Chapter 6
Cost Behaviour: Analysis and Use
Solutions to Questions
6-1 An activity base is a measure of whatever
causes the incurrence of a variable cost.
6-2
a. Unit fixed costs increase as volume decreases.
b. Unit variable costs remain constant as volume decreases.
c. Total fixed costs remain constant as volume
decreases.
d. Total variable costs decrease as volume decreases.
6-3
a. Cost behaviour: Cost behaviour refers to the
way in which costs change in response to
changes in a measure of activity such as
sales volume, production volume, or orders
processed.
b. Relevant range: The relevant range is the
range of activity within which assumptions
about variable and fixed cost behaviour are
valid.
6-4
A curvilinear cost is one where the relationship between the cost and activity is a curve
rather than a straight line. Examples include:
utilities where the amount charged per unit increases as the amount used increases; and
wages where the rate per hour increases as
more hours are worked and overtime is paid.
6-5
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. Step-variable cost: A step-variable cost is a
cost that is incurred in large chunks, and
which increases or decreases only in response to fairly wide changes in activity.
Mixed Cost
Variable Cost
Cost
Step-Variable Cost
Activity
6-6
The linear assumption is reasonably valid providing that the cost formula is used only
within the relevant range.
6-7
A discretionary fixed cost has a fairly
short planning horizon—usually a year. Such
costs arise from annual decisions by management to spend on certain fixed cost items, such
as advertising, research, and management development. A committed fixed cost 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, they are “locked
in” for many years.
6-8
a. Committed
b. Discretionary
c. Discretionary
d. Committed
e. Committed
f. Discretionary
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Solutions Manual, Chapter 6
1
6-9
Yes. As the anticipated level of activity
changes, the level of fixed costs needed to support operations may also change. Most fixed
costs are adjusted upward and downward in
large steps, rather than being absolutely fixed at
one level for all ranges of activity.
6-10 The engineering approach to cost analysis is a detailed analysis of cost behaviour based
on an industrial engineer’s evaluation of the inputs that are required to carry out an activity
and of the costs of those inputs. It could be
used to estimate the costs of a new product not
previously produced. It could also be used to
determine the cost of providing a particular service or department such as customer complaints.
6-11 The major disadvantage of the high-low
method is that it uses only two data points, the
highest and lowest levels of activity. If either of
these points is an extreme value (well above or
well below normal activity levels) the accuracy
of the cost estimation model will be reduced.
levels are being used to predict the costs, not
vice-versa. Accordingly, the high-low activity
levels provide the greatest possible variation in
the selected cost driver.
6-13 The formula for a mixed cost is Y = a +
bX. In cost analysis, the “a” term represents the
fixed cost, and the “b” term represents the variable cost per unit of activity.
6-14 The contribution approach income
statement organizes costs by behaviour, first
deducting variable expenses to obtain contribution margin, and then deducting fixed expenses
to obtain operating income. The traditional
approach organizes costs by function, such as
production, selling, and administration. Within a
functional area, fixed and variable costs are intermingled.
6-12 The high-low activity levels are used
instead of the high-low costs because activity
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2
Managerial Accounting, 9th Canadian Edition
Exercise 6-1 (15 minutes)
1.
Smoothies Served
in a Week
2,100
2,800
3,500
Fixed cost ......................................................................
$2,500
$2,500
$2,500
Variable cost ($0.75 per cup) ..........................................
1,575
2,100
2,625
Total cost ......................................................................
$4,075
$4,600
$5,125
Cost per smoothie served * ............................................
$1.94
$1.64
$1.46
* Total cost ÷ smoothies served in a week
2. The average cost of a smoothie declines as the number of smoothies
served increases because the fixed cost is spread over more units.
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Solutions Manual, Chapter 6
3
Exercise 6-2 (30 minutes)
1. The completed scattergraph is presented below:
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4
Managerial Accounting, 9th Canadian Edition
Exercise 6-2 (continued)
2. (Students’ answers will vary considerably due to the inherent imprecision and subjectivity of the scattergraph method of estimating variable
and fixed costs.)
The approximate monthly fixed cost is $6,000—the point where the
straight line intersects the cost axis.
The variable cost per unit processed can be estimated as follows using
the 8,000-unit level of activity, which falls on the straight line:
Total cost at the 8,000-unit level of activity ...........
Less fixed costs ...................................................
Variable costs at the 8,000-unit level of activity .....
$14,000
6,000
$ 8,000
$8,000 ÷ 8,000 units = $1 per unit.
Observe from the scattergraph that if the company used the high-low
method to determine the slope of the line, the line would be too steep.
This would result in underestimating the fixed cost and overestimating
the variable cost per unit.
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Solutions Manual, Chapter 6
5
Exercise 6-3 (20 minutes)
1.
Month
High activity level (August) ..
Low activity level (October)..
Change ...............................
OccupancyDays
3,608
186
3,422
Electrical
Costs
$8,111
1,712
$6,399
Variable cost = Change in cost ÷ Change in activity
= $6,399 ÷ 3,422 occupancy-days
= $1.87 per occupancy-day
Total cost (August) ....................................................
Variable cost element
($1.87 per occupancy-day × 3,608 occupancy-days)
Fixed cost element ....................................................
$8,111
6,747
$1,364
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 effects on the fixed electrical costs.
Additionally, fixed costs will be affected by how many days are in a
month. In other words, costs like the costs of lighting common 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.
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6
Managerial Accounting, 9th Canadian Edition
Exercise 6-4 (20 minutes)
1
.
The Rhythm Shop
Income Statement—Acoustic Guitar Department
For the Quarter Ended March 31
Sales ................................................................
Variable expenses:
Cost of goods sold ($400 per guitar ×
$800,000
2,000 guitars*) ............................................
Selling expenses ($75 per guitar × 2,000
150,000
guitars) .......................................................
Administrative expenses (25% ×
50,000
$200,000) ...................................................
Contribution margin ..........................................
Fixed expenses:
Selling expenses (400,000-150,000) ................250,000
Administrative expenses(75% x 200,000) ........150,000
Operating income .............................................
$1,600,000
1,000,000
600,000
400,000
$ 200,000
*$1,600,000 sales ÷ $800 per guitar = 2,000 guitars.
2. Since 2,000 guitars were sold and the contribution margin totaled
$600,000 for the quarter, the contribution of each guitar toward fixed
expenses and profits was $300 ($600,000 ÷ 2,000 guitars = $300 per
guitar). Another way to compute the $300 is:
Selling price per guitar .......................
Less variable expenses:
Cost per guitar ................................
Selling expenses..............................
Administrative expenses
($50,000 ÷ 2,000 guitar) ..............
Contribution margin per guitar ............
$800
$400
75
25
500
$300
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Solutions Manual, Chapter 6
7
Exercise 6-4 (continued)
3. If the Rhythm Shop sells 100 more guitars in the quarter ending June
30, than they did for the quarter ending March 31, profits will increase
by:
100 x $300* per guitar = $30,000
*$800 selling price - $500 total variable cost per guitar
Total operating income for the quarter ended June 30 will be:
Operating income for the Quarter ended March 31
Contribution margin from additional unit sales
Total operating income**
** Check:
2,100 guitars sold x $300/guitar
Less fixed expenses
Total operating income
$200,000
30,000
$230,000
$630,000
400,000
$230,000
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8
Managerial Accounting, 9th Canadian Edition
Exercise 6-5 (20 minutes)
1. The company’s variable cost per unit would be:
$150,000
=$2.50 per unit.
60,000 units
Taking into account the difference in behaviour between variable and
fixed costs, the completed schedule would be:
Units produced and sold
Total costs:
Variable costs .......................
Fixed costs ...........................
Total costs ..............................
Cost per unit:
Variable cost .........................
Fixed cost .............................
Total cost per unit ...................
*Given.
60,000
80,000
100,000
$150,000 *
360,000 *
$510,000 *
$200,000
360,000
$560,000
$250,000
360,000
$610,000
$2.50
6.00
$8.50
$2.50
4.50
$7.00
$2.50
3.60
$6.10
2. The company’s income statement in the contribution format would be:
Sales (90,000 units × $7.50 per unit) ............................
Variable expenses (90,000 units × $2.50 per unit) .........
Contribution margin......................................................
Fixed expenses ............................................................
Operating income .........................................................
$675,000
225,000
450,000
360,000
$ 90,000
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Solutions Manual, Chapter 6
9
Exercise 6-6 (45 minutes)
1.
High activity level ............
Low activity level .............
Change ..........................
Units Shipped
8
2
6
Shipping Expense
$3,600
1,500
$2,100
Variable cost element:
Change in cost
$2,100
=
=$350 per unit
Change in activity 6 units
Fixed cost element:
Shipping expense at the high activity level ...................
Less variable cost element ($350 per unit × 8 units).....
Total fixed cost ...........................................................
$3,600
2,800
$ 800
The cost formula is $800 per month plus $350 per unit shipped or
Y = $800 + $350X,
where X is the number of units shipped.
2. a. See the scattergraph on the following page.
b. (Note: Students’ answers will vary due to the imprecision and subjective nature of this method of estimating variable and fixed costs.)
Total cost at 5 units shipped per month [a point
falling on the line in (a)] ......................................
Less fixed cost element (intersection of the Y axis)..
Variable cost element.............................................
$2,600
1,100
$1,500
$1,500 ÷ 5 units = $300 per unit.
The cost formula is $1,100 per month plus $300 per unit shipped or
Y = $1,100 + 300X,
where X is the number of units shipped.
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10
Managerial Accounting, 9th Canadian Edition
Exercise 6-6 (continued)
2. a. The scattergraph appears below:
3. The cost of shipping units is likely to depend on the weight and volume
of the units shipped and the distance traveled as well as on the number
of units shipped. In addition, higher cost shipping might be necessary to
meet a deadline.
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Solutions Manual, Chapter 6
11
Exercise 6-7 (20 minutes)
1.
High level of activity ............
Low level of activity .............
Change ...............................
Kilometres
Driven
120,000
80,000
40,000
Total Annual
Cost*
$13,920
10,880
$ 3,040
* 120,000 kilometres × $0.116 per kilometre = $13,920
80,000 kilometres × $0.136 per kilometre = $10,880
Variable cost per kilometre:
Change in cost =
Change in activity
$3,040____ = $0.076 per kilometre
40,000 kilometres
Fixed cost per year:
Total cost at 120,000 kilometres ...........................
Less variable cost element:
120,000 kilometres × $0.076 per kilometre ........
Fixed cost per year ..............................................
$13,920
9,120
$ 4,800
2. Y = $4,800 + $0.076X
3. Fixed cost ...............................................................
Variable cost: 100,000 kilometres × $0.076 per
kilometre ..............................................................
Total annual cost .....................................................
$ 4,800
7,600
$12,400
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12
Managerial Accounting, 9th Canadian Edition
Exercise 6-8 (20 minutes)
1.
High activity level (February)........
Low activity level (June) ..............
Change .......................................
Blood Tests
3,500
1,500
2,000
Costs
$14,500
8,500
$ 6,000
Variable cost per blood test:
Change in cost =
$6,000
= $3 per blood test
Change in activity
2,000 blood tests
Fixed cost per month:
Blood test cost at the high activity level ................
Less variable cost element:
3,500 blood tests × $3.00 per test .....................
Total fixed cost ....................................................
$14,500
10,500
$ 4,000
The cost formula is $4,000 per month plus $3.00 per blood test performed or, in terms of the equation for a straight line:
Y = $4,000 + $3.00X
where X is the number of blood tests performed.
2. Expected blood test costs when 2,300 tests are performed:
Variable cost: 2,300 blood tests × $3.00 per test.......
Fixed cost ...............................................................
Total cost ................................................................
$6,900
4,000
$10,900
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Solutions Manual, Chapter 6
13
Exercise 6-9 (30 minutes)
1. The scattergraph appears below.
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14
Managerial Accounting, 9th Canadian Edition
Exercise 6-9 (continued)
2. (Note: Students’ answers will vary considerably due to the inherent lack
of precision and subjectivity of the scattergraph method.)
Total costs at 2,500 blood tests per month [a point
falling on the line in (1)] ......................................... $11,500
Less fixed cost element (intersection of the Y axis).....
3,250
Variable cost element................................................ $8,250
$8,250 ÷ 2,500 blood tests = $3.30 per blood test.
The cost formula is therefore $3,250 per month plus $3.30 per blood
test performed. Written in equation form, the cost formula is:
Y = $3,250 + $3.30X,
where X is the number of blood tests performed.
3. The high-low method would not provide an accurate cost formula in this
situation, since a line drawn through the high and low points would have
a slope that is too flat. Consequently, the high-low method would overestimate the fixed cost and underestimate the variable cost per unit.
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Solutions Manual, Chapter 6
15
Exercise 6-10 (30 minutes)
1. Monthly operating costs at 70% occupancy:
2,000 rooms × 70% = 1,400 rooms;
1,400 rooms × $21 per room per day × 30 days ..
Monthly operating costs at 45% occupancy (given) .
Change in cost ......................................................
Difference in rooms occupied:
70% occupancy (2,000 rooms × 70%).................
45% occupancy (2,000 rooms × 45%).................
Difference in rooms (change in activity) ..................
Variable cost=
$882,000
792,000
$ 90,000
1,400
900
500
Change in cost
$90,000
=
=$180 per room.
Change in activity 500 rooms
$180 per room ÷ 30 days = $6 per room per day.
2. Monthly operating costs at 70% occupancy (above) ..
Less variable costs:
1,400 rooms × $6 per room per day × 30 days ......
Fixed operating costs per month ..............................
$882,000
252,000
$630,000
3. 2,000 rooms × 60% = 1,200 rooms occupied.
Fixed costs ..............................................................
Variable costs:
1,200 rooms × $6 per room per day × 30 days ......
Total expected costs ................................................
$630,000
216,000
$846,000
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16
Managerial Accounting, 9th Canadian Edition
Problem 6-11 (45 minutes)
1.
Home Entertainment
Income Statement
For the Month Ended April 30
Sales (150 televisions × $1,500 per set) .............
Cost of goods sold
(150 televisions × $900 per set) ......................
Gross margin ....................................................
Selling and administrative expenses:
Selling expenses:
Advertising ..................................................
Delivery of televisions
(150 televisions × $40 per set) ...................
Sales salaries and commissions
[$2,900 + (4% × $225,000)] .....................
Utilities ........................................................
Depreciation of sales facilities .......................
Total selling expenses .....................................
Administrative expenses:
Executive salaries .........................................
Depreciation of office equipment...................
Clerical
[$1,500 + (150 televisions × $40 per set)] .
Insurance ....................................................
Total administrative expenses ..........................
Total selling and administrative expenses ............
Operating income ..............................................
$225,000
135,000
90,000
$
950
6,000
11,900
400
3,000
22,250
8,000
500
7,500
400
16,400
38,650
$ 51,350
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Solutions Manual, Chapter 6
17
Problem 6-11 (continued)
2.
Home Entertainment
Income Statement
For the Month Ended April 30
Sales (150 televisions × $1,500 per set) .............
Variable expenses:
Cost of goods sold
(150 televisions × $900 per set) ...................
Delivery of televisions
(150 televisions × $40 per set) .....................
Sales commissions (4% × $225,000) ...............
Clerical (150 televisions × $40 per set) ............
Total variable expenses.................................
Contribution margin...........................................
Fixed expenses:
Advertising .....................................................
Sales salaries ..................................................
Utilities...........................................................
Depreciation of sales facilities ..........................
Executive salaries ...........................................
Depreciation of office equipment .....................
Clerical ...........................................................
Insurance .......................................................
Total fixed expenses ..........................................
Operating income ..............................................
Total
$225,000
Per Unit
$1,500
135,000
900
6,000
9,000
6,000
156,000
69,000
40
60
40
1,040
$ 460
950
2,900
400
3,000
8,000
500
1,500
400
17,650
$ 51,350
3. Fixed costs remain constant in total but vary on a per unit basis with
changes in the activity level. For example, as the activity level increases,
fixed costs decrease on a per unit basis. Showing fixed costs on a per
unit basis on the income statement make them appear to be variable
costs. That is, management might be misled into thinking that the per
unit fixed costs would be the same regardless of how many televisions
were sold during the month. For this reason, fixed costs should be
shown only in totals on a contribution-type income statement.
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18
Managerial Accounting, 9th Canadian Edition
Problem 6-12 (45 minutes)
1. Cost of goods sold ....................
Shipping expense .....................
Advertising expense .................
Salaries and commissions .........
Insurance expense ...................
Depreciation expense ...............
Variable
Mixed
Fixed
Mixed
Fixed
Fixed
2. Analysis of the mixed expenses:
High level of activity .....
Low level of activity ......
Change ........................
Units
4,500
3,000
1,500
Shipping
Expense
£56,000
44,000
£12,000
Salaries and
Comm. Expense
£143,000
107,000
£ 36,000
Variable cost element:
Variable cost per unit =
Shipping expense:
Change in cost
Change in activity
£12,000
= £8 per unit
1,500 units
Salaries and comm. expense:
£36,000
= £24 per unit
1,500 units
Fixed cost element:
Cost at high level of activity ...
Less variable cost element:
4,500 units × £8 per unit ....
4,500 units × £24 per unit...
Fixed cost element ................
Shipping
Expense
£56,000
36,000
£20,000
Salaries and
Comm. Expense
£143,000
108,000
£ 35,000
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Solutions Manual, Chapter 6
19
Problem 6-12 (continued)
The cost formulas are:
Shipping expense: £20,000 per month plus £8 per unit or
Y = £20,000 + £8X.
Salaries and Comm. expense: £35,000 per month plus £24 per unit or
Y = £35,000 + £24X.
3.
Frankel Ltd.
Income Statement
For the Month Ended June 30
Sales revenue ............................................
Variable expenses:
Cost of goods sold
(4,500 units × £56* per unit) ................
Shipping expense
(4,500 units × £8 per unit) ....................
Salaries and commissions expense
(4,500 units × £24 per unit) ..................
Contribution margin....................................
Fixed expenses:
Shipping expense ....................................
Advertising ..............................................
Salaries and commissions .........................
Insurance ................................................
Depreciation ............................................
Operating income .......................................
£630,000
£252,000
36,000
108,000
20,000
70,000
35,000
9,000
42,000
396,000
234,000
176,000
£ 58,000
*Per unit amount based on low level of sales activity: £168,000 ÷ 3,000
= £56
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20
Managerial Accounting, 9th Canadian Edition
Problem 6-13 (30 minutes)
1. a.
b.
c.
d.
e.
f.
g.
h.
i.
6
11
1
4
2
10
3
7
9
2. Without a 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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Solutions Manual, Chapter 6
21
Problem 6-14 (45 minutes)
1. High-low method:
High activity level ..............
Low activity level ...............
Change .............................
Number of
Jobs
Repair
Costs
260
80
180
$24,000
9,600
$14,400
Variable cost per job:
Change in cost =
Change in activity
$14,400
180 jobs
= $80 per job
Fixed cost: Total repair cost at high activity level ........
Less variable element:
260 jobs × $80 per job .........................
Fixed cost element ..................................
$24,000
20,800
$ 3,200
Therefore, the cost formula is: Y = $3,200 + $80X.
2. Scattergraph method (see the scattergraph on the following page):
(Note: Students’ answers will vary due to the inherent imprecision and
subjectivity of the scattergraph method of estimating fixed and variable
costs.)
The line intersects the cost axis at about $4,250. The variable cost can
be estimated as follows:
Total cost at 180 jobs (a point that falls on the line) ...
Less the fixed cost element (intersection of the Y axis
on the graph) ........................................................
Variable cost element at 180 jobs (total) ....................
$18,000
4,250
$13,750
$13,750 ÷ 180 jobs = $76.38 per job.
Therefore, the cost formula is: Y = $4,250 + $76.38X.
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22
Managerial Accounting, 9th Canadian Edition
Problem 6-14 (continued)
The completed scattergraph follows:
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Solutions Manual, Chapter 6
23
Problem 6-14 (continued)
3.
Total predicted repair costs for 200 jobs:
Y = $3,200 + $80(x)
Y = $3,200 + $80(200)
Y = $3,200 + $16,000
Y = $19,200
4.
Neither of the formulas developed in parts 1 and 2 should be used to
predict costs for a 600-job month because that level of activity appears to be well outside of the relevant range. The next closest activity level is only 260 jobs (May), which is less than half of the number
of jobs the manager wants to predict costs for. Both fixed and variable costs could increase if the level of activity is 600 jobs. For example, additional mechanics may need to be hired, more repair equipment may be needed and facilities may need to be expanded (even
temporarily) to accommodate an increase of that magnitude.
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24
Managerial Accounting, 9th Canadian Edition
Problem 6-15 (45 minutes)
1. Maintenance cost at the 140,000 machine-hour level of activity can be
isolated as follows:
Total factory overhead cost .............
Deduct:
Utilities cost @ $1.30 per MH* ......
Supervisory salaries .....................
Maintenance cost ...........................
Level of Activity
80,000 MH 140,000 MH
$340,400
$483,200
104,000
120,000
$116,400
182,000
120,000
$181,200
*$104,000 ÷ 80,000 MHs = $1.30 per MH
2. High-low analysis of maintenance cost:
High activity level ..............
Low activity level ...............
Change .............................
Maintenance MachineCost
Hours
$181,200
116,400
$ 64,800
140,000
80,000
60,000
Note: in this problem the high level of activity (140,000 hours) does not
correspond to the highest level of total overhead costs, which occurs in
November.
Variable cost per unit of activity:
Change in cost =
Change in activity
$64,800
60,000 MHs
= $1.08 per MH
Total fixed cost:
Total maintenance cost at the low activity level ............ $116,400
Less the variable cost element
(80,000 MHs × $1.08 per MH) ..................................
86,400
Fixed cost element ..................................................... $30,000
Therefore, the cost formula is $30,000 per month plus $1.08 per
machine-hour or Y = $30,000 + $1.08X, where X represents machinehours.
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Solutions Manual, Chapter 6
25
Problem 6-15 (continued)
3.
Maintenance cost ..............
Utilities cost:
$104,000/80,000 ...............
Supervisory salaries cost ....
Totals ...............................
Variable Rate per
Machine-Hour
Fixed Cost
$1.08
1.30
$2.38
$ 30,000
120,000
$150,000
Therefore, the cost formula would be $150,000 plus $2.38 per machinehour, or Y = $150,000 + $2.38X.
4. Fixed costs ..........................................................
Variable costs: $2.38 per MH × 90,000 MHs..........
Total overhead costs ............................................
$150,000
214,200
$364,200
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26
Managerial Accounting, 9th Canadian Edition
Problem 6-16 (45 minutes)
1.
Direct materials cost @ $15 per unit
Direct labour cost @ $6 per unit ......
Manufacturing overhead cost ..........
Total manufacturing costs ...............
Add: Work in process, beginning .....
Deduct: Work in process, ending .....
Cost of goods manufactured ...........
July—Low
9,000 Units
$135,000
54,000
107,000 *
296,000
14,000
310,000
25,000
$285,000
October—High
12,000 Units
$180,000
72,000
131,000 *
383,000
22,000
405,000
15,000
$390,000
*Computed by working backwards from cost of goods manufactured.
2.
October—High level of activity ..........
July—Low level of activity .................
Change ............................................
Variable cost =
=
Units
Produced
12,000
9,000
3,000
Cost
Observed
$131,000
107,000
$ 24,000
Change in cost
Change in activity
$24,000
= $8 per unit
3,000 units
Total cost at the high level of activity ..................
Less variable cost element
($8 per unit × 12,000 units) ............................
Fixed cost element .............................................
$131,000
96,000
$ 35,000
Therefore, the cost formula is: $35,000 per month plus $8 per unit produced, or Y = $35,000 + $8X, where X represents the number of units
produced.
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Solutions Manual, Chapter 6
27
Problem 6-16 (continued)
3.
The cost of goods manufactured if 9,500 units are produced:
Direct materials cost (9,500 units × $15 per unit)..
$142,500
Direct labour cost (9,500 units × $6 per unit) .......
57,000
Manufacturing overhead cost:
Fixed portion .................................................... $35,000
Variable portion (9,500 units × $8 per unit) ........ 76,000 111,000
Total manufacturing costs ....................................
310,500
Add: Work in process, beginning ..........................
16,000
326,500
Deduct: Work in process, ending ..........................
19,000
Cost of goods manufactured ................................
$307,500
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28
Managerial Accounting, 9th Canadian Edition
Problem 6-17 (30 minutes)
1. Maintenance cost at the 80,000 machine-hour level of activity can be
isolated as follows:
Level of Activity
60,000 MH
80,000 MH
Total factory overhead cost .. 274,000 pesos
Deduct:
Indirect materials @ 1.50
pesos per MH* ............... 90,000
Rent ................................. 130,000
Maintenance cost ................ 54,000 pesos
312,000 pesos
120,000
130,000
62,000 pesos
* 90,000 pesos ÷ 60,000 MHs = 1.50 pesos per MH
2. High-low analysis of maintenance cost:
High activity level ..............
Low activity level ...............
Change observed...............
Variable cost =
=
Maintenance Cost
62,000 pesos
54,000
8,000 pesos
Machine-Hours
80,000
60,000
20,000
Change in cost
Change in activity
8,000 pesos
= 0.40 peso per MH
20,000 MHs
Fixed cost element = Total cost – Variable cost element
= 54,000 pesos – (60,000 MHs × 0.40 pesos)
= 30,000 pesos
Therefore, the cost formula is 30,000 pesos per year, plus 0.40 peso per
machine-hour or
Y = 30,000 pesos + 0.40 peso X.
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Solutions Manual, Chapter 6
29
Problem 6-17 (continued)
3. Indirect materials (65,000 MHs ×
1.50 pesos per MH) .......................
Rent ................................................
Maintenance:
Variable cost element (65,000 MHs
× 0.40 peso per MH) ................... 26,000 pesos
Fixed cost element ......................... 30,000
Total factory overhead cost ...............
97,500 pesos
130,000
56,000
283,500 pesos
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30
Managerial Accounting, 9th Canadian Edition
Case 6-18 (30 minutes)
1. The completed scattergraph for the number of direct labour hours as
the activity base is presented below:
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Solutions Manual, Chapter 6
31
Case 6-18 (continued)
2. The completed scattergraph for the number of jobs as the activity base
is presented below:
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32
Managerial Accounting, 9th Canadian Edition
Case 6-18 (continued)
3. The number of direct labour-hours should be used as the activity base
for predicting overhead costs. There are several reasons for this. First, a
visual inspection of the scattergraphs suggest that it is easer to approximate the relationship between labour-hours and overhead costs with a
straight line than it is for total number of jobs completed in a month.
Although both activity measures appear to have linear relationship with
overhead costs, direct labour-hours appears to a better fit. Second, jobs
differ with respect to complexity with more complex jobs requiring more
direct labour-hours since they take longer to complete. Thus more complex jobs would likely result in the incurrence of more variable overhead
costs such as electricity. Evidence of the differing mix of job complexity
is indicated by the fact that during several months, around 500 jobs
were completed (January, July, September, and December) but overhead
ranged from $75,045 to $83,434 across those months. Third, management has the flexibility to change the mix of welders used across jobs.
More experienced welders are more efficient and waste less indirect materials suggesting labour-hours may be a better predictor of overhead
costs.
4.
August—High level of activity ............
May—Low level of activity .................
Change ............................................
Direct LabourHours
6,114
1,914
4,200
Overhead Costs
$81,582
60,162
$ 21,420
Variable cost per unit of activity:
Change in cost =
Change in activity
$21,420
4,200 DLHs
= $5.10 per DLH
Total cost at the high level of activity ..................
Less variable cost element
($5.10 per unit × 6,114 hours)
Fixed cost element .............................................
$81,582.0
0
31,181.4
0
$ 50,400.
60
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Solutions Manual, Chapter 6
33
Case 6-18 (continued)
Therefore, the cost formula is:
$ Y = $50,400.60 + $5.10X, where X represents the number of direct
labour-hours.
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34
Managerial Accounting, 9th Canadian Edition
CASE 6-19 (90 minutes)
1. Direct labour-hour allocation base:
Electrical costs (a) .................................
Direct labour-hours (b)...........................
Predetermined overhead rate (a) ÷ (b) ...
Machine-hour allocation base:
Electrical costs (a) .................................
Machine-hours (b) .................................
Predetermined overhead rate (a) ÷ (b) ...
SFr 3,868,620
427,500 DLHs
SFr 9.05 per DLH
SFr 3,868,620
365,520 MHs
SFr 10.58 per MH
2. Electrical cost for the custom tool job using direct labour-hours:
Predetermined overhead rate (a) ............
SFr 9.05 per DLH
Direct labour-hours for the job (b) ..........
30 DLHs
Electrical cost applied to the job (a) × (b)
SFr 271.50
Electrical cost for the custom tool job using machine-hours:
Predetermined overhead rate (a) ............
SFr 10.58 per MH
Machine-hours for the job (b) .................
25 MHs
Electrical cost applied to the job (a) × (b)
SFr 264.50
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Solutions Manual, Chapter 6
35
CASE 6-19 (continued)
The scattergraph for electrical costs and direct labour-hours appears
below:
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36
Managerial Accounting, 9th Canadian Edition
CASE 6-19 (continued)
The scattergraph for electrical costs and machine-hours appears below:
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Solutions Manual, Chapter 6
37
CASE 6-19 (continued)
In general, the allocation base should actually cause the cost being allocated. If it doesn’t, costs will be incorrectly assigned to jobs. Incorrectly
assigned costs are useless for decision-making.
Examining the two scattergraphs reveals that electrical costs do not
appear to be related to direct labour-hours. Electrical costs do vary, but
apparently not in response to changes in direct labour-hours. On the
other hand, looking at the scattergraph for machine-hours, electrical
costs do tend to increase as the machine-hours increase. So if one must
choose between machine-hours and direct labour-hours as an allocation
base, machine-hours seems to be the better choice. Even so, it looks
like little of the overhead cost is really explained even by machine hours.
Electrical cost has a large fixed component and much of the variation in
the cost is unrelated to machine hours.
4. High-low method:
Week 2—High level of activity ...........
Week 7—Low level of activity ............
Change ............................................
Machine
Hours
8,620
6,000
2,620
Electrical
Costs
SFr 82,270
73,100
SFr 9,170
Variable cost per unit of activity:
Total cost at the high level of activity ..................
Less variable cost element
SFr 3.50 per MH × 8,620
hours)…………………….
Fixed cost element .............................................
SFr82,270
30,170
SFr 52,100
Therefore, the cost formula is:
SFr Y = $52,100 + SFr 3.50X, where X represents the number of machine hours.
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38
Managerial Accounting, 9th Canadian Edition
CASE 6-19 (continued)
5. The custom tool job requires 25 machine-hours. At SFr 3.50 per
machine-hour, the electrical cost actually caused by the job would be only
SFr 87.50. This contrasts with the electrical cost of SFr 271.50 under the
old cost system and SFr 264.50 under the new ABC system calculated in
part 2 above. Both the old cost system and the new ABC system grossly
overstate the electrical costs of the job. This is because under both cost
systems, the large fixed electrical costs of SFr 52,100 per week are allocated to jobs along with the electrical costs that actually vary with the
amount of work
being done. In practice, almost all categories of overhead costs pose similar problems. As a consequence, the costs of individual jobs are likely to
be seriously overstated for decision-making purposes under both traditional and ABC systems. Both systems provide acceptable cost data for
external reporting, but both provide potentially misleading data for
internal decision-making unless suitable adjustments are made.
6. Electricity is used for heating and lighting the building as well as to run
equipment. Therefore, consumption of electrical power is likely to be
affected at least by the weather and by the time of the year as well as by
how many hours the equipment is run. (Shorter days mean the lights
have to be on longer.)
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Solutions Manual, Chapter 6
39
CASE 6-20 (90 minutes)
Note to the instructor: This case requires the ability to build on concepts
that are introduced only briefly in the text. To some degree, this case anticipates issues that will be covered in more depth in later chapters.
1. In order to estimate the contribution to profit of the charity event, it is
first necessary to estimate the variable costs of catering the event. The
costs of food and beverages and labour are all apparently variable with
respect to the number of guests. However, the situation with respect
overhead expenses is less clear. A good first step is to plot the labour
hour and overhead expense data in a scattergraph as shown below.
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40
Managerial Accounting, 9th Canadian Edition
CASE 6-20 (continued)
This scattergraph reveals several interesting points about the behaviour
of overhead costs:
• The relation between overhead expense and labour hours is approximated reasonably well by a straight line. (However, there appears to
be a slight downward bend in the plot as the labour hours increase—
evidence of increasing returns to scale. This is a common occurrence
in practice.
• The data points are all fairly close to the straight line. This indicates
that most of the variation in overhead expenses is explained by
labour hours. As a consequence, there probably wouldn’t be much
benefit to investigating other possible cost drivers for the overhead
expenses.
• Most (about $40,000) of the overhead expense appears to be fixed.
Christine should ask herself if this is reasonable. Does the company
have large fixed expenses such as rent, depreciation, and salaries?
The overhead expenses can be decomposed into fixed and variable elements using the high-low method, least-squares regression method, or
even the quick-and-dirty method based on the scattergraph.
• The high-low method throws away most of the data and bases the
estimates of variable and fixed costs on data for only two months. For
that reason, it is a decidedly inferior method in this situation. Nevertheless, if the high-low method were used, the estimates would be
computed as follows:
High level of activity ......
Low level of activity .......
Change ......................
Labour
Hours
4,500
1,500
3,000
Overhead
Expense
$67,750
48,400
$19,350
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Solutions Manual, Chapter 6
41
CASE 6-20 (continued)
Variable cost per unit of activity:
Change in cost =
Change in activity
Fixed cost element
$19,350
3,000 MHs
= $6.45 per DLH
= Total cost – Variable cost
= $67,750 – ($6.45 x 4,500)
= $38,725
Using the high-low method estimate of the variable overhead cost per
direct labour hour, the total variable cost per guest is computed as follows:
Food and beverages .............................
Labour (0.5 hour @ $15 per hour) ........
Overhead (0.5 hour @ $6.45 per hour) .
Total variable cost per guest .................
$19.00
7.50
3.22
$29.72
The total contribution from 200 guests paying $50 each is computed as
follows:
Revenue (200 guests @ $50.00 per guest) .........
Variable cost (200 guests @ $29.72 per guest) ...
Contribution to profit ........................................
$10,000.0
0
5,944.00
$4,056.00
Fixed costs are not included in the above computation because there is
no indication that any additional fixed costs would be incurred as a consequence of catering the cocktail party. If additional fixed costs were incurred, they should also be subtracted from revenue.
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42
Managerial Accounting, 9th Canadian Edition
CASE 6-20 (continued)
2. Assuming that no additional fixed costs are incurred as a result of catering the charity event, any price greater than the variable cost per guest
of $29.72 would contribute to profits.
3. Bidding slightly less than $45 to get the contract is advisable. Any bid
above $29.72 would contribute to profits and a bid at the normal price
of $50 is unlikely to land the contract. Apart from the contribution to
profit, catering the event would also show off the company’s capabilities
to potential clients. The danger is that a price that is lower than the
normal bid of $50 might set a precedent for the future or it might initiate a price war among caterers. However, the price need not be publicized and the lower price could be justified to future clients because this
is a charity event. Another possibility would be for Christine to maintain
her normal price but throw in additional services at no cost to the customer. Whether to compete on price or service is a delicate issue that
Christine will have to decide after getting to know the personality and
preferences of the customer.
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Solutions Manual, Chapter 6
43
Research and Application 6-21
Answers will vary among groups.
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44
Managerial Accounting, 9th Canadian Edition
Exercise 6A-1 (20 minutes)
The least-squares regression estimates of fixed and variable costs can be
computed using any of a variety of statistical and mathematical software
packages or even by hand. The solution below was calculated using Microsoft® Excel.
The fixed cost element is estimated to be $3,426 per month, and the variable cost element is $2.80 per rental return. Expressed as an equation, the
relation between cleaning costs and rental returns is
Y = $3,426 + $2.80x
where X is the number of rental returns.
The R2 estimated by Excel, is 0.92, which is quite high, and indicates a
strong linear relationship between cleaning costs and rental returns.
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Solutions Manual, Chapter 6
45
Exercise 6A-1 (continued)
While not a requirement of the exercise, it is always a good to plot the data
on a scattergraph. The scattergraph can help spot nonlinearities or other
problems with the data. In this case, the regression line (shown below) is a
reasonably good approximation to the relationship between cleaning costs
and rental returns.
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46
Managerial Accounting, 9th Canadian Edition
Exercise 6A-2 (30 minutes)
1.
Month
January
February
March
April
May
June
July
Units
Shipped
(X)
4
7
5
2
3
6
8
Shipping
Expense
(Y)
$2,200
$3,100
$2,600
$1,500
$2,200
$3,000
$3,600
A spreadsheet application such as Microsoft® Excel or a statistical software package can be used to compute the slope and intercept of the
least-squares regression line for the above data. The results are:
Intercept (fixed cost) ...............
Slope (variable cost per unit) ....
R2 ...........................................
$1,011
$318
0.96
Therefore, the cost formula is $1,011 per month plus $318 per unit
shipped or
Y = $1,011 + $318X.
Note that the R2 is 0.96, which means that 96% of the variation in shipping costs is explained by the number of units shipped. This is a very
high R2 and indicates a very good fit.
2.
Scattergraph method ..........................
High-low method ................................
Least-squares regression method ........
Variable
Cost per
Unit
$300
$350
$318
Fixed
Cost
per
Month
$1,100
$800
$1,011
Note that the high-low method gives estimates that are quite different
from the estimates provided by least-squares regression.
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Solutions Manual, Chapter 6
47
Exercise 6A-3 (30 minutes)
1.
Units
(X)
24
15
30
12
18
27
Total Quality Control
Cost
(Y)
$540
$400
$620
$380
$480
$580
A spreadsheet application such as Microsoft® Excel or a statistical software package can be used to compute the slope and intercept of the
least-squares regression line for the above data. The results are:
Intercept (fixed cost) ...............
Slope (variable cost per unit) ....
R2 ...........................................
$215
$13.57
0.98
Therefore, the cost formula is $215 per week plus $13.57 per unit.
Note that the R2 is 0.98, which means that 98% of the variation in quality control costs is explained by the number of units produced. This is a
very high R2 and indicates a very good fit.
2. Y = $215 + $13.57X, where X is the number of units produced.
3. Total expected quality control costs if 20 units are produced:
Variable cost: 20 units × $13.57 per unit ..............
Fixed cost ...........................................................
Total expected cost ..............................................
$271.40
215.00
$486.40
4. It seems very plausible that as more units are produced, quality control
costs would increase since each unit produced goes through a quality control process.
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48
Managerial Accounting, 9th Canadian Edition
Problem 6A-4 (45 minutes)
1.
Number of Leagues
(X)
5
2
4
6
3
Total Cost
(Y)
$13,000
$7,000
$10,500
$14,000
$10,000
A spreadsheet application such as Excel or a statistical software package
can be used to compute the slope and intercept of the least-squares regression line for the above data. The results are:
Intercept (fixed cost) ..................
Slope (variable cost per unit) .......
R2 ..............................................
$4,100
$1,700
0.96
Therefore, the variable cost per league is $1,700 and the fixed cost is
$4,100 per year.
Note that the R2 is 0.96, which means that 96% of the variation in cost
is explained by the number of leagues. This is a very high R2 and indicates a very good fit.
2. Y = $4,100 + $1,700X
3. The expected total cost for 7 leagues would be:
Fixed cost .........................................................
Variable cost (7 leagues × $1,700 per league).....
Total cost ..........................................................
$ 4,100
11,900
$16,000
The problem with using the cost formula from (2) to estimate total cost
in this particular case is that an activity level of 7 leagues may be outside the relevant range—the range of activity within which the fixed cost
is approximately $4,100 per year and the variable cost is approximately
$1,700 per league. These approximations appear to be reasonably accurate within the range of 2 to 6 leagues, but they may be invalid outside
this range.
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Solutions Manual, Chapter 6
49
Problem 6A-4 (continued)
4.
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50
Managerial Accounting, 9th Canadian Edition
Problem 6A-5 (45 minutes)
1. Units Sold
(000s)
(X)
16
18
23
19
17
20
25
22
Shipping
Expense
(Y)
$160,000
$175,000
$210,000
$180,000
$170,000
$190,000
$230,000
$205,000
A spreadsheet application such as Excel or a statistical software package
can be used to compute the slope and intercept of the least-squares
regression line for the above data. The results are:
Intercept (fixed cost) ...............
Slope (variable cost per unit) ....
R2 ...........................................
$40,000
$7,500
0.99
Therefore the cost formula for shipping expense is $40,000 per quarter
plus $7,500 per thousand units sold ($7.50 per unit), or
Y = $40,000 + $7.50X,
where X is the number of units sold.
Note that the R2 is 0.99, which means that 99% of the variation in shipping cost is explained by the number of meals served. This is a very
high R2 and indicates a very good fit.
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Solutions Manual, Chapter 6
51
Problem 6A-5 (continued)
2.
Mayer Company
Budgeted Income Statement
For the First Quarter of Year 3
Sales (21,000 units × $50 per unit) ....................
$1,050,000
Variable expenses:
Cost of goods sold
(21,000 units × $20 per unit) ....................... $420,000
Shipping expense
(21,000 units × $7.50 per unit) ..................... 157,500
Sales commission ($1,050,000 × 0.05) ............
52,500
Total variable expenses ......................................
630,000
Contribution margin...........................................
420,000
Fixed expenses:
Shipping expenses ..........................................
40,000
Advertising expense ........................................ 170,000
Administrative salaries ....................................
80,000
Depreciation expense ......................................
50,000
Total fixed expenses ..........................................
340,000
Operating income ..............................................
$ 80,000
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52
Managerial Accounting, 9th Canadian Edition
Case 6A-6 (90 minutes)
1a.
Units
Produced
(X)
60,000
44,000
84,000
48,000
72,000
100,000
120,000
112,000
Utilities
Cost
(Y)
$200,000
$180,000
$240,000
$300,000
$400,000
$420,000
$340,000
$480,000
A spreadsheet application such as Excel or a statistical software package
can be used to compute the slope and intercept of the least-squares regression line for the above data. The results are:
Intercept (fixed cost) ...............
Slope (variable cost per unit) ....
R2 ...........................................
$113,407
$2.58
0.47
Therefore, the cost formula using units produced as the activity base is
$113,407 per month plus $2.58 per unit produced, or
Y = $113,407 + $2.58X.
Note that the R2 is 0.47, which means that only 47% of the variation in
utility costs is explained by the number of units produced.
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Solutions Manual, Chapter 6
53
Case 6A-6 (continued)
b. The scattergraph plot of utility costs versus units produced appears
below:
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54
Managerial Accounting, 9th Canadian Edition
Case 6A-6 (continued)
2a.
DLHs
(X)
15,000
9,000
12,000
18,000
30,000
27,000
24,000
33,000
Utilities Cost
(Y)
$200,000
$180,000
$240,000
$300,000
$400,000
$420,000
$340,000
$480,000
A spreadsheet application such as Excel or a statistical software package
can be used to compute the slope and intercept of the least-squares
regression line for the above data. The results are:
Intercept (fixed cost) ...............
Slope (variable cost per unit) ....
R2 ...........................................
$68,000
$12
0.94
Therefore, the cost formula using direct labour-hours as the activity
base is $68,000 per quarter plus $12 direct labour-hour, or
Y = $68,000 + $12X.
Note that the R2 is 0.94, which means that 94% of the variation in utility
costs is explained by the number of direct labour-hours. This is a very
high R2 and is an indication of a good fit.
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Solutions Manual, Chapter 6
55
Case 6A-6 (continued)
b. The scattergraph plot of utility costs versus direct labour-hours appears below:
3. The company should probably use direct labour-hours as the activity
base, since the fit of the regression line to the data is much tighter than
it is with units produced. The R2 for the regression using direct labourhours as the activity base is twice as large as for the regression using
units produced as the activity base. However, managers should look
more closely at the costs and try to determine why utilities costs are
more closely tied to direct labour-hours than to the number of units
produced.
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56
Managerial Accounting, 9th Canadian Edition
Case 6A-6 (continued)
4. It is plausible that both units produced and direct labour hours would be
related to utilities costs. However, because different models require different amounts of direct labour, it seems more plausible to expect a
strong association between labour hours and utilities costs. Using units
produced as the independent variable assumes no difference in labour
hour requirements across the various models. Not surprisingly, the results of the regression analysis are consistent with the qualitative assessment of economic plausibility with a much higher R2 value for the
model using direct labour hours.
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Solutions Manual, Chapter 6
57