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Chapter 6 - Solutions
Managerial Accounting (Fanshawe College)
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Chapter 6
Cost Behaviour: Analysis and Use
Solutions to Questions
6-1
a. Variable cost: A variable cost
remains constant on a per unit
basis, but changes in total in
direct relation to changes in
volume.
b. Fixed cost: A fixed cost remains
constant in total amount, but
changes, if expressed on a per
unit basis, inversely with
changes in volume.
c. Mixed cost: A mixed cost
contains both variable and fixed
cost elements.
of a variable cost. Examples of
activity bases include units
produced, units sold, letters typed,
beds in a hospital, meals served in
a cafe, service calls made, etc.
6-2
a. Unit fixed costs will decrease as
volume increases.
b. Unit variable costs will remain
constant as volume increases.
c. Total fixed costs will remain
constant as volume increases.
d. Total variable costs will increase
as volume increases.
6-3
a. Cost behaviour: Cost behaviour
can be defined as the way in
which costs change in response
to changes in some underlying
activity, such as sales volume,
production volume, or orders
processed.
b. Relevant range: The relevant
range can be defined as that
range of activity within which
assumptions relative to variable
and fixed cost behaviour are
valid.
6-4 An activity base is a measure
of whatever causes the incurrence
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6-5 (See the exhibit below.)
a. Variable cost: A variable cost
remains constant on a per unit
basis, but increases or
decreases in total in direct
relation to changes in activity.
b. Mixed cost: A mixed cost is a
cost that contains both variable
and fixed cost elements.
c.
6-8
a. Committed d. Committed
b. Discretionary e.
Committed
c. Discretionary f.
Discretionary
6-9 Yes. As the anticipated level
of activity changes, the level of
fixed costs needed to support
operations will also change. In
essence, fixed costs should be
viewed as going upward and
downward in broad steps, rather
than being absolutely fixed at one
level for all ranges of activity.
Step-variable cost: A step-variable cost is a
cost that is not strictly proportional to a unit
change in activity level. Instead it increases
or decreases only in response to more than
a unitchange in activity level.
$5,000
$4,500
6-10 The major
disadvantage of the high-low
method is that it uses only
two points in determining a
cost formula and these two
points are likely to be less
than typical since they
represent extremes of activity.
If one or both of the points
are outliers it can cause a
distorted formula.
$4,000
$3,500
Total Cost
$3,000
$2,500
$2,000
$1,500
$1,000
$500
$0
3
4
5
6
7
8
9
10
11
12
Total Mileage ( 000)
6-6 The linear assumption is
reasonably valid providing the cost
formula is used only within the
relevant range.
6-7 A discretionary fixed cost is
one that has a fairly short
planning horizon—usually a year.
Such costs arise from annual
decisions by management to
spend in certain fixed cost areas,
such as advertising, research, and
management development. A
committed fixed cost is one that
has a long planning horizon—
generally many years. Such costs
relate to a company’s investment
in facilities, equipment, and basic
organization. Once such costs
have been incurred, a company
becomes “locked in” to the
decision for many years.
13
14
15
16
6-11 The high-low method,
the scattergraph method, and
the least-squares regression
method are used to analyze mixed
costs. The least-squares
regression method is generally
considered to be most accurate,
since it derives the fixed and
variable elements of a mixed cost
by means of statistical analysis.
The scattergraph method derives
these elements by visual
inspection only, and the high-low
method utilizes only two points in
doing a cost analysis, making it
the least accurate of the three
methods.
6-12 The regression line is a line
that is fitted to an array of plotted
points. A regression line can be
expressed in formula form as Y =
a + bX. In cost analysis, the “a”
term represents the fixed cost
element, and the “b” term
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represents the variable cost
element per unit of activity.
6-13 The fixed cost element is
represented by the point where
the regression line intersects the
vertical axis on the graph. The
variable cost per unit is
represented by the slope of the
line.
6-14 The term “least-squares
regression” means that the sum of
the squares of the deviations from
the plotted points on a graph to
the regression line is smaller than
could be obtained from any other
line that could be fitted to the
data.
6-18 The contribution margin is
total sales revenue less total
variable expenses.
6-19 The contribution approach to
the income statement organizes
costs by behaviour, first deducting
variable expenses to obtain
contribution margin, and then
deducting fixed expenses to obtain
net income. The traditional
approach organizes costs by
function, such as production,
selling, and administration. Within
a functional area, fixed and
variable costs are intermingled.
6-15 The least-squares regression
method, compared to the high-low
method, has two main
advantages: (1) it considers all the
data points (observations) instead
of just the high and the low
observations, and (2) it is a
statistical technique, and gives an
objective measure of the
“goodness of fit” of the regression
line.
6-16 The main difference
between the least-squares
regression method and the
scattergraph method is that the
regression method uses a
statistical technique to fit the
regression line and compute the
coefficients of the constant term
and the variable of interest. In
contrast, the scattergraph employs
a visual fit (approximation)
method to draw the regression
line which is then used to compute
the values of the coefficients.
6-17 True. A higher R2 means
that a greater proportion of the
variation in the dependent variable
(Y) is explained by the variation in
the independent variable of
interest (X).
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Foundational Fifteen (LO1 – CC1, 3, 6; LO2 – CC7, 9; LO3 – CC12)
The following table shows the cost per unit for each of the three months. This table,
along with the table in the question, will help in developing the cost equations and
computing the required amounts.
July
Sales in units
Sales revenue
Direct materials
Direct labour
Manufacturing
overhead
Sales commission
Other selling
expenses
Administrative
expenses
4,000
$100.00
$
18.50
$
22.15
$
15.87
$
7.50
$
10.49
$
7.89
August
September
4,200
4,800
$100.00
$100.00
$ 18.50
$ 18.50
$ 22.15
$ 22.15
$ 15.51
$ 14.73
$
7.50
$
7.50
$ 10.39
$
9.24
$
$
6.57
7.51
6-1. $100 per unit
6-2. Y = $18.50X (variable cost)1
6-3. Y = $22.15X(variable cost)1
6-4. Y = $27,480 + $9.00X (mixed cost)2
6-5. Y = $7.50X (variable cost)1
6-6. Y = $29,960 + $3.00X (mixed cost)2
6-7. Y = $31,550 (fixed cost)3
6-8. $18.50 + $22.15 + $9.00 = $49.65
6-9. $7.50 + $3.00 = $10.50
6-10. $7.50 x 4,100 = $30,750
6-11. $27,480 + ($9.00 x 4,500) = $67,980
6-12. $88,990 + (60.15 x 4,700) = $371,6954
6-13. $100 - $60.15 = $39.85
6-14. $39.85 x 4,000 = $159,400
6-15. ($39.85 x 4,600) - $88,990 = $94,3205
Notes:
1. As shown in the table above the cost per unit for these three cost items is
constant across all months. Therefore, these cost items are classified as variable
costs.
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2. The cost per unit for these items is inversely proportional to the sales in units.
However, the total cost per month is directly proportional with the sales in units.
Therefore, these cost items are classified as mixed costs.
The variable portion for each of the two mixed cost items is computed as shown
below.
Sales Units
High activity –
September
Low activity July
Difference
Observed Costs
Manufacturing
Other Selling
Overhead
Expenses
4,800
$70,680
$44,360
4,000
$63,480
$41,960
800
$ 7,200
$2,400
The variable cost portion for Manufacturing Overhead and Other Selling Expenses,
respectively, are computed as shown below:
Change in cost
$7,200
=
=$9 per unit
Change in activity 800 units
Change in cost
$2,400
=
=$3 per unit
Change in activity 800 units
The fixed portion for Manufacturing Overhead and Other Selling Expenses, respectively,
are computed as shown below:
$70,680 – ($9 ˣ 4,800)
$41,960 – ($3 ˣ 4,000)
= $27,480
= $29,960
3. The total cost is constant across all months; therefore this cost item is classified
as a fixed cost.
4. The fixed portion of this cost equation is computed as follows:
$27,480 + $29,960 + 31,550
The variable portion of this cost equation is computed as follows:
$18.50 + $22.15 + $9.00 +7.50 + $3.00
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5. Income is computed as total contribution margin for the 4,600 units sold
(@$39.85 per unit as shown in #13 above, multiplied by 4,600) minus the total
fixed costs of $88,990 (as shown in #12 above and also Note #4 above).
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Solutions to Brief Exercises
Brief Exercise6-1 (15 minutes) (LO1 CC1, 3)
1.
Cups of Coffee Served
in a Week
3,000
3,200
3,400
$2,200
$2,200
$2,200
540
576
612
$2,740
$2,776
$2,812
$0.913
$0.868
$0.827
Fixed cost
Variable cost
Total cost
Cost per cup of coffee served *
* Total cost ÷ cups of coffee served in a week.
2. The average cost of a cup of coffee declines as the number of cups of coffee served
increases because the fixed cost is spread over more cups of coffee.
Brief Exercise 6-2 (20 minutes) (LO2 CC9)
1.
Month
High activity level (March)
Low activity level (October)
Change
OccupancyDays
2,536
Electrical
Costs
$5,383
224
2,312
1,988
$3,395
Variable cost = Change in cost ÷ Change in activity
= $3,395 ÷ 2,312 occupancy-days
= $1.47 per occupancy-day.
Total cost (March).........................................................................$5,383
Variable cost element
3,728
($1.47 per occupancy-day × 2,536 occupancy-days)....................
Fixed cost element........................................................................$1,655
Cost equation for electrical costs can be stated as follows:
Electrical costs (Y) = $1,655 per month + $1.47 per occupancy-day
2. Electrical costs may reflect seasonal factors other than just the variation in
occupancy days. For example, common areas such as the reception area must be
lighted for longer periods during the winter. This will result in seasonal fluctuations
in the fixed electrical costs. Additionally, the fixed costs will be affected by the
number of days in a month. In other words, costs like the costs of lighting common
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areas are variable with respect to the number of days in the month, but are fixed
with respect to how many rooms are occupied during the month. Other, less
systematic, factors may also affect electrical costs such as the frugality of individual
guests. Some guests will turn off lights when they leave a room. Others will not.
Brief Exercise 6-3 (30 minutes) (LO2 CC10)
1. See the scattergraph on the following page.
2. Students’ answers will vary, depending on their placement of the regression line.
The variable cost per unit processed is:
Total cost at the 10,000-unit level of activity [approximate
amount based on visual inspection]............................................
$48,750
Total cost at the 5,000-unit level of activity [approximate
amount based on visual inspection]............................................
$36,250
Change in cost
$12,500
Variable cost element per unit produced
[$12,500 ÷ 5,000 units produced]...............................................$2.50
Fixed cost element [where the regression line intersects
the Y-axis].................................................................................
25,000
Therefore, the cost formula is $25,000 per month plus $2.50 per unit processed.
(Observe from the scattergraph that if the company used the high-low method to
determine the slope of the regression line, the line would be too parallel to the line
shown in the plot but below it, causing estimated fixed costs to be lower than they
should be, and the variable cost per unit to be close to what is computed above.)
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Brief Exercise 6-3 (continued)
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Brief Exercise 6-4 (20 minutes) (LO2 CC11)
The estimates of the fixed and variable costs using least-squares regression is as
follows:
Fixed cost:
$25,193 per month
Variable cost:$2.42 per unit produced.
The R2 is about 92%, which means that the cost manager of Oki Products can be fairly
confident that units produced is a reliable basis for estimating processing costs.
Students can be asked to compare these estimates with those from the scattergraph
method in the previous exercise.
The INTERCEPT and SLOPE functions can be used in Excel to calculate the fixed and
variable cost numbers, and the RSQ function to calculate R 2.
Brief Exercise 6-5 (10 minutes)(LO1 CC1, 3; LO3 CC12)
Contribution margin income statement.
Sales
Less: variable costs1
Contribution margin
Less: fixed expenses2
Net income
$45,000
27,000
$18,000
12,000
$ 6,000
1
Using sales revenue and average selling price, we can compute the number of units
sold as 3,000 ($45,000 ÷ $15). Therefore, total variable costs = 3,000 × $9 =
$27,000.
2
Fixed expenses = $39,000 - $27,000 = $12,000
Brief exercise 6-6 (10 minutes) (LO1 CC6; LO2 CC7, 8)
Cost functions 1, 2, 3, and 4 are linear functions (although 3 is simply a constant
function, which means the value of the dependent variable will not vary with any
variation in the value of the independent variable). Cost function 5 is a non-linear
function.
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Cost functions 1, 2, and 5 are mixed cost functions in that they include a constant term
and a variable term. The remaining two cost functions are not mixed (#3 has only a
fixed cost element and #4 has only a variable cost element).
Brief Exercise 6-7 (15 minutes) (LO2 CC9)
Pizzas Cost
High activity level
Low activity level
Change
Variable portion
32,000
24,000
12,520
8,000 3,520
16,040
= Change in cost÷change in activity
= $3,520 ÷ 8,000 = $0.44 per pizza.
Fixed portion:
High
Total cost
$16,040
Less variable portion @$0.44 per pizza 14,080
Fixed cost element
$ 1,960
Low
$12,520
10,560
$ 1,960
Cost equation can be stated as follows:
Utilitycosts (Y) = $1,960 per month + $0.44 per pizza
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Brief Exercise 6-8 (20 minutes) (LO3 CC12)
1.
THE ALPINE HOUSE, INC.
Income Statement—Ski Department
For the Quarter Ended March 31
Sales............................................................................................
Less variable expenses:
Cost of goods sold ($450 per pair × 800 pairs*)..........................
$360,000
Selling expenses ($50 per pair × 800 pairs).................................
40,000
Administrative expenses (20% × $20,000)..................................4,000
Contribution margin......................................................................
Less fixed expenses:
Cost of goods sold
[$390,000 – ($450 per pair × 800 pairs]
30,000
Selling expenses
[$60,000 – ($50 per pair × 800 pairs)].....................................
20,000
Administrative expenses (80% × $20,000)..................................
16,000
Net income...................................................................................
$560,000
404,000
156,000
66,000
$ 90,000
*$560,000 ÷ $700 per pair = 800 pairs.
2. Since 800 pairs of skis were sold and the contribution margin totalled $156,000 for
the quarter, the contribution of each pair of skis toward covering fixed costs and
toward profits was $195 ($156,000 ÷ 800 pairs).
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Solutions to Exercises
Exercise 6-1 (30 minutes) (LO2 CC9)
1.
GuestDays
28,500
12,500
16,000
High activity level (June)
Low activity level (April)
Change
Custodial
Supplies
Expense
$28,850
19,250
$ 9,600
Variable cost portion:
Change in expense ÷Change in activity = $9,600÷16,000 = $0.60 per guest day
Fixed cost portion:
Custodial supplies expense at high activity level..............................
$28,850
Less variable cost element
28,500 guest-days × $0.60 per guest-day...................................
17,100
Total fixed cost.............................................................................
$11,750
The cost formula is $11,750 per month plus $0.60 per guest-day or
Y = $11,750 + $0.60x.
2. Custodial supplies expense for 13,000 guest-days:
Variable cost
13,000 guest-days × $0.60 per guest-day...................................
$ 7,800
Fixed cost.....................................................................................
11,750
Total cost.....................................................................................
$19,550
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Exercise 6-2 (30 minutes) (LO2 CC11)
The use of a spreadsheet to conduct the least-squares regression analysis returns the
following results:
Fixed cost:
$11,591
Variable cost:$0.62 per guest-day occupied.
Cost formula:Y = $11,591 + $0.62x.
Custodial supplies expense for 13,000 guest-days:
Variable cost
13,000 guest-days × $0.62 per guest-day...................................
$ 8,060
Fixed cost.....................................................................................
11,591
Total cost.....................................................................................
$19,651
The estimated cost for 13,000 guest-days using least-squares regression is slightly
higherthan the estimate using high-low method. Least-squares regression is a superior
method because it uses all data points in the computation of the cost estimates.
The R2 of the cost estimates is 98.6% which means only 1.4% of the variation in
custodial expenses is not explained by variation in guest-days.
The INTERCEPT and SLOPE functions can be used in Excel to calculate the fixed and
variable cost numbers, and the RSQ function to calculate R 2.
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Exercise 6-3 (45 minutes) (LO2 CC8, 9, 10)
1.
The scattergraph would be:
Custodial Supplies Expense versus Occupancy-Days
$35,000
Custodial Supplies Expense
$30,000
$25,000
$20,000
$15,000
$10,000
$5,000
$10,000 12,000 14,000 16,000 18,000 20,000 22,000 24,000 26,000 28,000 30,000
Guest Occupany Days
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Exercise 6-3 (continued)
Note: Students’ answers will vary, depending on how they visually fit the regression line
to the data.
2. Total costs at 15,000 guest-days per month [approximate
amount]....................................................................................$20,900
Total costs at 25,000 guest-days per month [approximate
amount].................................................................................... $27,100
Change in cost
$ 6,200
Variable cost element per guest-day
[$6,200 ÷ 10,000 guest-days]..................................................... $0.62
Fixed cost element [where the regression line intersects the Yaxis]
$12,000
The cost formula is therefore $12,000 per month, plus $0.62 per guest-day or
Y = $12,000 + $0.62X.
3. The high-low method would not provide an accurate cost formula in this situation,
since a regression line cutting the high and low points would have a flatter slope
than both the scattergraph and least square regression lines, and would be placed
too high, cutting the cost axis at about $12,500 per month. Although the high and
low points are not representative of all of the data in this situation, the high-low
regression line in this case is not too far different from the result that the least
square regression method yields. The high and low points are not considered
outliers. If they were, calculating the high-low method would result in a considerable
difference between that and the square regression method and scattergraph
method.
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Exercise 6-4 (45 minutes) (LO2 CC9, 10)
1.
High activity level (June)
Low activity level (July)
Change
Units Shipped
8
2
6
Shipping Expense
$2,700
1,200
$1,500
Variable cost element:
Change in expense $1,500
=
=$250 per unit.
Change in activity 6 units
Fixed cost element:
Shipping expense at high activity level........................................... $2,700
Less variable cost element ($250 per unit × 8 units)....................... 2,000
Total fixed cost............................................................................. $ 700
The cost formula is $700 per month plus $250 per unit shipped or
Y = $700 + $250X.
2. a) See the graph on the following page.
b) Note: Students’ answers will vary, depending on how they visually fit the
regression line to the data.
Total cost at 4 units shipped per month [approximate
amount]....................................................................................
Total cost at 6 units shipped per month [approximate
amount]....................................................................................
Change in cost..............................................................................
Variable cost per unit [$430 ÷ 2 units]
Fixed cost element (where the regression line intersects the Y
axis)..........................................................................................
$ 1,700
$2,130
$ 430
$ 215
$ 820
The cost formula is $820per month plus $215 per unit shipped or
Y = $820+ $215X.
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Exercise 6-4 (continued)
2. a) The scattergraph would be:
$3,000
Shipping Expense
$2,500
$2,000
$1,500
$1,000
$500
$0
1
2
3
4
5
6
7
8
9
3. The
cost of
shipping
units is
likely to
depend on
the weight
and volume
of the units
and the
distance
traveled as
well as on
the number
of units
shipped.
Units Shipped
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Exercise 6-5 (30 minutes) (LO2 CC7, 9)
Kilometres
Driven
105,000
70,000
35,000
1.
High level of activity
Low level of activity
Change
Total Annual
Cost*
$13,298
10,150
$ 3,148
105,000 kilometres × $0.12665 per kilometre= $13,298
70,000 kilometres × $0.145 per kilometre = $10,150
Variable cost per kilometre:
Change in cost
$3,148
=
=$0.09 per kilometer.
Change in activity 35,000 kilometers
Fixed cost per year:
Total cost at 70,000 kilometres......................................................
$10,150
Less variable portion
70,000 kilometres × $0.09 per kilometre.....................................
6,300
Fixed cost per year........................................................................
$ 3,850
2. Y = $3,850 + $0.009X.
3. Fixed cost.....................................................................................
$ 3,850
Variable cost
80,000 kilometres × $0.09 per kilometre.....................................7,200
Total annual cost...........................................................................
$11,050
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Exercise 6-6 (15 minutes) (LO1 CC1, 3; LO2 CC7; LO3 CC12)
1. The company’s variable cost per unit would be:
DM + DL + VOH + Sales commission = $12 + $7 + $3+ $31= $25.00
1
Sales Commission ($60 * 5%) = $3
Cost equation = Y = a + bX
Y = $38,000 + $25X
2. The contribution margin per bike:
Sales ...........................................................................................
$60
Less variable expenses..................................................................
25
Contribution margin......................................................................
$35
For each bike, contribution margin = $35, and
Contribution margin percentage = $35 ÷ $ 60 ≈ 58.33%
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Exercise 6-7 (30 minutes) (LO1 CC1, 3; LO3 CC12)
1. The company’s variable cost per unit would be:
$180,000
=$6 per unit.
30,000 units
The company’s average fixed cost per unit at 40,000 units of volume is $7.50. This
means that total fixed cost amounts to $300,000 (40,000 ˣ $7.50 per unit).
In accordance with the behaviour of variable and fixed costs, the completed schedule
would be:
Units produced and sold
30,000
40,000
50,000
Total costs:
Variable costs @ 6/unit
Fixed costs
Total costs
Cost per unit:
Variable cost
Fixed cost
Total cost per unit
$180,000
300,000
$480,000
$240,000
300,000
$540,000
$300,000
300,000
$600,000
$ 6.00
10.00
$16.00
$ 6.00
7.50
$13.50
$ 6.00
6.00
$12.00
2. The company’s income statement in the contribution format would be:
Sales (45,000 units × $16 per unit)................................................
$720,000
Less variable expenses
(45,000 units × $6 per unit).......................................................
270,000
Contribution margin......................................................................
450,000
Less fixed expense........................................................................
300,000
Net income...................................................................................
$150,000
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Problem 6-1(LO2 CC9) (30 minutes)
1. a) Change in cost:
Monthly operating costs at 90% occupancy (high level of
activity):
450 beds × 90% = 405 beds;
405 beds × 30 days × $29 per bed-day...................................... $352,350
Monthly operating costs at 50% occupancy (low level, given).......... 326,700
Change in cost.............................................................................. $ 25,650
Change in activity:
90% occupancy (450 beds × 90% × 30 days).............................
50% occupancy (450 beds × 50% × 30 days).............................
Change in activity......................................................................
12,150
6,750
5,400
Change in cost
$25,650
=
=$4.75 per bed-day.
Change in activity 5,400 bed-days
b) Monthly operating costs at 90% occupancy (above)........................$352,350
Less variable costs
405 beds × 30 days × $4.75 per bed-day.................................... 57,713
Fixed operating costs per month....................................................$294,637
2. 450 beds × 70% = 315 beds occupied.
Fixed costs...................................................................................
Variable costs: 315 beds × 30 days × $4.75 per bed-day................
Total expected costs......................................................................
$294,637
44,888
$339,525
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Problem 6-2(LO2 CC10) (45 minutes)
1. The scattergraph is presented below.
Y
Total cost
18400
18100
18000
17000
16500
15700
15300
15000
14300
13000
Total cost
X
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Problem 6-2 (continued)
2. (Note: Students’ answers will vary, depending on how they draw their regression
line.)
The fixed cost element can be obtained by noting the point where the regression
line intersects the vertical (cost) axis. As shown on the scattergraph, this point is at
approximately $2,500 per month. Given this figure, the variable cost element can be
obtained by the following computation:
Total cost at 10,000 kilometres driven per month
[approximate amount]...............................................................
$16,110
Total cost at 5,000 kilometres driven per month
[approximate amount]...............................................................
$13,730
Change in cost..............................................................................
$ 2,380
Variable cost per kilometre [$2,380 ÷ 5,000 kilometre]...................
$ 0.476
Fixed cost (where the regression line intersects the Y axis)..............
$11,350
Therefore, the cost of operating the autos can be expressed as $11,350 per month
plus $0.476 per kilometre driven or
Y = $11,350 + $0.476X.
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Problem 6-3(LO2 CC8, 9, 10) (60 minutes)
1. High-low method:
High level of activity
Low level of activity
Change
Variable rate:
Fixed cost:
Number of
Scans
260
40
220
Utilities Cost
$16,000
4,250
$11,750
Change in cost
$11,750
=
=$53.41 per scan
Change in activity 220 scans
.
Total cost at high level of activity...................................................
$16,000
Less variable element:
260 scans × $53.41 per scan......................................................
13,887
Fixed cost element........................................................................
$2,113
Therefore, the cost formula is: Y = $2,113 + $53.41X.
2. Scattergraph method (see the scattergraph on the following page):
(Note: Students’ answers will vary according to their placement of the regression
line.)
Total cost at 200 scans [approximate amount]................................$13,250
Total cost at 100 scans [approximate amount]................................$ 7,290
Change in cost
$5,960
Variable element per scan [$5,960 ÷ 100 scans]
$59.60
Fixed cost element [where the regression line intersects the Yaxis].......................................................................................... $ 1,530
Therefore, the cost formula is: Y = $1,530 + $59.60X.
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Problem 6-3 (continued)
The completed scattergraph:
3. Least-squares Regression
Cost formula:
Y = $1,716 + $59.92X.
4. The cost formulas from the three methods are as follows:
High-low method:
Y = $2,113 + $53.41X.
Scattergraph:
Y = $1,530 + $59.60X.
Least-squares regression: Y = $1,716 + $59.92X.
The estimates from the scattergraph and least-squares regression are close but the
estimates from the high-low method are significantly different. This one again shows
that using only two end points to compute the cost estimates can be problematic.
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Problem 6-4(LO1 CC1, 3, 6; LO2 CC9; LO3 CC12) (45 minutes)
1. Cost of goods sold
Advertising expense
Shipping expense
Salaries and commissions
Insurance expense
Depreciation expense
Variable
Fixed
Mixed
Mixed
Fixed
Fixed
2. Analysis of the mixed expenses:
Shipping
Expense
A$38,000
34,000
A$ 4,000
Units
5,000
4,000
1,000
High level of activity
Low level of activity
Change
Salaries and
Commission
Expense
A$90,000
78,000
A$12,000
Variable cost element:
Variable rate=
Change in cost
Change in activity
Shipping expense:
A$4,000
=A$4 per unit.
1,000 units
Salaries and Commission Expense:
A$12,000
=A$12 per unit.
1,000 units
Fixed cost element:
Cost at high level of activity
Less variable cost element:
5,000 units × A$4 per unit
5,000 units × A$12 per unit
Fixed cost element
Shipping
Expense
A$38,000
Salaries and
Commission
Expense
A$90,000
20,000
A$18,000
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A$30,000
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Problem 6-4 (continued)
The cost formulas are:
Shipping expense:
A$18,000 per month plus A$4 per unit
or
Y = A$18,000 + A$4X.
Salaries and commission expense:
A$30,000 per month plus A$12 per unit
or
Y = A$30,000 + A$12X.
3.
Morrisey& Brown, Ltd.
Income Statement
For the Month Ended September 30
Sales in units................................................................................
Sales revenue (@ A$100 per unit)..................................................
Less variable expenses:
Cost of goods sold (@ A$60 per unit)..........................................
A$300,000
Shipping expense (@ A$4 per unit).............................................
20,000
Salaries and commissions expense
(@ A$12 per unit)...................................................................
60,000
Contribution margin......................................................................
Less fixed expenses:
Advertising expense...................................................................
21,000
Shipping expense.......................................................................
18,000
Salaries and commissions expense..............................................
30,000
Insurance expense.....................................................................
6,000
Depreciation expense.................................................................
15,000
Net income...................................................................................
5,000
A$500,000
380,000
120,000
90,000
A$30,000
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Problem 6-5 (LO1 CC1, 2, 3, 6)(30 minutes)
1.
a.
b.
3
6
c.
d.
11
1
e.
f.
4
10
g.
h.
2
7
i. 9
2. Without knowledge of the underlying cost behaviour patterns, it would be difficult if
not impossible for a manager to properly analyze the firm’s cost structure. The
reason is that all costs don’t behave in the same way. One cost might move in one
direction as a result of a particular action, and another cost might move in an
opposite direction. Unless the behaviour pattern of each cost is clearly understood,
the impact of a firm’s activities on its costs will not be known until after the activity
has occurred.
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Problem 6-6(LO2 CC9)(60 minutes)
1. Maintenance cost at the 150,000 direct labour-hour level of activity can be isolated
as follows:
Total factory overhead cost
Deduct:
Indirect materials @ ¥42 per DLH*
Rent
Maintenance cost
Level of Activity
100,000 DLH
150,000 DLH
¥12,450,000
¥15,275,000
(4,200,000)
(5,500,000)
¥ 2,750,000
(6,300,000)
(5,500,000)
¥ 3,475,000
* ¥4,200,000 ÷ 100,000 DLH = ¥42 per DLH.
2. High-low analysis of maintenance cost:
Direct LabourHours
150,000
100,000
50,000
High level of activity
Low level of activity
Change
Maintenance Cost
¥3,475,000
2,750,000
¥ 725,000
Variable cost element:
Change in cost
¥725,000
=
=¥14.50 per DLH
Change in activity 50,000 DLH
.
Fixed cost element:
Total cost at the high level of activity.............................................
¥3,475,000
Less variable cost element
(¥14.50 per DLH × 150,000 DLH)...............................................
2,175,000
Fixed cost element........................................................................
¥1,300,000
Therefore, the cost formula for maintenance is: ¥1,300,000 per year plus ¥14.50 per
direct labour-hour or
Y = ¥1,300,000 + ¥14.50X.
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Problem 6-6 (continued)
3. Total factory overhead cost at 70,000 direct labour-hours would be:
Indirect materials
(70,000 DLH × ¥42 per DLH)...................................................... ¥ 2,940,000
Rent.............................................................................................
5,500,000
Maintenance:
Variable cost element
(70,000 DLH × ¥14.50 per DLH)..............................................
¥1,015,000
Fixed cost element.....................................................................
1,300,000
2,315,000
Total factory overhead cost............................................................ ¥10,755,000
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Problem 6-7(LO2 CC9)(60 minutes)
1. Maintenance cost at the 90,000 machine-hour level of activity can be isolated as
follows:
Level of Activity
60,000 MHs
90,000 MHs
$174,000
$246,000
Total factory overhead cost
Deduct:
Utilities cost @ $0.80 per MH*
Supervisory salaries
Maintenance cost
48,000
21,000
$105,000
72,000
21,000
$153,000
*$48,000 ÷ 60,000 MHs = $0.80 per MH.
2. High-low analysis of maintenance cost:
High activity level
Low activity level
Change
MachineHours
90,000
60,000
30,000
Maintenance
Cost
$153,000
105,000
$ 48,000
Variable rate:
Change in cost
$48,000
=
=$1.60 per MH.
Change in activity 30,000 MHs
Total fixed cost:
Total maintenance cost at the high activity level..............................
$153,000
Less variable cost element
(90,000 MHs × $1.60 per MH)....................................................
144,000
Fixed cost element........................................................................
$ 9,000
Therefore, the cost formula for maintenance is: $9,000 per month plus $1.60 per
machine-hour or
Y = $9,000 + $1.60X.
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Problem 6-7 (continued)
3.
Maintenance cost
Utilities cost
Supervisory salaries cost
Totals
Variable Rate
per MachineHour
$1.60
0.80
$2.40
Fixed Cost
$ 9,000
21,000
$30,000
Thus, the cost formula would be: Y = $30,000 + $2.40X.
4. Total overhead cost at an activity level of 75,000 machine-hours:
Fixed costs...................................................................................
$ 30,000
Variable costs: $2.40 per MH × 75,000 MHs...................................
180,000
Total overhead costs.....................................................................
$210,000
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Problem 6-8 (LO2 CC9; CHAPTER 2 LO6 CC12) (75 minutes)
1.
Direct materials cost @ $10.00 per unit
Direct labour cost @ $12.00 per unit
Manufacturing overhead cost*
Total manufacturing costs
Add: Work in process, beginning
Deduct: Work in process, ending
Cost of goods manufactured
March—Low
5,000 Units
$ 50,000
60,000
144,000
254,000
29,000
283,000
15,000
$268,000
June—High
9,000 Units
$ 90,000
108,000
168,000
366,000
52,000
418,000
21,000
$397,000
*Computed by working upwards through the statements.
2.
June—High level of activity
March—Low level of activity
Change
Units
Produced
9,000
5,000
4,000
Cost
Observed
$168,000
144,000
$ 24,000
Change in cost
$24,000
=
=$6 per unit
Change in activity
4,000 units
.
Total cost at the high level of activity.............................................
$168,000
Less variable cost element
($6 per unit × 9,000 units).........................................................
54,000
Fixed cost element........................................................................
$ 114,000
Therefore, the cost formula is: $114,000 per month, plus $6.00 per unit produced or
Y = $114,000 + $6.00X.
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Problem 6-8 (continued)
3. The cost of goods manufactured if 7,000 units are produced:
Direct materials cost ($10.00 per unit × 7,000 units).......................
Direct labour cost ($12.00 per unit × 7,000 units)...........................
Manufacturing overhead cost:
Fixed portion.............................................................................
$114,000
Variable portion ($6.00 per unit × 7,000 units)............................
42,000
Total manufacturing costs..............................................................
$ 70,000
84,000
Cost of goods manufactured..........................................................
$310,000
156,000
310,000
Note: The question states that there is no change in work-in-process inventory;
therefore the Cost of goods manufactured will be the same as the Total manufacturing
costs.
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Problem 6-9 (LO1 CC5; LO2 CC9, 11) (60 minutes)
1.
1
We can use the equation format Y= a + bX, where
y = customer service costs,
a = fixed cost portion
b = variable cost per customer
x = number of customers
b = ($679,440 - $479,280) ÷ (498 - 318)
= $200,160 ÷ 180 = $1,112 per customer
a = $679,440 - ($1,112 X 498)
= $679,440 - $553,776 = $125,664 per month
Monthly cost equation: Y = $125,664 + $1,112X per customer
2.
2Y550 = $125,664 + $1,112 × 550 = $737,264
Although this calculation may provide a rough estimate of the costs at the level of 550
customers the estimate suffers from the limitation that 550 customers is outside of the
high-low range of customers which were used to perform the computations. It is quite
possible that the cost structure could be different when operating outside of the
relevant range of operations (e.g., fixed costs may increase).
3.
3
Least-squares Regression
Cost formula:
Y = $82,231 + $1,227.02X
The R2 is 91.5%, which means that only 8.5% of the variation in customer service costs
is not explained by the number of customers. This would suggest that number of
customers in the month is a reliable basis for estimating customer service cost.
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Problem 6-10 (LO3 CC12) (30 minutes)
1.
Variable portion of the cost of goods sold (COGS) = 65%
= 65% × $3,840,000
= $2,496,000
On a per unit basis, variable cost
= $2,496,000 ÷ 2,500 units
= $998.40 per unit
Therefore, fixed portion of GOGS
= $3,840,000 - $2,496,000
= $1,344,000
Therefore the cost formula for COGS is as follows:
Y = $1,344,000 per quarter + $998.40X
Where X = number of units
Fixed portion of selling expenses = $800,000
Therefore, variable portion
= $1,024,000 - $800,000
= $224,000
On a per unit basis, variable cost
= $224,000 ÷ 2,500 units
= $89.60 per unit
Therefore the cost formula for selling expenses is as follows:
Y = $800,000 per quarter + $89.60X
Administrative expenses of $1,000,000 are entirely fixed.
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Problem 6-10 (continued)
2.
The contribution margin income statement will be as follows:
Sales (2,500 units@$2,800 per
unit)
Less: Variable Costs
COGS
Selling expenses
Contribution margin
Less: fixed expenses
COGS
Selling expenses
Administrative expenses
Income
$ 2,496,000
$
224,000
$ 1,344,000
$
800,000
$ 1,000,000
$
7,000,000
$
2,720,000
$
4,280,000
$
$
3,144,000
1,136,000
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Problem 6-11 (LO1 – CC1, 3, 6; LO2 – CC7, 9; LO3 – CC12) (40 minutes)
1.
Three of the six expense items are fixed in nature: Advertising; Insurance and
Depreciation. The cost equations for these expenses are as follows:
Advertising:
Insurance:
Depreciation:
Y= $70,000
Y=$9,000
Y=$42,000
The remaining three are mixed in nature. We can use the high-low method to separate
the variable and fixed components of these mixed costs.
The variable component can be computed as shown below:
Observed Costs
Sales Units
High activity –
June
Low activity April
Difference
COGS
Shipping
Salaries &
Commissions
6,000
$426,000
$71,000
$180,500
4,500
$342,000
$56,000
$143,000
1,500
$ 84,000
$15,000
$ 37,500
The variable cost portion for COGS, Shipping & Salaries and Commissions, respectively,
are computed as shown below:
Change in cost
$84,000
=
=$56 per unit
Change in activity 1,500 units
Change in cost
$15,000
=
=$10 per unit
Change in activity 1,500 units
Change in cost
$37,500
=
=$25 per unit
Change in activity 1,500 units
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Problem 6-11 (continued)
The fixed cost portion is computed as follows:
COGS:
Fixed cost
= $426,000 – (6,000ˣ $56) =
= $342,000 – (4,500 ˣ $56) =
$90,000
$90,000
= $71,000 – (6,000ˣ $10) =
= $71,000 – (4,500 ˣ $10) =
$11,000
$11,000
Shipping:
Fixed cost
Salaries and Commissions:
Fixed cost
= $180,500 – (6,000ˣ $25) =
= $143,000 – (4,500 ˣ $25) =
$30,500
$30,500
The cost equations are as follows:
COGS:
Y= $90,000 + 56X
Shipping:
Y=$11,000 + 10X
Salaries and commissions:
Y=$30,500 + 25X
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Problem 6-11 (continued)
2.
Central Valley Company
Contribution Income Statement
For the month ended September 30
Sales (5,500 ˣ $1401)
Variable costs:
COGS
(5,500 ˣ $56)
Shipping (5,500 ˣ $10)
Commissions2 (5,500 ˣ $25)
Contribution margin
Less fixed costs:
Cost of goods sold
Shipping
Advertising
Salaries2
Insurance
Depreciation
Net income
$770,000
$308,000
55,000
137,500
90,000
11,000
70,000
30,500
9,000
42,000
500,500
269,500
252,500
$ 17,000
1
Average sales price is computed by dividing the sales revenue by the number of units
sold for any of the four months for which data is provided (e.g., $840,000 ÷ 6,000 =
$140).
2
Of the Salaries & Commissions expense, it is assumed that ‘commissions’ is the
variable portion and ‘salaries’ is the fixed portion.
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Comprehensive Problem (LO1CC5; LO2CC9, 10)(60 minutes)
1. High-low method:
Year 1
High level of activity
Low level of activity
Change
Hours
84,000
35,000
49,000
Cost
$990,450
645,000
$345,450
Variable element: $345,450 ÷ 49,000 DLH = $7.05 per DLH.
Fixed element:
Total cost at 84,000 DLH
Less variable element:
84,000 DLH × $7.05 per DLH
Fixed element
$990,450
592,200
$398,250
Therefore, the cost formula is: Y = $398,250 + $7.05X.
Year 2
High level of activity
Low level of activity
Change
Hours
87,500
42,000
45,500
Cost
$928,450
675,000
$253,450
Variable element: $253,450 ÷ 45,500 DLH ≈ $5.57 per DLH.
Fixed element:
Total cost at 87,500 DLH
Less variable element:
87,500 DLH × $5.57 per DLH
Fixed element
$928,450
487,375
$441,075
Therefore, the cost formula is: Y = $441,075 + $5.57X.
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Combined
Hours
87,500
35,000
52,500
High level of activity
Low level of activity
Change
Cost
$928,450
645,000
$283,450
Variable element: $283,450 ÷ 52,500 DLH ≈ $5.40 per DLH.
Fixed element:
Total cost at 87,500 DLH
Less variable element:
87,500 DLH × $5.40 per DLH
Fixed element
$928,450
472,500
$455,590
Therefore, the cost formula is: Y = $455,590 + $5.40X.
2. Least-squares regression method:
Year 1
Variable cost
Fixed cost
≈ $6.00 per DLH
≈ $410,307
Therefore, the cost formula is as follows: Y = $410,307 + $6.00X (Adjusted R 2 =
80.8%)
Year 2
Variable cost
Fixed cost
≈ $6.09 per DLH
≈ $397,315
Therefore, the cost formula is as follows: Y = $397,315 + $6.09X (Adjusted R 2 =
87.8%)
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Comprehensive Problem (continued)
Combined
Variable cost
Fixed cost
≈ $6.04 per DLH
≈ $404,522
Therefore, the cost formula is as follows: Y = $404,522 + $6.04X (Adjusted R 2 =
84.7%)
3. a) High-low method:
Variable (@$5.40 per DLH)
Fixed
Total
78,750 labour hours
$425,250
455,590
$880,840
54,500 labour hours
$294,300
455,590
$749,890
b) Least-squares regression method:
Variable (@$6.04 per DLH)
Fixed
Total
4.
78,750 labour hours
$475,650
404,522
$880,172
54,500 labour hours
$329,180
404,522
$733,702
It is interesting to note that the total costs are very similar for an estimated
78,750 direct labour hours but not for 54,500 direct labour hours. This clearly
indicates that management has to be careful about the method that is chosen to
develop a cost equation. This may be a good example of why ascattergraph
should be the starting point in all cost analysis work – it is a visual method. The
problem also states that at least one overhead cost item (equipment lease) has a
cost pattern where the amount is fixed up to 70,000 direct labour hours, whereas
a cost formula does not necessarily recognize such a pattern. Therefore in this
particular case neither of the two methods may be very reliable.
Moreover the high-low method is always suspect since it relies on only two points
(which in this case gives the regression line too steep of a slope). In contrast,
the least-squares regression method uses all data points.
5. The relevant range concept is particularly important in this company due to the flat
fee on lease equipment up to a certain volume of direct labour hours.
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Analytical Thinking (LO2 CC9, 11) (60 minutes)
1. High-low method (using number of orders):
Orders
High level of activity
1,650
Low level of activity
900
Change
750
Cost
$25,000
15,000
$10,000
Variable element: $10,000 ÷ 750 orders = $13.333 per order.
Fixed element:
Total cost—1,650 orders
Less variable element:
1,650 orders × $13.333 per order
Fixed element
$25,000
22,000
$3,000
Therefore, the cost formula is: Y = $3,000 + $13.333X.
High-low method (using kilograms of materials):
Kgs.
Cost
High level of activity
55,000
$25,500
Low level of activity
23,000
15,240
Change
32,000
$10,260
Variable element: $10,260 ÷ 32,000 kgs. = $0.321 per kg.
Fixed element:
Total cost—55,000 kgs.
Less variable element:
55,000 orders × $0.321 per kg
Fixed element
$25,500
17,634
$7,866
Therefore, the cost formula is: Y = $7,866 + $0.321X.
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Analytical Thinking Question (continued)
2.
Least Squares Regression Method (using number of orders)
The cost formula is Y = $1,364 per month + $15.219X
Least Squares Regression Method (using kilograms of materials)
The cost formula is Y = $10,958 per month + $0.268X
Note to instructor = The above formulas were developed based on regression results
computed using Excel.
3.
Cost estimation based on number of orders:
Month
1 (1,200 orders)
2 (1,200 orders)
1
2
High-Low Method
$19,0001
$19,000
Regression Method
$19,6272
$19,627
$3,000 + $13.333 × 1,200 orders ≈$19,000
$1,364 + $15.219 × 1,200 orders ≈$19,627
Cost estimation based on kilograms of materials:
Month
1 (40,000 kilograms)
2 (50,000 kilograms)
1
2
3
4
High-Low Method
$20,6911
$23,8972
Regression Method
$21,6783
$24,3584
$7,866 + $0.321 × 40,000 kilograms = $20,691
$7,866 + $0.321 × 50,000 kilograms = $23,897
$10,958 + $0.268 × 40,000 kilograms = $21,678
$10,958 + $0.268 × 50,000 kilograms = $24,358
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Analytical Thinking Question (continued)
4.
Clearly, there is a difference in the cost formulas when using the different methods and
the different activity bases. Conceptually, the least-squares regression method is
superior to the high-low method because it uses all the data points in calculating the
slope (variable portion) and the intercept (fixed portion).
As to whether number of orders or kilograms of materials is a better activity base, it
would be useful to look at the R2 for the two regressions. The adjusted R2,when
number of orders is used, is about 94.8% which means that just 5.2% of the variation
in Y is not explained by the variation in X. On the other hand the adjusted R 2, when
kilograms of materials is used, is just 45% which means close to 55% of the variation in
Y is not explained by the variation in X. This clearly suggests that number of orders is a
superior independent variable (activity base) for the set of data used in the calculations.
Note to the instructor: This question can provide a good discussion of activity-based
costing covered in Chapter 5.
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Communicating in Practice(LO1 CC1, 2, 3, 5, 6)(45 minutes)
Note to the instructor: The issues raised in this assignment will challenge your students
to think about the application of the concepts covered in this chapter.
Date:
To:
From:
Subject:
Current Date
Maria Chavez
Student’s Name
Cost Estimate
You must consider cost behaviour when estimating future costs, such as the cost of
catering a cocktail party. A variable cost is a cost whose total dollar amount varies in
direct proportion to changes in the activity level (in your case, the number of guests). A
fixed cost is a cost whose total dollar amount remains constant within a relevant range
of activity. A mixed cost is one that contains both variable and fixed cost elements.
Food and beverage and labour are examples of variable costs. These costs increase in
total as the number of guests increases. On the other hand, overhead cost is an
example of a mixed cost. It has both variable and fixed cost elements. The personnel
costs that increase as you take on additional jobs are an example of a variable cost,
while the annual office rent is an example of a fixed cost.
Before you make a decision about what to bid on this event, you should remove the
amount of fixed overhead from your total estimated cost per guest to arrive at your
total estimated variable cost per guest. To do this, you need to break your overhead
cost down into its variable and fixed components. There are a variety of methods that
you can use to break down this mixed cost.
Finally, you noted that you are not willing to lose money on the fund-raising cocktail
party. Because this cocktail party will not require you to incur any additional fixed
expenses, your bid just needs to cover your variable expenses in order for the party to
be profitable. (Note: This assumes that your other orders generate enough revenue to
cover your fixed expenses and generate a profit.) As such, any bid amount that exceeds
your total variable cost per guest will generate a contribution margin that will help you
cover fixed expenses and generate a profit. When all your fixed expenses are fully
covered, the contribution margin generated by an additional order will directly increase
your profit.
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Ethics Challenge(LO1 – CC1, 3; LO2 – CC9, 10, 11; LO3 – CC12)
1. Unlike the high-low and least squares regression method, the scatter-graph
method relies on the analyst’s interpretation of the scatter-plots of the data, and
this can introduce an element of subjectivity in terms of how the analyst may
draw the line to compute the slope and the intercept. Altering the slope can lead
to reporting a higher (lower) variable cost which then affects the contribution
margin. This has the potential to affect decisions that a manager may make.
2. Any manager who knowingly alters the cost pattern to influence decisions may
be in violation of the ‘integrity’ and ‘competence’ elements of professional
conduct.
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Teamwork in Action
1.
A variable cost is a cost whose total dollar amount varies in direct proportion to changes
in the activity level.A fixed cost remains constant in total dollar amount within a certain
relevant range of activity.A mixed cost is one that includes both a variable portion and a
fixed portion.
2.
The costs necessary to manufacture chocolate chip cookies might include, but would
not be limited to, the following:
Product Components and Costs
Ingredients (such as flour, chocolate,
chips, sugar, salt, etc.)
Packages
Corrugated shipping boxes
Assembly line workers (mixers, bakers,
packagers, etc.)
Depreciation on building
Depreciation on machinery
Insurance
Factory supplies
Lubricants
Property taxes on building
Supervisors
Telephone
Utilities (electricity, water, etc.)
Type of
Product Cost
Type of
Cost Behaviour
Direct materials
Direct materials
Direct materials
Variable
Variable
Variable
Direct labour
Overhead
Overhead
Overhead
Overhead
Overhead
Overhead
Overhead
Overhead
Overhead
Variable (1)
Fixed
Fixed (2)
Fixed
Mixed
Variable
Fixed
Fixed (if salaried)
Mixed
Mixed
1.
Assumed; however, see related discussion of whether direct labour is a variable
or fixed cost in the text.
2.
Unless units of production method is used to calculate depreciation expense, then
variable.
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