$72,000,000
Variable costs
3,600,000
Contribution margin
68,400,000
Fixed costs
65,000,000
Profit
$ 3,400,000
$80,000,000
4,000,000
76,000,000
65,000,000
$11,000,000
Special contract
$180 million
$200 million
Revenues (40%)
Variable costs
Contribution margin
Fixed costs
Profit
$72,000,000
14,400,000
57,600,000
50,000,000
$ 7,600,000
$80,000,000
16,000,000
64,000,000
50,000,000
$14,000,000
In either case, Blockbusters will prefer the special contract. As
problem 243, requirement 3 showed, the special contract will be preferred by
Blockbusters only when revenues to the producer are less than $100 million.
(b) Drift will prefer the normal contract. At $180 million, the normal
contract would pay Drift $23.6 million ($20 million salary + 3.6 million
variable) while the special contract would pay Drift $19.4 million. At $200
million Drift’s pay would be $24 million under the normal contract and $21
million under the special contract.
2. (a) Blockbusters will prefer the normal contract.
Revenues
Variable costs
Contribution margin
Fixed costs
Profit
Normal
$120,000,000
6,000,000
114,000,000
65,000,000
$ 49,000,000
Special
$120,000,000
24,000,000
96,000,000
50,000,000
$ 46,000,000
(b) Drift will prefer the special contract. The normal contract would pay
$26 million while the special contract would pay $29 million.
327 Regression Analysis (15 minutes)
The point here is that observations are so widely scattered that the
regression equation is virtually worthless. The r2 is 0.019. Because
regression analysis always gives an equation (unless the independent variable
has the same value for every observation), people sometimes count on it more
than is desirable. The following Excel output provides relevant measures.
SUMMARY OUTPUT
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Regression Statistics
Multiple R
0.137572
R Square
0.018926
Adjusted R Square
(0.121227)
Standard Error
48,652.19
Observations
9
Intercept
Units Produced
Standard
Coefficients
Error
t Stat Pvalue Lower 95%
Upper 95%
262,203.39 74,407.37 3.524 0.010 86,258.05 438,148.73
13.1961 35.9103 0.367 0.724 (71.7181) 98.1104
Notice also that with a standard error of the regression equation of $48,652,
the 68% confidence interval is very wide. The variable, Units Produced, is
not statistically significant.
328 CVP Analysis with Changes in Costs (2025 minutes)
1. $200,000 (350,000 x [$20 $8]) $4,000,000
2. $21 The increase in material cost is $1.00 ($4.00 x 25%), so the price
increase must cover the increase in variable costs. Some students will
simply add the $12 per unit contribution margin to the new perunit variable
cost of $9 to arrive at the $21 price. Some students will solve from
scratch.
Sales = $4,000,000 + (350,000 x $9) + $200,000 = $7,350,000
$7,350,000/350,000 = $21
3. (a) $22.50 ($9.00/40%) The current contribution margin percentage is
60%, ($20 $8)/$20, so the variable cost ratio is 40%. The new variable
cost is $9, so the selling price is $9 divided by 40%.
Some students will have trouble with this part, which is not explicitly
illustrated in the text. However, all it requires is understanding that 100%
minus the contribution margin percentage is the variable cost percentage.
(b) Profit will be higher because contribution margin per unit will be
higher ($22.50 x 60% = $13.50, rather than $12). This requirement emphasizes
that contribution margin per unit and contribution margin percentage are
different. Assuming no change in unit volume, if prices are increased so as
to maintain the perunit contribution margin, profit is maintained at the
previous level. If prices are increased so as to maintain the contribution
margin percentage, perunit contribution margin increases and so profit
increases.
329 Cost Structures and Average Costs (25 minutes)
1. Sally: 100,000 x ($10 $9) = $100,000
Sam: 200,000 x ($10 $9) = $200,000
2. Computations:
Sally Sam
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Total costs at 200,000 units
200,000 x $6 $1,200,000
200,000 x $9 $1,800,000
Total costs at 100,000 units
100,000 x $9 900,000
Total costs at 80,000 units
80,000 x ($10 + $0.50) 840,000
Changes in total costs $300,000 $ 960,000
Changes in volume 100,000 120,000
Unit variable costs $3 $8
Total variable costs at 200,000 units
200,000 x $3 $600,000
200,000 x $8 $1,600,000
Total fixed costs
$1,200,000 $600,000 $600,000
$1,800,000 $1,600,000 $200,000
Contribution margin
$10 $3 $7
$6 $4 $2
3. Sally: $600,000/($10 $3) = 85,714
Sam: $200,000/($10 $8) = 100,000
4. Since the selling price is the same for each division, they will show
equal profits when they have equal costs. Letting V represent the volume,
Sally Sam
$600,000 + $3 x V = $200,000 + $8 x V
$400,000 = $5 x V
80,000 = V
Since this volume is less than the breakeven for either division, this is the
sales level where they will show equal losses. At volumes greater than
80,000, Sally will show a higher profit.
330 Avoidable Costs (20 to 25 minutes)
1. The equation prepared by Halton's friend is incorrect unless Halton
purchases and sells exactly 200 arrangements (so that there are no losses as
a result of purchasedbutunsold arrangements). In effect, the equation
ignores Halton's purchasing situation. Halton turns a normally variable cost
into a fixed (and unavoidable) cost because he cannot sell units after a
week. CVP analysis assumes saleability of purchased units.
Note to the Instructor: Before going on to the next question, it might
be useful to explore the implications of accepting the proposed equation,
even for planning purposes. For example, the nature of the product is such
that some will be less desirable than others by the end of the week, so that
lateintheweek sales might not be as expected. (And, of course, if the
product is not arrangements but groups of flowers of various types, it is
certainly possible that the flowers available for arranging at the end of the
week will not be appropriate for the sales opportunities available at that
time.) An important point to remember is that we are dealing with average
data here (purchase and sales prices), which suggests some need to provide
leeway in planning. And, in addition to the previous considerations, Halton
should recognize that if he buys and sells 200 arrangements, he could lose
the contribution margin from sales orders that he cannot meet.
317
2. The purchase cost of the arrangements (or the flowers, as the case may
be) cannot be readily classified. Once a specific quantity has been bought,
the total purchase cost becomes an unavoidable fixed cost, the variable cost
per sale becomes zero, and contribution margin equals selling price.
3. About 234 units if 300 units are purchased and 267 if 400 are purchased.
Incorporating the idea expressed in the Note to the Instructor for
requirement 1, the purchase cost becomes another fixed cost and the target
sales volumes can be computed as follows:
If purchases are 300,
target sales volume = $3,000 + ($10 x 300) + $1,000 = 234 units, rounded
$30 $0
If purchases are 400,
target sales volume = $3,000 + ($10 x 400) + $1,000 = 267 units, rounded
$30 $0
Another approach is to rely on the basic idea that revenues costs = profit.
Using this simple approach:
If purchases are 300, and letting Q = the number of units sold:
$30Q $10Q $3,000 $10(300 Q) = $1,000 Q = 234 units
If purchases are 400, and letting Q = number of units sold:
$30Q $10Q $3,000 $10(400 Q) = $1,000 Q = 267 units
In line with the comments offered under the Note to the Instructor in
requirement 1, some students might well ask why Halton does not just order
200 units to avoid the problem of unsold units. The issue is, of course,
balancing risk and reward, and a risk of $10 (on average) for a potential
reward of $30 (again, on average) is likely to be quite attractive.
331 Cost EstimationService Business (35 minutes)
The pattern of behavior, as shown in the scatterdiagram, is that the
cost is relatively constant from 2,800 to 3,500 hours. It then rises at a
rate of about $1.80 to $1.95.
Several reasons could explain the behavior. Because we have no
observations below 2,800 hours, we do not know whether the $3,000 or so cost
that we see from 2,800 to 3,500 hours is fixed or a step in a function of a
stepvariable cost. It might be that Jarvis keeps a steady parttime force
until he finds that volume is rising and he then needs to add workers or
increase the hours of the existing ones.
318
Calculated variable cost rates in different ranges:
Range Rate
3,500 4,800 $1.77 ($5,400 $3,100)/(4,800 3,500)
4,800 5,200 1.95 ($6,180 $5,400)/(5,200 4,800)
5,200 5,600 1.80 ($6,900 $6,180)/(5,600 5,200)
3,500 5,600 1.81 ($6,900 $3,100)/(5,600 3,500)
The rates are fairly constant, indicating that a pattern does exist over
the upper range of volume.
Cost
$7,000
x
6,000 x
x
5,000
4,000
x
x
3,000 x x
__________________________________________________________
1,000 2,000 3,000 4,000 5,000 6,000
Hours
332 CVP Analysis for an Airline (25 minutes)
1. 20,000 passengers or 53.33% of capacity of 37,500
Fixed costs:
Overall per month $ 130,000
Flight costs at 250 flights (250 x $4,000) 1,000,000
Total fixed costs 1,130,000
Desired profit 70,000
Required contribution margin $1,200,000
Divided by perpassenger CM ($66 $6) $ 60
Number of passengers required 20,000
Divided by capacity (250 x 150) 37,500
Equals percentage of capacity required 53.33%
2. 16,667 passengers or 55.56% of capacity of 30,000
Fixed costs:
Overall per month $ 130,000
Flight costs for 200 flights (200 x $4,000) 800,000
Total 930,000
Desired profit 70,000
Required contribution margin $1,000,000
Divided by perpassenger CM ($66 $6) $ 60
Number of passengers required 16,667
Divided by capacity (200 x 150) 30,000
Equals percentage of capacity 55.56%
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3. Flight costs are an example of a cost that varies with an activity other
than sales. The flight cost is fixed from the point of view of a specific
flight, but is variable with the number of flights.
4. The most obvious characteristic of the airline's cost structure is the
high level of fixed costs. For such companies, volume is the key to
successful operations. For example, with the data given in requirement 1,
the breakeven point is 18,833 passengers, or 50.22% of capacity.
[$130,000 + (250 x 4,000)]/($66 $6)
Thus, an increase of slightly over three percentage points (53.33% 50.22%)
in capacity utilization produces a $70,000 change in profit. This is an
increase of only 1,167 passengers. Another increase of 1,167 passengers
doubles profit to $140,000.
Note to the Instructor: A point of particular interest in this problem
is the behavior of flight costs, which are variable but not with sales. Note
also that the number of planes available has no direct bearing on the
problem. Some students try to incorporate that number in their solution, at
first as a determinate of capacity. The particular plane used for one of the
200 or 250 flights has no bearing on the costs or capacity. The total fixed
cost is affected by the number of planes owned to provide the capacity
expressed as the number of flights.
333 Promotional Campaign (20 minutes)
1. $5,850,000
Subscription revenue to Ajax 20,000,000 x 15% x $35 x 25% $26,250,000
Costs $10,000,000 + $10,400,000 20,400,000
Profit $ 5,850,000
2. 11.66% Ajax has a contribution margin per $35 order of $8.75 ($35 x
25%). The breakeven point in number of orders is 2,331,429
($20,400,000/$8.75), or 11.66% response rate (2,331,429/20,000,000).
Note to the Instructor: You might want to mention that the prize money
in these giveaways is paid over a lengthy time, often 20 years. You might,
even before covering Chapter 8, ask the class what effect the delayed payment
has on the profitability of the campaign. Though they have not yet studied
the time value of money, most students will see that the campaign would be
more profitable because Ajax can invest the money for a long time.
334 Brain Teaser
Calculating Contribution Margin Percentage (1025
minutes)
1. 40% (1 minus the 60% variablecost percentage computed below)
First, convert the 6% aftertax ROS to a l0% beforetax ROS [ 6%/(1
40%)], which means that total costs are 90% (1 10%) of current sales.
Knowing the margin of safety and that, at the breakeven point, total costs
equal total sales, the basic facts are:
Sales Total Costs = Profit
Current sales S 90%S 10%S
Breakeven sales 75%S 75%S 0
320
This matrix can be converted to the typical highlow matrix as:
Sales Total Costs
High volume 1.00 .90
Low volume .75 .75
Difference .25 .15
Change in total cost divided by change in volume = .15/.25 = 60%
2. $36,000 Again, converting the aftertax 6% ROS to a 10% beforetax ROS,
and applying the basic formulas regarding sales, costs, and breakeven, the
basic facts are:
Sales Total Costs = Profit
Current sales $120,000 $108,000 $12,000
Breakeven sales 75%
of current sales 90,000 90,000 0
Difference $ 30,000 $ 18,000 $12,000
Change in total cost divided by change in volume = $l8,000/$30,000 = 60%
Applying the variable cost percentage to the current sales volume (the break
even volume could also be used, of course):
Total costs = variable costs + fixed cost
$108,000 = (60% x $120,000) + fixed cost
$108,000 $72,000 = fixed cost
$36,000 = fixed cost
335 Cost Structure and Risk (20 minutes)
Monthly 5 Years
Annual sales $250,000 $250,000
Variable costs 100,000 100,000
Contribution margin 150,000 150,000
Fixed costs:
12 x $6,000 72,000
12 x $5,200 62,400
Annual profit $ 78,000 $ 87,600
If sales and variable costs materialize as forecast, Gladack will earn
$9,600 more annually under the fiveyear lease. However, the acceptance of
the product (and hence the product's useful life) is also relevant.
If, for example, the product stops selling after four years, the company
will be unable to avoid the last year's lease payment of $62,400, while the
added profit under the fiveyear lease will be only $38,400 ($9,600 x 4
years). The president should therefore be interested in determining the
indifference point, how long the product would have to sell to equate the
costs and profits under the two choices. The calculations, with M = the
number of months the company must use the machine are:
Cost of MonthtoMonth Lease Cost of FiveYear Lease
$6,000M = $5,200 x 12 x 5
M = 52
Thus, if the company uses the machine for 52 months, it shows the same
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total cost and total profit under either alternative. At this point you
might wish to bring up the time value of money, saying that even if the
company uses the machine for exactly 52 months, it is better off with the
yearyear lease because its cash payments are delayed under that choice.
That is, the company saves $800 per month for 52 months, a total of $41,600.
It pays the $41,600 during the last eight months at $5,200 per month, so that
the present value of the savings of the fiveyear lease is positive. The 52
month period is only eight months short of five years, so by taking the five
year lease the company is accepting the risk that the product will be
profitable for nearly the entire life of the lease. The lower the
indifference point, the more attractive the fiveyear lease.
The commitment for the fiveyear period cuts both ways. There is no
guarantee that the lease will remain at $6,000 per month for the five years
under the monthly option. The lessor could raise the rent at any time, as
the problem states (the lessor can cancel the lease, which amounts to saying
that it could also raise the rent). Thus, the fiveyear lease does protect
the company against the risk of increased rent.
Note to the Instructor: This is a good problem to point out the
uncertainties with which businesspeople must regularly deal. Here the
president is facing uncertainty regarding consumer acceptance and at the same
time must deal only with estimates of revenues and variable costs. If a
decision is based on the best information available at the time, the
president need not regret the choice. If subsequent information does not
agree with reasonable estimates at the time of the decision, it is the
estimates that were wrong (or "bad"), not the decision.
336 Loss per Unit (20 minutes)
1. $4 per unit. The total loss at 40,000 units is $120,000 ($3 x 40,000)
and at 50,000 units is $80,000 ($1.60 x 50,000). The change in the loss is
$40,000, which, when divided by 10,000 units, gives $4 per unit.
2. $280,000. At sales of 40,000 units, total contribution margin is
$160,000 (40,000 x $4) and the loss is $120,000. Fixed costs are therefore
$280,000 greater than contribution margin. At 50,000 units, contribution
margin is $200,000 ($4 x 50,000), and the loss is $80,000, also giving
$280,000 for fixed costs.
3. 70,000 units ($280,000/$4)
337 CVP AnalysisMeasures of Volume (30 minutes)
This problem focuses on identifying a measure of sales volume that is
suitable for use in CVP analysis. Requirement 3 will give many students a
great deal of trouble and affords an opportunity to discuss alternative ways
to express revenues and costs.
1. At 100 loaves per month the company will earn $12,000, selling 450,000
board feet of good output (5,000 x 90% x 100 loaves).
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Revenue:
Good output (450,000 bd. ft. x $.30) $135,000
Scrap (50,000 x $.11) 5,500
Total revenue ($1,405 per loaf) 140,500
Variable costs:
Price of loaf ($900 x 100) $90,000
Cutting costs ($175 x 100) 17,500
Total variable costs 107,500
Contribution margin ($330 per loaf) $ 33,000
Fixed costs 21,000
Income $ 12,000
2. 63.6 loaves ($21,000/$330 contribution margin per loaf)
It is theoretically possible for the company to process part of a loaf
because the production process could be viewed as more or less continuous. A
loaf could be 35% or so processed at the end of a month. Such an answer
would be calculated anyway if loaves per day were asked for, with 22 working
days in a month.
3. There are alternative ways to approach this part. The easiest is to
divide contribution margin per loaf of $330 (requirement 1) by 4,500 good
board feet per loaf, giving $.0733 contribution per good board foot. It is
also possible to work directly with board feet. It is easier to treat scrap
sales as variable cost reductions, than as revenue.
Revenue per good board foot $0.3000
Variable cost per loaf $1,075
Less scrap sales per loaf (500 x $.11) 55
Net variable cost 1,020
Divided by 4,500 good board feet 0.2267
Contribution margin per board foot $0.0733
The sales of good board feet required to earn $15,000 are 491,132 [($21,000 +
$15,000)/$.0733].
338 Measures of Volume (50 minutes)
The first step is to scan the data to identify likely correlations.
Thus, selling expenses are more probably related to sales than to labor
hours, and the last two listed observations confirm this intuitive
conclusion.
The following results are from Excel spreadsheets.
Production costs = $5,397 + $7.50 per labor hour
r2 = .991, Std Error = $238
Selling expenses = $1,997 + $0.101 per sales dollar
r2 = .998, Std Error = $52
Administrative expenses = $2,681 + $0.058 per sales dollar
r2 = .918, Std Error = $208
The fits are all excellent, indicating that we have the right drivers. We
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tested other possible combinations. The r2 for production costs against
sales is .18: for selling expenses against labor hours it is .38. Fits of
other combinations, such as selling expenses to DLH are low. We have only
six observations (to keep data entry to a minimum), so we cannot be as happy
as we would with 25 or so, but with such good fits we have equations that
should predict well. We must guard against regressing everything in sight on
everything else, always a temptation when we have a datarich environment and
virtually unlimited computing capability.
339 Selecting a Regression Equation (1015 minutes)
The memo should make the following points.
The equation using machine hours will provide better predictions than
the one using direct labor hours. Labor hours is not a statistically
significant variable (notice the 95% confidence interval includes a value of
zero). Moreover, the equation using machine hours will give reasonable
results and so we should use it.
Labor Hours Machine Hours
Standard error $19,272 $10,105
r2 .24 .79
variable cost significant? no yes
The machinehour equation is better on the important measures of
goodness of fit. We should get reasonable predictions using the machinehour
equation.
We might do even better by using both variables in a multiple regression
analysis. If we do, we must take care to check for multicollinearity. If
machine hours and labor hours are themselves correlated, we would have a
problem.
340 ValueAdding and NonValueAdding Activities and Costs (30 minutes)
This assignment is virtually the same as 114, except that 114 asks
about differences between a company's operations and JIT operations.
MUL warehouses materials and components. A JIT manufacturer orders stock
as needed, eliminating the handling and storage. MUL goes to great lengths
to get the best prices on materials and components. A JIT manufacturer is
more concerned about quality and meeting delivery schedules. MUL deals with
many suppliers, while a JIT manufacturer deals with relatively few.
MUL inspects all incoming shipments. Instead, like a JIT manufacturer
it should stop inspecting once it determines that a vendor delivers defect
free components. MUL also inspects for deterioration before it puts
components into process. Keeping lower inventories would eliminate this
activity.
MUL maintains inventories at work stations, has long setup times, and
considerable moving of goods during production. These activities could be
eliminated by paying more attention to quality so that there would be no need
to hold inventories at stations. Using manufacturing cells would reduce
(perhaps eliminate) setup times and eliminate moving semifinished product
around the factory.
324
MUL inspects at the end of production. It also makes 10% more units than
needed as a buffer against defects. The company's workers could instead
inspect product continually, making it possible to keep little inventory and
eliminate separate inspection.
MUL tries to trace defects, which adds no value. If its workers
inspected continually it would not have that activity.
MUL's cycle times are high. It could reduce them by adopting JIT
principles, as indicated above.
325
