1. Knowledge of cost behavior allows a manager to assess changes in costs that result from
changes in activity. This allows a manager to examine the effects of choices that change activity.
For example, if excess capacity exists, bids that at least cover variable costs may be totally
appropriate. Knowing what costs are variable and what costs are fixed can help a manager make
better bids and, ultimately, better business decisions.
2. A driver is a factor that causes or leads to a change in a cost or activity; it is an output measure.
The driver for general machine maintenance cost in a factory could be machine hours. The driver
for raw materials used is the number of units produced.
3. The cost formula for monthly shipping cost is:
Monthly Shipping Cost = $3,560 + $6.70 × Packages Shipped
The independent variable is packages shipped. The dependent variable is monthly shipping cost.
The fixed cost per month is $3,560. The variable rate is $6.70.
4. Some account categories are primarily fixed or variable. Even if the cost is mixed, either the fixed
component or the variable component is relatively small. As a result, assigning all of the cost to
either a fixed or variable category is unlikely to result in large errors. For example, depreciation on
property, plant, and equipment is largely fixed. The cost of telephone expense for the sales office,
if it consisted primarily of long-distance calls, could be seen as largely variable (variable with
respect to the number of customers).
5. Committed fixed costs are those incurred for the acquisition of long-term activity capacity and are
not subject to change in the short run. Annual resource expenditure is independent of actual
usage. For example, the cost of a factory building is a committed fixed cost. Discretionary fixed
costs are those incurred for the acquisition of short-term activity capacity, the levels of which can
be altered quickly. In the short run, resource expenditure is also independent of actual activity
usage. Salaries of engineers are an example of such an expenditure.
6. The concept of relevant range is important in dealing with step costs because if the relevant range
is contained completely within one step, the cost behaves as a fixed cost. However, if the relevant
range spans two or more steps, the accountant must be aware of the cost increase as output
goes up within the relevant range.
7. Mixed costs are usually reported in total in the accounting records. How much of the cost is fixed
and how much is variable is unknown and must be estimated.
8. The cost formula for a strictly fixed cost has only a fixed cost amount. There is no variable rate
and no independent variable. For the depreciation example, the cost formula looks like this:
Depreciation per Year = $15,000
9. The cost formula for a strictly variable cost has only the variable rate and independent variable.
There is no fixed component. For the electrical power example, the cost formula looks like this:
Electrical Power = $1.15 × Machine Hours
3 COST BEHAVIOR AND
FORECASTING
DISCUSSION QUESTIONS
3-1
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CHAPTER 3 Cost Behavior and Forecasting
10. A scattergraph allows a visual portrayal of the relationship between cost and activity. It
reveals to the investigator whether a relationship may exist and, if so, whether a linear
function can be used to approximate the relationship.
11. Managers can use their knowledge of the cost relationships to estimate the fixed and
variable components. A scattergraph can be used as an aid in this process. From a
scattergraph, a manager can select two points that best represent the relationship.
These two points can then be used to derive a linear cost formula. The high-low method
tells the manager which two points to select to compute the linear cost formula. The
selection of the two points is not left to judgment.
12. Because the scattergraph method is not restricted to the high and low points, it is
possible to select two points that better represent the relationship between activity and
costs, producing a better estimate of fixed and variable costs. The main advantage of the
high-low method is that it removes subjectivity from the choice process. The same line
will be produced by two different people.
13. Assuming that the scattergraph reveals that a linear cost function is suitable, then the
method of least squares selects a line that best fits the data points. The method also
provides a measure of goodness of fit so that the strength of the relationship between
cost and activity can be assessed.
14. The best-fitting line is the one that is “closest” to the data points. This is usually
measured by the line that has the smallest sum of squared deviations from the individual
data points.
15. The only difference between absorption costing and variable costing is the way in which
fixed overhead costs are assigned. Under variable costing, fixed overhead is a period cost;
under absorption costing, it is a product cost.
16. Absorption-costing income is greater because some of the period’s fixed overhead is placed
in inventory and not recognized as part of cost of goods sold on the absorption-costing
income statement.
17. The coefficient of determination is the percentage of total variability in costs explained by
activity. As such, it is a measure of goodness of fit, the strength of the relationship
between cost and activity.
3-2
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CHAPTER 3 Cost Behavior and Forecasting
3-1. c
3-2. e
3-3. b
3-4. d
3-5. a
3-6. d
3-7. c
3-8. d Total Cost = $235,000 + ($75 × 8,000) = $835,000
3-9. b
3-10. b
3-11. a
3-12. e
3-13. b
3-14. b
3-15. d
MULTIPLE-CHOICE QUESTIONS
3-3
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CHAPTER 3 Cost Behavior and Forecasting
BE 3-16
1. The cost formula takes the following form:
Total Cost = Fixed Cost + (Variable Rate × Number of Flash Drives)
The monthly fixed cost is the $15,000 cost of equipment depreciation, as it does not
vary according to the number of flash drives manufactured. The variable costs are
materials and manufacturing overhead, as both do vary with the number of flash
drives produced.
Cost of materials per flash drive is:
10,000 ounces/5,000 flash drives = 2 ounces per flash drive
Given that, the material cost per drive = $3 × 2 ounces per drive = $6.00 per drive.
Cost of manufacturing overhead per flash drive is:
$22,500/5,000 flash drives = $4.50 per drive
Therefore, the variable rate per flash drive is $6.00 + $4.50 = $10.50
The cost formula is:
Total Cost of Flash Drives = $15,000 + ($10.50 × Number of Flash Drives)
2. Expected fixed cost for next month is $15,000.
Expected variable cost for next month is:
$10.50 × 6,000 flash drives = $63,000
Expected total manufacturing cost for next month is:
$15,000 + $63,000 = $78,000
BRIEF EXERCISES: SET A
3-4
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CHAPTER 3 Cost Behavior and Forecasting
BE 3-17
Step 1: Find the high and low points: The high number of employee hours is in March,
and the low number of employee hours is in August.
Step 2: Calculate the variable rate:
Variable Rate =
= ($9,899 – $7,531)/(630 – 310)
= $2,368/320
= $7.40 per employee hour
Step 3: Calculate the fixed cost:
Fixed Cost = Total Cost – (Variable Rate × Employee Hours)
Let’s choose the low point with total cost of $7,531 and employee hours of 310.
Fixed Cost = $7,531 – ($7.40 × 310) = $7,531 – $2,294 = $5,237
(Hint : Check your work by computing fixed cost using the high point.)
Step 4: Construct a cost formula:
If the variable rate is $7.40 per employee hour and fixed cost is $5,237 per month, then
the formula for total monthly labor cost is:
Total Labor Cost = $5,237 + ($7.40 × Employee Hours)
BE 3-18
1. Total Variable Labor Cost = Variable Rate × Employee Hours
= $7.40* × 675 hours
= $4,995
2. Total Labor Cost = Fixed Cost + (Variable Rate × Employee Hours)
= $5,237* + ($7.40 × 675)
= $5,237 + $4,995
* Refer to the solution for Brief Exercise 3-17 for detailed explanation of the computations for
variable cost per unit ($7.40) and total fixed cost ($5,237).
= $10,232
High Cost – Low Cost
High Employee Hours – Low Employee Hours
3-5
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CHAPTER 3 Cost Behavior and Forecasting
BE 3-19
1. Total Variable Labor Cost = Variable Rate × Employee Hours
= $7.40* × 4,000 hours
2. There’s a trick here; the cost formula is for the month, but we are being asked to budget
labor cost for the year. So, we will need to multiply the fixed cost for the month by 12
(the number of months in a year).
Total Fixed Labor Cost = Fixed Cost × 12 Months in a Year
= $5,237* × 12
3. Total Labor Cost = (12 × $5,237) + ($7.40 × 4,000)
= $62,844 + $29,600
* Refer to the solution for Brief Exercise 3-17 for detailed explanation of the computations for
variable cost per unit ($7.40) and total monthly fixed cost ($5,237).
BE 3-20
1. The fixed cost and the variable rate are given directly by regression.
Fixed Cost = $4,517
Variable Rate = $8.20
2. The cost formula is:
Total Labor Cost = $4,517 + ($8.20 × Employee Hours)
3. Budgeted Labor Cost = $4,517 + ($8.20 × 675)
= $10,052
= $29,600
= $62,844
= $92,444
3-6
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CHAPTER 3 Cost Behavior and Forecasting
BE 3-21
1. Units Ending Inventory = Units Beginning Inventory + Units Produced –
Units Sold
= 300 + 15,000 – 12,700
= 2,600 units
2. Direct materials………………………… $ 20
Direct labor……………………………… 60
Variable overhead……………………… 12
Fixed overhead………………………… 30
Unit product cost……………………… $122
3. Value of Ending Inventory = 2,600 units × $122 = $317,200
BE 3-22
1. Units Ending Inventory = Units Beginning Inventory + Units Produced –
Units Sold
= 300 + 15,000 – 12,700
= 2,600 units
2. Direct materials………………………… $20
Direct labor……………………………… 60
Variable overhead……………………… 12
Unit product cost……………………… $92
3. Value of Ending Inventory = 2,600 units × $92 = $239,200
BE 3-23
1. Direct materials………………………… $ 9
Direct labor……………………………… 6
Variable overhead……………………… 4
Fixed overhead………………………… 5
Unit product cost……………………… $24
Total Cost of Goods Sold = $24 × 9,300 units = $223,200
3-7
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CHAPTER 3 Cost Behavior and Forecasting
BE 3-23 (Concluded)
2.
Sales ($47 × 9,300)………………………………………………………………… $437,100
Less: Cost of goods sold………………………………………………………… 223,200
Gross margin…………………………………………………………..………… $213,900
Less: Selling and administrative expense………………………….………… 138,000
Operating income…………………………………………………………………… $ 75,900
BE 3-24
1. Direct materials……………………………………………………………………… $ 9
Direct labor…………………………………………………………………………… 6
Variable overhead…………………………………………………………………… 4
Unit product cost…………………………………………………………………… $19
Total Cost of Goods Sold = $19 × 9,300 units = $176,700
2.
Sales ($47 × 9,300)………………………….……………………… $437,100
Less: Variable costs……………………………………………… 176,700
Contribution margin…………………………………………… $260,400
Less fixed expense:
Fixed overhead ($5 × 10,000) ……………………………… $ 50,000
Fixed selling and administrative expenses……………… 138,000 188,000
Operating income………………………………………………… $ 72,400
Osterman Company
Income Statement under Variable Costing
For the Most Recent Year
Osterman Company
Income Statement under Absorption Costing
For the Most Recent Year
3-8
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CHAPTER 3 Cost Behavior and Forecasting
BE 3-25
1. The cost formula takes the following form:
Total Cost = Fixed Cost + (Variable Rate × Number of SUVs)
The monthly fixed cost is the $10,000,000 cost of machinery and warehouse
depreciation, as it does not vary according to the number of SUVs manufactured. The
variable costs are materials and manufacturing overhead, as both do vary with the
number of SUVs produced.
Cost of materials per SUV is:
75,000,000 pounds/50,000 SUVs = 1,500 pounds per SUV
Given that, the material cost per SUV = $0.20 × 1,500 pounds per SUV = $300.00 per SUV.
Cost of manufacturing overhead per SUV is:
$200,000,000/50,000 SUVs = $4,000.00 per SUV
Therefore, the variable rate per SUV is $300.00 + $4,000.00 = $4,300.00.
The cost formula is:
Total Cost of SUVs = $10,000,000 + ($4,300.00 × Number of SUVs)
2. Expected fixed cost for next month is $10,000,000.
Expected variable cost for next month is:
$4,300.00 × 55,000 SUVs = $236,500,000
Expected total manufacturing cost for next month is:
$10,000,000 + $236,500,000 = $246,500,000
BRIEF EXERCISES: SET B
3-9
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CHAPTER 3 Cost Behavior and Forecasting
BE 3-26
Step 1: Find the high and low points: The high number of deliveries is in November
and the low number of deliveries is in May.
Step 2: Calculate the variable rate:
Variable Rate =
= ($75,450 – $63,450)/(2,800 – 1,800)
= $12,000/1,000
= $12.00 per delivery
Step 3: Calculate the fixed cost:
Fixed Cost = Total Cost – (Variable Rate × Number of Deliveries)
Let’s choose the low point with total cost of $63,450 and number of deliveries of 1,800.
Fixed Cost = $63,450 – ($12.00 × 1,800) = $63,450 – $21,600 = $41,850
(Hint : Check your work by computing fixed cost using the high point.)
Step 4: Construct a cost formula:
If the variable rate is $12.00 per delivery and fixed cost is $41,850 per month, then
the formula for total monthly delivery cost is:
Total Delivery Cost = $41,850 + ($12.00 × Number of Deliveries)
BE 3-27
1. Total Variable Delivery Cost = Variable Rate × Number of Deliveries
= $12.00* × 3,000 deliveries
= $36,000
2. Total Delivery Cost = Fixed Cost + (Variable Rate × Number of Deliveries)
= $41,850* + ($12.00 × 3,000)
= $41,850 + $36,000
* Refer to the solution for Brief Exercise 3-26 for detailed explanation of the computations for
variable cost per unit ($12.00) and total fixed cost ($41,850).
= $77,850
High Cost – Low Cost
High Number of Deliveries – Low Number of Deliveries
3-10
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CHAPTER 3 Cost Behavior and Forecasting
BE 3-28
1. Total Variable Delivery Cost = Variable Rate × Number of Deliveries
= $12.00* × 3,000 deliveries
2. There’s a trick here; the cost formula is for the month, but we are being asked to
budget total delivery cost for the year. So, we will need to multiply the fixed cost for
the month by 12 (the number of months in a year).
Total Fixed Delivery Cost = Fixed Cost × 12 Months in a Year
= $41,850* × 12
3. Total Delivery Cost = (12 × $41,850) + ($12.00 × 3,000)
= $502,200 + $36,000
* Refer to the solution for Brief Exercise 3-26 for detailed explanation of the computations for
variable cost per unit ($12.00) and total monthly fixed cost ($41,850).
BE 3-29
1. The fixed cost and the variable rate are given directly by regression.
Fixed Cost = $43,293
Variable Rate = $11.34
2. The cost formula is:
Total Delivery Cost = $43,293 + ($11.34 × Number of Deliveries)
3. Budgeted Delivery Cost = $43,293 + ($11.34 × 3,000)
= $36,000
= $502,200
= $538,200
= $77,313
3-11
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CHAPTER 3 Cost Behavior and Forecasting
BE 3-30
1. Units Ending Inventory = Units Beginning Inventory + Units Produced –
Units Sold
= 400 + 14,000 – 13,700
= 700 units
2. Direct materials………………………… $ 15
Direct labor……………………………… 36
Variable overhead……………………… 9
Fixed overhead…………………………… 40
Unit product cost………………………… $100
3. Value of Ending Inventory = 700 units × $100 = $70,000
BE 3-31
1. Units Ending Inventory = Units Beginning Inventory + Units Produced –
Units Sold
= 400 + 14,000 – 13,700
= 700 units
2. Direct materials………………………… $15
Direct labor……………………………… 36
Variable overhead……………………… 9
Unit product cost………………………… $60
3. Value of Ending Inventory = 700 units × $60 = $42,000
BE 3-32
1. Direct materials………………………… $12
Direct labor……………………………… 7
Variable overhead……………………… 5
Fixed overhead…………………………… 8
Unit product cost………………………… $32
Total Cost of Goods Sold = $32 × 8,800 units = $281,600
3-12
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CHAPTER 3 Cost Behavior and Forecasting
BE 3-32 (Concluded)
2.
Sales ($60 × 8,800)……………………………………………………………… $528,000
Less: Cost of goods sold……………………………………………………… 281,600
Gross margin…………………………………………………………..…… $246,400
Less: Selling and administrative expense………………………….……… 138,000
Operating income……………………………………………………………… $108,400
BE 3-33
1. Direct materials…………………………………… $12
Direct labor………………………………………… 7
Variable overhead………………………………… 5
Unit product cost…………………………………… $24
Total Cost of Goods Sold = $24 × 8,800 units = $211,200
2.
Sales ($60 × 8,800)………………………….…………………… $528,000
Less: Variable costs………………………………………….. 211,200
Contribution margin………………………………………… $316,800
Less fixed expense:
Fixed overhead ($8 × 10,000)……………………………… $ 80,000
Fixed selling and administrative expenses…………… 138,000 218,000
Operating income……………………………………………… $ 98,800
Beyta Company
Income Statement under Variable Costing
For the Most Recent Year
Beyta Company
Income Statement under Absorption Costing
For the Most Recent Year
3-13
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CHAPTER 3 Cost Behavior and Forecasting
E 3-34
a. Power to operate a drill (to drill holes in the wooden frames of the futons)—
Variable cost
b. Cloth to cover the futon mattress—Variable cost
c. Salary of the factory receptionist—Fixed cost
d. Cost of food and decorations for the annual Fourth of July party for all factory
employees—Fixed cost
e. Fuel for a forklift used to move materials in a factory—Variable cost
f. Depreciation on the factory—Fixed cost
g. Depreciation on a forklift used to move partially completed goods—Fixed cost
h. Wages paid to workers who assemble the futon frame—Variable cost
i. Wages paid to workers who maintain the factory equipment—Fixed cost
j. Cloth rags used to wipe the excess stain off the wooden frames—Variable cost
E 3-35
1.
EXERCISES
$0
$50,000
$100,000
$150,000
$200,000
$250,000
0 10 20 30 40 50 60 70 80 90 100
Depreciation Cost
Cubic Yards of Concrete (in thousands)
Truck Depreciation
3-14
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CHAPTER 3 Cost Behavior and Forecasting
E 3-35 (Concluded)
2.
3. Truck depreciation: Fixed cost
Raw materials cost: Variable cost
4. Truck depreciation is a fixed cost (with respect to the driver “cubic yards of cement”).
Therefore, it cannot be managed by altering the number of cubic yards of cement,
within the relevant range of course. Instead, the cost of truck depreciation could be
reduced (or increased) by changing the depreciation method that is used to allocate
the cost to each accounting period. Also, a more long-term approach to managing the
total annual cost of truck depreciation would involve decisions to sell some trucks
(make the fleet smaller), replace certain trucks (keep the fleet the same size), or buy
additional trucks (make the fleet larger). In addition, the company could manage the
depreciation cost by arranging to rent (rather than purchase) additional trucks (and
thus only show a rent expense rather than a depreciation expense on its books) or
obtain on-site mixing equipment for large jobs (and thus not be responsible for
providing the trucks).
5. Raw materials is a variable cost (with respect to the driver “cubic yards of cement”).
Therefore, total raw materials cost likely is best reduced (or managed) either by using
fewer cubic yards of cement per job (i.e., more efficient use of cement) or by paying
less to purchase or manufacture each cubic yard of cement (i.e., more efficient
purchasing or manufacturing of cement). Also, a more long-term approach to reducing
raw materials cost would be to discover different, cheaper materials that can be used
in the business that yield the same quality of output as the existing materials.
E 3-36
Technician salaries
Laboratory facility
Laboratory equipment
Chemicals and other supplies
X
Committed
Fixed Cost
X
XX
Cost Category
Variable
Cost
Discretionary
Fixed Cost
$0
$500
$1,000
$1,500
$2,000
$2,500
0 20 40 60 80 100
Cost (in thousands)
Cubic Yards of Concrete (in thousands)
Raw Materials Cost
3-15
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CHAPTER 3 Cost Behavior and Forecasting
E 3-37
1. Total Maintenance Cost = $1,750,000 + ($125.00 × 50,000) = $8,000,000
2. Total Fixed Maintenance Cost = $1,750,000
3. Total Variable Maintenance Cost = $125.00 × 50,000 = $6,250,000
4. Total Maintenance
Cost per Unit
= $8,000,000/50,000 units
= $160.00
5. Fixed Maintenance Cost per Unit = $1,750,000/50,000 units = $35.00
6. Variable Maintenance Cost per Unit = $125.00
7. Alisha management could identify (via research or conversations with its operations
personnel or employees at other similar organizations) additional drivers of maintenance
costs besides the total number of medical stents manufactured. For example, different
types of medical stents might require different types of raw materials, different amounts
of machine time, or different types of machines. Any or all of these potential additional
factors might drive, or affect, the total amount of maintenance costs incurred by Alisha’s
manufacturing facility. If so, their inclusion in Alisha’s cost formula likely would improve
its ability to understand historical maintenance costs and predict future maintenance
costs.
E 3-38
1. Total Maintenance Cost = $1,750,000 + ($125.00 × 25,000) = $4,875,000
2. Total Fixed Maintenance Cost = $1,750,000
3. Total Variable Maintenance Cost = $125.00 × 25,000 = $3,125,000
4. Total Maintenance Cost
per Unit
= $4,875,000/25,000 units
= $195.00
5. Fixed Maintenance Cost per Unit = $1,750,000/25,000 units = $70.00
6. Variable Maintenance Cost per Unit = $125.00
7. The maintenance cost per unit in Exercise 3-38 is higher ($195) than in Exercise 3-37
($160) because Alisha incurs fixed costs of $1,750,000 to produce its stents. Assuming
25,000 and 50,000 stents are within the relevant range, Alisha’s fixed costs do not vary
with the number of stents it produces. Therefore, even though its production volume
declines by 50% (from 50,000 units down to 25,000 units), its total fixed costs remain at
$1,750,000 and are spread out over a smaller number of units. As a result, Alisha’s
maintenance costs per unit increase when its output volume decreases. It is important to
= [$1,750,000 + ($125.00 × 25,000)]/25,000 units
= [$1,750,000 + ($125.00 × 50,000)]/50,000 units
3-16
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CHAPTER 3 Cost Behavior and Forecasting
E 3-38 (Concluded)
realize that the opposite result occurs when output volume increases (i.e., total cost
per unit decreases as volume increases because fixed costs are spread out over a
greater number of units, again assuming the same relevant range). Finally, Alisha’s
management can consider maintenance costs per unit in certain decisions, but it
must remember that unit costs at one output level cannot be used to estimate total
costs at other output levels (again because unit costs differ across different volumes).
E 3-39
1.
The direct labor cost in the machining department is a step cost (with narrow steps).
2.
The cost of supervision for the machining department is a step cost (with wide steps).
3. Direct Labor Cost Increase = $144,000 – $108,000 = $36,000
Supervision Increase = $80,000 – $40,000 = $40,000
E 3-40
1. K
2. H
3. A
4. J
5. I
6. E
7. L
$0
$50,000
$100,000
$150,000
$200,000
$250,000
$300,000
$350,000
0 1,000 2,000 3,000 4,000 5,000
Cost of Direct Labor
Number of Units
Direct Labor Cost
$0
$50,000
$100,000
$150,000
0 1,000 2,000 3,000 4,000 5,000
Cost of Supervision
Number of Units
Supervision Cost
3-17
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CHAPTER 3 Cost Behavior and Forecasting
A. The cost depicted in the curve in graph A is zero up to a certain level of output (i.e., up to
three squares on the output range horizontal axis). Once a certain level of output is
reached (i.e., beyond the three squares), the cost becomes VARIABLE in nature.
However, after yet another level of output is reached (i.e., about five squares), the
variable cost per unit (or rate) decreases.
B. The cost depicted in the curve in graph B is a VARIABLE cost. However, the variable
cost per unit (or rate) decreases at certain set intervals (e.g., just before the second
square and again after the fifth square). Note: This cost curve is not a semi-variable
cost because the rate of change does not change at every single unit of output, but
instead only changes after particular levels of output are reached (i.e., at certain
intervals).
C. The cost depicted in the curve in graph C is zero up to a certain level of output (i.e., up
to three squares). Once a certain level of output is reached (i.e., at three squares), the
cost becomes a VARIABLE cost. Finally, after yet another level of output is reached (i.e.,
about five squares along the horizontal axis), the cost becomes a FIXED cost in nature
(i.e., the variable component ceases).
D. The cost depicted in the curve in graph D begins as a FIXED cost. Once a certain level of
output is reached (i.e., five squares along the ouput range horizontal axis), the cost
becomes MIXED in nature (i.e., a variable component is added onto the existing fixed
component). Finally, after another level of output is reached (i.e., at eight squares), the
cost remains mixed but the variable cost per unit (or rate) increases.
E. The cost depicted in the curve in graph E is a VARIABLE cost. However, the variable
cost per unit (or rate) increases at certain set intervals (e.g., just after the fourth square
and again after the seventh square). Note: This cost curve is not a semi-variable cost
because the rate of change does not change at every single unit of output, but instead
only changes after particular levels of output are reached (i.e., at certain intervals).
F. The cost depicted in the curve in graph F is a MIXED cost. However, the rate of change
(for the variable component) increases at certain set intervals (e.g., just after the fourth
square and again after the seventh square).
G. The cost depicted in the curve in graph G begins as a SEMI-VARIABLE cost that in total
increases at a decreasing rate. However, once a certain level of output is reached (i.e.,
at eight squares along the output range horizontal axis), the cost becomes a FIXED cost.
H. The cost depicted in the curve in graph H is a STEP FUNCTION cost.
I. The cost depicted in the curve in graph I is a SEMI-VARIABLE cost that in total increases
at a decreasing rate.
J. The cost depicted in the curve in graph J is a VARIABLE cost.
K. The cost depicted in the curve in graph K is a FIXED cost.
L. The cost depicted in the curve in graph L is a SEMI-VARIABLE cost that in total increases
at an increasing rate.
E 3-41
3-18
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CHAPTER 3 Cost Behavior and Forecasting
E 3-42
This is a strictly variable cost.
2.
This is a fixed cost.
1.
$0
$1,000
$2,000
$3,000
$4,000
$5,000
$6,000
$7,000
$8,000
0 5 10 15 19
Cost
Number of Opening Shows
Cost of Giving Opening Shows
$0
$20,000
$40,000
$60,000
$80,000
$100,000
0 5 10 15 19
Cost
Number of Opening Shows
Cost of Running Gallery
3-19
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CHAPTER 3 Cost Behavior and Forecasting
E 3-42 (Concluded)
3.
This is a mixed cost.
E 3-43
1. Total Cost = $80,000 + ($500 × Number of Opening Shows)
2. Total Cost = $80,000 + ($500 × 12) = $86,000
Total Cost = $80,000 + ($500 × 14) = $87,000
$79,000
$80,000
$81,000
$82,000
$83,000
$84,000
$85,000
$86,000
$87,000
$88,000
0 5 10 15 20
Total Cost
Number of Opening Shows
Ben’s Total Costs
3-20
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CHAPTER 3 Cost Behavior and Forecasting
E 3-44
1. The high point is March with 3,500 appointments. The low point is May
with 1,500 appointments.
2. Variable Rate = ($2,790 – $1,790)/(3,500 – 1,500)
= $1,000/2,000 appointments
= $0.50 per tanning appointment
Using the high point:
Fixed Cost = $2,790 – ($0.50 × 3,500) = $1,040
OR
Using the low point:
Fixed Cost = $1,790 – ($0.50 × 1,500) = $1,040
3. Total Tanning Service Cost = $1,040 + ($0.50 × Number of Appointments)
4. Total Predicted Cost for September = $1,040 + ($0.50 × 2,500) = $2,290
Total Fixed Cost for September = $1,040
Total Predicted Variable Cost for September = $0.50 × 2,500 = $1,250
5. Using the high-low method means that Luisa’s estimate of the cost formula (and
therefore the cost behavior patterns) is based on only two data points and ignores
all of the other data. She should investigate to be sure that neither the high nor the
low data point are outliers that would distort the cost formula results. Also, Luisa
might be wise to calculate the cost formula 6 to 12 months later after a longer
time period has elapsed since starting the tanning business. More time, and
data, would help her judge whether the high and low points are outliers or are
representative of the typical cost behavior patterns in her tanning business.
Finally, Luisa might be wise to ensure that all of the data from the previous 8
months were collected from within the relevant range of operations, which is
important when estimating total fixed costs and variable cost per unit. For example,
in some months, the number of tanning appointments is about three times that
of other months. It appears there is significant excess tanning bed capacity in
slow months or machines are being run to their utmost capacity in busy months.
This might lead to greater machine breakdown and maintenance costs.
3-21
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CHAPTER 3 Cost Behavior and Forecasting
E 3-45
Yes, it appears that there is a linear relationship between tanning cost and number
of appointments.
E 3-46
1. Total Cost of Tanning Services = $1,016 + ($0.53 × Number of Appointments)
2. Total Predicted Cost for September = $1,016 + ($0.53 × 2,500) = $2,341
$0
$500
$1,000
$1,500
$2,000
$2,500
$3,000
0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000
Monthly Cost
Number of Appointments
Scattergraph of Tanning Services
3-22
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CHAPTER 3 Cost Behavior and Forecasting
E 3-47
1. Airplane depreciation:
Variable Rate = ($18,000,000 – $18,000,000)/(44,000 – 28,000) = $0
Fixed Cost = $18,000,000 – ($0 × 44,000) = $18,000,000
2. Total Cost of Airplane Depreciation = $18,000,000
Airplane depreciation is a strictly fixed cost.
3. Fuel:
Variable Rate = ($445,896,000 – $283,752,000)/(44,000 – 28,000) = $10,134
Fixed Cost = $445,896,000 – ($10,134 × 44,000) = $0
4. Total Cost of Fuel = $10,134 × (Number of Airplane Flight Hours)
Fuel is a strictly variable cost.
5. Airplane maintenance:
Variable Rate = ($15,792,000 – $11,504,000)/(44,000 – 28,000) = $268
Fixed Cost = $15,792,000 – ($268 × 44,000) = $4,000,000
6. Total cost of airplane maintenance:
$4,000,000 + ($268 × Number of Airplane Flight Hours)
Airplane maintenance is a mixed cost.
7. Total cost of each resource at 36,000 machine hours:
Total Cost of Airplane Depreciation
Total Cost of Fuel = $10,134 × 36,000
Total Cost of Airplane Maintenance = $4,000,000 + ($268 × 36,000)
= $13,648,000
= $18,000,000
= $364,824,000
3-23
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CHAPTER 3 Cost Behavior and Forecasting
E 3-48
1. Total Annual Cost of Airplane Depreciation = 12 × $18,000,000
= $216,000,000
Total Annual Cost of Fuel = $10,134 × (Annual Number of Airplane Flight Hours)
Total Annual Cost of Airplane Maintenance =
(12 × $4,000,000) + ($268 × Number of Airplane Flight Hours)
Note: Fixed and variable costs, based on monthly data, are computed in
Exercise 3-47.
2. Total Annual Cost of Airplane Depreciation = 12 × $18,000,000
= $216,000,000
Total Annual Cost of Fuel = $10,134 × 480,000 = $4,864,320,000
Total Annual Cost of Airplane Maintenance:
(12 × $4,000,000) + ($268 × 480,000) = $176,640,000
E 3-49
1. Total Cost of Receiving = $147,400 + ($210 × Number of Parts Inspected)
2. Independent variable—number of parts inspected
Dependent variable—total cost of receiving
Variable rate—$210 per part inspected
Fixed cost per month—$147,400
3. Total Cost of Receiving = $147,400 + ($210 × 6,800)
= $1,575,400
3-24
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CHAPTER 3 Cost Behavior and Forecasting
E 3-50
1. Total Annual Cost of Receiving:
= (12 × $147,400) + ($210 × Number of Parts Inspected in a Year)
= $1,768,800 + ($210 × Number of Parts Inspected in a Year)
Note: Fixed and variable costs, based on monthly data, are computed in
Exercise 3-49.
2. Total Annual Cost of Receiving = $1,768,800 + ($210 × 70,000)
= $16,468,800
E 3-51
1. Overhead cost……………… Dependent variable
$150,000…………………… Fixed cost (intercept)
$52…………………………… Variable rate (slope)
Direct labor hours………… Independent variable
2. Next Month’s Budgeted Overhead Cost = $150,000 + ($52 × 8,000)
= $566,000
3. Next Quarter’s Budgeted Overhead Cost = (3 × $150,000) + ($52 × 23,000)
= $450,000 + $1,196,000
= $1,646,000
4. Next Year’s Budgeted Overhead Cost = (12 × $150,000) + ($52 × 99,000)
= $1,800,000 + $5,148,000
= $6,948,000
3-25
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CHAPTER 3 Cost Behavior and Forecasting
E 3-52
1. Unit Direct Materials Cost = $80,000/20,000 units = $4.00
Unit Direct Labor Cost = $101,400/20,000 units = $5.07
Unit Variable Overhead Cost = $15,600/20,000 units = $0.78
Unit Fixed Overhead Cost = $54,600/20,000 units = $2.73
2. Unit direct materials cost………………………………………………… $ 4.00
Unit direct labor cost……………………………………………………… 5.07
Unit variable overhead cost……………………………………………… 0.78
Unit fixed overhead cost…………………………………………………… 2.73
Absorption cost per unit……………………………………………… $12.58
3. Ending Inventory in Units = 20,000 – 18,900 = 1,100 units
4. Absorption-Costing Ending Inventory = $12.58 × 1,100 units = $13,838
E 3-53
1. Unit direct materials cost ($123,000/50,000 units)…………………… $2.46
Unit direct labor cost ($93,000/50,000 units)…………………………… 1.86
Unit variable overhead cost ($65,000/50,000 units)…………………… 1.30
Variable-costing cost per unit………………………………………… $5.62
2. Variable-Costing Ending Inventory = $5.62 × (50,000 – 47,300) = $15,174
3-26
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CHAPTER 3 Cost Behavior and Forecasting
E 3-54
1. Unit direct materials cost……………………… $ 9.95
Unit direct labor cost…………………………… 2.75
Unit variable overhead cost…………………… 1.65
Unit fixed overhead cost………………………… 2.50
Absorption cost per unit…………………… $16.85
2. Unit direct materials cost……………………… $ 9.95
Unit direct labor cost…………………………… 2.75
Unit variable overhead cost…………………… 1.65
Variable cost per unit………………………… $14.35
3. Absorption-costing income:
Sales ($32 × 28,700)…………………………………………… $918,400
Less: Cost of goods sold ($16.85 × 28,700)……………… 483,595
Gross margin……………………………………..………… $434,805
Less:
Variable selling expense ($2 × 28,700)………………… $ 57,400
Fixed selling expense……………………………………… 65,500
Fixed administrative expense………………….………… 231,000 353,900
Operating income……………………………………………… $ 80,905
4. Variable-costing income:
Sales ($32 × 28,700)…………………………………………… $918,400
Less variable expenses:
Cost of goods sold ($14.35 × 28,700)…………………… $411,845
Selling expense ($2.00 × 28,700)……..………………… 57,400 469,245
Contribution margin……………………………….………… $449,155
Less fixed expenses:
Fixed overhead ($2.50 × 30,000)………………………… $ 75,000
Selling and administrative expenses………..………… 296,500 371,500
Operating income…………………………………..………… $ 77,655
3-27
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CHAPTER 3 Cost Behavior and Forecasting
E 3-55
1. SUMMARY OUTPUT
Multiple R 0.95657699
R Square 0.915039537
Adjusted R Square 0.90087946
Standard Error 27.97952866
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 50588.87585 50588.87585 64.62108425 0.000198083
Residual 6 4697.124145 782.8540242
Total 7 55286
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 4315.593336 158.0347739 27.30787174 1.59382E-07 3928.896176 4702.290497 3928.896176 4702.290497
DL hours 1.846241957 0.229668533 8.038724044 0.000198083 1.284263303 2.40822061 1.284263303 2.40822061
2. Overhead Cost = $4,316 + ($1.85 × Number of Direct Labor Hours)
3. The R² is 0.915, or 91.5%. In other words, 91.5% of the variation in the overhead costs from month to month
can be explained by the variability in the number of direct labor hours. Another factor (or factors) accounts
for 8.5% of the variability in monthly overhead cost. Thus, direct labor hours is a good predictor of overhead
cost. Another factor (or factors) accounts for the remaining 8.5% of overhead cost.
4. Overhead Cost = $4,316 + ($1.85 × 700) = $5,611
Regression Statistics
3-28
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CHAPTER 3 Cost Behavior and Forecasting
E 3-56
1. SUMMARY OUTPUT
Multiple R 0.917226463
R Square 0.841304384
Adjusted R Square 0.825434822
Standard Error 164.5461114
Observations 12
ANOVA
df SS MS F Significance F
Regression 1 1435368.689 1435368.689 53.01371284 2.6597E-05
Residual 10 270754.2279 27075.42279
Total 11 1706122.917
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 942.1029802 88.16653478 10.68549402 8.62887E-07 745.6556994 1138.550261 745.6556994 1138.550261
Deliveries 1.78781384 0.245543354 7.28105163 2.6597E-05 1.240709154 2.334918525 1.240709154 2.334918525
2. Delivery Cost = $942 + ($1.79 × Number of Deliveries)
3. The R² is 0.841, or 84.1%. In other words, 84.1% of the variation in the monthly cost of delivery from month to month
can be explained by the variability in the number of deliveries. Another factor (or factors) accounts for just under 16%
of the variability in monthly delivery cost. This means that the number of deliveries is a fairly good predictor of the
cost.
4. Delivery Cost = $942 + ($1.79 × 300) = $1,479
Regression Statistics
3-29
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CHAPTER 3 Cost Behavior and Forecasting
P 3-57
1. a. Mixed cost
b. Variable cost
c. Variable cost
d. Step cost with narrow steps
e. Fixed cost
f. Fixed cost
g. Variable cost (assumes counter help can be called in or sent back home as the
need arises)
h. Step cost
i. Mixed cost
2. a. While the contract stays the same ($150 per month plus $15 per hour of technical
time), the company’s need for computer technical help is so stable that the same
number of hours are required each month. Now, the cost is essentially fixed.
b. The company drives the vehicles on identical trips each month. Thus, the mileage
and type of trip (highway versus in town) never vary. Now, the cost is essentially
fixed.
c. If beer is purchased in advance each day, in barrels to be tapped at night, and the
leftover beer is poured down the drain at the close of business each day, the cost
would be a step cost.
d. The college may use so much paper that it considers the cost of maintaining the
printers and copiers as essentially variable.
e. Suppose that the dental office is located in a large shopping mall that charges rent
based on the level of sales. Rent would be variable.
f. If the law office expanded and an additional, temporary receptionist was hired on
days with a heavy volume of appointments, the cost would be mixed.
g. If the individuals working behind the counter are assured that their complete shift
would be worked once they arrive, the cost would be a step cost (assumes more
counter help could be called in if demand rose).
h. If the hygienists were paid based on number of patients seen, the cost would be
variable.
i. If a company decided that the fixed amount of $15 per month was very small
relative to the total electrical bill (e.g., $500 per month), then the cost could be
viewed as variable.
PROBLEMS
3-30
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CHAPTER 3 Cost Behavior and Forecasting
P 3-58
a. This must be the high-low method because she has only two data points (one for
each year).
b. This is the method of least squares done on a personal computer. While it is
possible to use a personal computer to do the other methods, it is unlikely that
Francis would have gone to all the trouble of entering 60 months of data simply
to use the high-low method.
c. Ron is making a scattergraph.
d. In all probability, Lois is using the high-low method. She can do this quickly and
get some rough results in time for her meeting.
P 3-59
a. Variable cost
b. Committed fixed cost
c. Discretionary fixed cost
d. Discretionary fixed cost
e. Discretionary fixed cost
f. Variable cost
g. Variable cost
h. Discretionary fixed cost
i. Discretionary fixed cost
j. Variable cost
3-31
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CHAPTER 3 Cost Behavior and Forecasting
P 3-60
1.
Yes, the relationship appears to be reasonably linear.
2. Using the high-low method:
Variable Receiving Cost = ($27,000 – $15,000)/(1,700 – 700) = $12
Fixed Receiving Cost = $15,000 – ($12 × 700) = $6,600
Predicted cost for 1,450 receiving orders:
Receiving Cost = $6,600 + ($12 × 1,450) = $24,000
3. Receiving Cost for the Quarter = (3 × $6,600) + ($12 × 4,650)
= $19,800 + $55,800
= $75,600
Receiving Cost for the Year = (12 × $6,600) + ($12 × 18,000)
= $79,200 + $216,000
= $295,200
$0
$5,000
$10,000
$15,000
$20,000
$25,000
$30,000
$35,000
0 200 400 600 800 1,000 1,200 1,400 1,600 1,800
Receiving Cost
Number of Receiving Orders
Scattergraph of Receiving Activity
3-32
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CHAPTER 3 Cost Behavior and Forecasting
P 3-61
1. Receiving Cost = $3,212 + ($15.15 × Number of Receiving Orders)
2. Receiving Cost = $3,212 + ($15.15 × 1,450) = $25,180
3. Receiving Cost for the Quarter = (3 × $3,212) + ($15.15 × 4,650)
= $9,636 + $70,448*
= $80,084
* Rounded
Receiving Cost for the Year = (12 × $3,212) + ($15.15 × 18,000)
= $38,544 + $272,700
= $311,244
P 3-62
1. Salaries:
Senior accountant—fixed
Office assistant—fixed
Internet and software subscriptions—mixed
Consulting by senior partner—variable
Depreciation (equipment)—fixed
Supplies—mixed
Administration—fixed
Rent (offices)—fixed
Utilities—mixed
3-33
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CHAPTER 3 Cost Behavior and Forecasting
P 3-62 (Concluded)
2. Internet and software subscriptions:
Variable Rate = ($850 – $700)/(150 – 120) = $5
Fixed Amount = $850 – ($5 × 150) = $100
Supplies:
Variable Rate = ($1,100 – $905)/(150 – 120) = $6.50
Fixed Amount = $1,100 – ($6.50 × 150) = $125
Utilities:
Variable Rate = ($365 – $332)/(150 – 120) = $1.10
Fixed Amount = $365 – ($1.10 × 150) = $200
Unit Variable
Fixed Cost
3. Salaries:
Senior accountant…………………………………… $2,500 —
Office assistant………………………………………… 1,200 —
Internet and software subscriptions…………………… 100 $ 5.00
Consulting by senior partner…………………………… — 10.00
Depreciation (equipment)………………………………… 2,400 —
Supplies…………………………………………………… 125 6.50
Administration……………………………………………… 500 —
Rent (offices)……………………………………………… 2,000 —
Utilities……………………………………………………… 200 1.10
Total cost……………………………………………… $9,025 $22.60
Total Clinic Cost = $9,025 + ($22.60 × Professional Hours)
For 140 professional hours:
Clinic Cost = $9,025 + ($22.60 × 140) = $12,189
Charge per Hour = $12,189/140 = $87.06
Fixed Charge per Hour = $9,025/140 = $64.46
Variable Charge per Hour = $22.60
4. For 170 professional hours:
Charge per Hour = ($9,025/170) + $22.60 = $75.69
The charge drops because the fixed costs are spread over more professional
hours.
3-34
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CHAPTER 3 Cost Behavior and Forecasting
P 3-63
1. Committed resource charges: monthly fee, activation fee, cancellation fee
(if triggered by contract cancellation prior to 1 year)
Flexible resource charges: all additional charges for airtime, long distance,
and roaming.
2. Plan 1:
= +
60 minutes = 45 minutes + 15 minutes
Plan 2:
= +
120 minutes = 45 minutes + 75 minutes
Plan 1 is more cost effective. Jana will have some unused capacity (on
average, 15 minutes a month), and the overall cost will be lower by $10 per
month.
3. Plan 1:*
= +
60 minutes = 90 minutes + (30) minutes
= +
60 minutes = 60 minutes + 0 minutes
Additional Minutes = 30 minutes
* There are a number of ways to illustrate the use of minutes with Plan 1. Here are two
possibilities. The problem, of course, is that all included monthly minutes are used and Jana
must purchase additional minutes.
Plan 2:
= +
120 minutes = 90 minutes + 30 minutes
Plan 2 is now more cost effective, as the monthly cost is $30. Under Plan 1,
Jana will pay $20 plus $30 (30 minutes × $1.00) per month. (The $1.00
additional charge includes the airtime and regional roaming charge.)
4. Results of students’ analyses will vary.
Minutes Available Minutes Used Unused Minutes
Minutes Available Minutes Used Unused Minutes
Minutes Available Minutes Used Unused Minutes
Minutes Available Minutes Used Unused Minutes
Minutes Available Minutes Used Unused Minutes
3-35
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CHAPTER 3 Cost Behavior and Forecasting
P 3-64
1. Variable costs—salary of the two paralegals times the percentage of time spent in
processing uncontested claims; salary of the accountant times the percentage of time
spent in this activity; cost of claims forms, checks, envelopes, and postage.
Fixed costs—salaries of the two paralegals times the percentage of time spent in
handling contested claims; depreciation on office equipment used in claims processing
activity.
2. The independent variable is number of claims; the dependent variable is cost of claims
processing.
3. The low point is March with $31,260 cost and 4,900 claims; the high point is June with
$44,895 cost and 7,930 claims.
Variable Rate = ($44,895 – $31,260)/(7,930 – 4,900)
= $13,635/3,030 claims
= $4.50 per claim
Using the high point:
Fixed Cost = $44,895 – ($4.50 × 7,930) = $9,210
Total Cost of Claims Processing = $9,210 + ($4.50 × Claims)
4. Cost of Outsourcing = $4.60 × 75,600 = $347,760
Cost of Processing In-House = (12 × $9,210) + ($4.50 × 75,600)
= $110,520 + $340,200
= $450,720
Tiffany should outsource the claims processing for a savings of $102,960
($450,720 – $347,760).
3-36
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CHAPTER 3 Cost Behavior and Forecasting
P 3-65
1. The state unemployment insurance premiums and the average cost per injury are fixed
with respect to the number of speakers sold. The state unemployment insurance
premiums are variable (to an extent) with respect to the number of injury claims. That is,
over a certain base premium, the premium increases as the number of injuries
increases. The average cost per injury is variable with respect to the number of serious
versus nonserious injuries incurred. However, Kicker’s experience was that serious
injuries could be reduced through education and changes in dangerous practices.
The number of speakers sold was not relevant.
2. Yes, the safety program paid for itself. There was a $50,000 reduction in annual cost of
state unemployment insurance premiums and a $22,000 reduction in the total cost of
injuries per year [$22,500 ($1,500 × 15) – $500 ($50 × 10)]. This is a monetary reduction
of $72,000 per year versus the $60,000 salary of the safety director. In addition, the
number of workdays lost went from 30 to 0, and the number of serious injuries went
from 4 to 0. While these reductions were not quantified (outside the average injury cost),
they are important and are considered a benefit of the safety program.
3-37
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CHAPTER 3 Cost Behavior and Forecasting
P 3-66
1. Direct materials……………………….………………… $2.85
Direct labor……………………….……………………… 1.92
Variable overhead……………………….……………… 1.60
Fixed overhead ($180,000/200,000 units)…………… 0.90
Total……………………….…………………………… $7.27
Per-unit inventory cost on the balance sheet is $7.27.
Units in Ending Inventory = 8,200 units + 200,000 units – 204,300 units
= 3,900 units
Total Ending Inventory = $7.27 × 3,900 units = $28,353
2. Absorption-costing income:
Sales (204,300 units × $9)…….………….……………….………….… $1,838,700
Less: Cost of goods sold (204,300 units × $7.27)………………… 1,485,261
Gross margin………………………………………………………… $ 353,439
Less: Selling and administrative expenses……………………….… 279,870
Operating income…………………………………….……………… $ 73,569
3. Direct materials……………………….………………… $2.85
Direct labor……………………….……………………… 1.92
Variable overhead……………………….……………… 1.60
Total……………………….…………………………… $6.37
Per-unit inventory cost under variable costing equals $6.37.
This differs from the per-unit inventory cost in Requirement 1 because the
balance sheet is for external use and reflects absorption costing. Variable
costing does not include per-unit fixed overhead. Also, the difference
between the number of units produced versus sold, multiplied by the
fixed overhead per unit, equals the difference in operating income
between absorption and variable costing income statements.
4. Variable-costing income:
Sales (204,300 units × $9)…….………….……………….………….… $1,838,700
Less variable expenses:
Variable cost of goods sold (204,300 units × $6.37)…………… 1,301,391
Variable selling and administrative (204,300 units × $0.90)… 183,870
Contribution margin……………………………………………………… $ 353,439
Less fixed expenses:
Fixed overhead…………………………………………….………… 180,000
Fixed selling and administrative…………………………………… 96,000
Operating income………………………………………………………… $ 77,439
3-38
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CHAPTER 3 Cost Behavior and Forecasting
P 3-66 (Continued)
5. Absorption-costing income:
Sales (196,700 units × $9)……………………………………………… $1,770,300
Less: Cost of goods sold (196,700 units × $7.27)…………………… 1,430,009
Gross margin……………………………………………………………… $ 340,291
Less: Selling and administrative expenses……………………………… 273,030
Operating income…………………………………………………………… $ 67,261
Variable-costing income:
Sales (196,700 units × $9)……………………………………………… $1,770,300
Less variable expenses:
Variable cost of goods sold (196,700 units × $6.37)……………… 1,252,979
Variable selling and administrative (196,700 units × $0.90)……… 177,030
Contribution margin………………………………….……………………… $ 340,291
Less fixed expenses:
Fixed overhead…………………………………………………………… 180,000
Fixed selling and administrative………………………………….…… 96,000
Operating income…………………………………..………………………… $ 64,291
3-39
© 2018 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
CHAPTER 3 Cost Behavior and Forecasting
P 3-67
1. Results of regressions:
10 Months’ 12 Months’
Data Data
Intercept…………………… 3,212 3,820
Slope………………………… 15.15 15.10
R²…………………………… 0.85 0.75
2.
The regression run on the 11 months of data from “typical” months appears to be better
than the one for all 12 months. R² is higher for the regression without the outlier
(85.88% versus 74.51%), and the scattergraph gives Tracy confidence that the data
without the outlier describe a relatively linear relationship. Since the storm damage
is not expected to recur, Month 11 can safely be dropped from a regression meant to
help predict future receiving cost.
The point for the 11th month (1,200 receiving orders and $28,000 total receiving cost)
appears to be an outlier. Since the cost was so much higher in this month due to an
event that is not expected to happen again, this data point could easily be dropped.
Then, data from the 11 remaining months could be used to develop a cost formula
for receiving cost.
$0
$5,000
$10,000
$15,000
$20,000
$25,000
$30,000
$35,000
0 500 1,000 1,500 2,000
Receiving Cost
Number of Receiving Orders
Scattergraph of Receiving Activity—12 Month’s Data
3-40
© 2018 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
CHAPTER 3 Cost Behavior and Forecasting
P 3-67 (Concluded)
3. Results for the method of least squares after dropping Month 11.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.926737002
R Square 0.85884147
Adjusted R Square 0.843157189
Standard Error 2051.780599
Observations 11
ANOVA
df SS MS F Significance F
Regression 1 230520858.3 230520858.3 54.75810248 4.10397E-05
Residual 9 37888232.62 4209803.625
Total 10 268409090.9
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 3168.559746 2565.261709 1.235179917 0.248035426 -2634.465393 8971.584884 -2634.465393 8971.584884
Receiving Orders 15.17946388 2.051314444 7.399871788 4.10397E-05 10.53906823 19.81985953 10.53906823 19.81985953
Receiving Cost = $3,169 + ($15.18 × Number of Receiving Orders)
Predicted Receiving Cost for a Month = $3,169 + ($15.18 × 1,450) = $25,180
3-41
© 2018 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
CHAPTER 3 Cost Behavior and Forecasting
P 3-68
1.
The overall relationship looks reasonably linear—although the data point for the first
quarter may be an outlier.
2. Using the high-low method:
Variable Power Cost = ($42,500 – $29,000)/(30,000 – 18,000) = $1.125
Fixed Power Cost = $42,500 – ($1.125 × 30,000) = $8,750
Total Power Cost = $8,750 + ($1.125 × Number of Machine Hours)
$0
$5,000
$10,000
$15,000
$20,000
$25,000
$30,000
$35,000
$40,000
$45,000
0 10,000 20,000 30,000 40,000
Cost of Power
Number of Machine Hours
Scattergraph of Power Cost
3-42
© 2018 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
CHAPTER 3 Cost Behavior and Forecasting
P 3-68 (Continued)
3. Output of regression program:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.893359672
R Square 0.798091504
Adjusted R Square 0.764440088
Standard Error 2673.924883
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 169569504.3 169569504.3 23.71643159 0.002794513
Residual 6 42899245.69 7149874.282
Total 7 212468750
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 6899.784483 5910.387735 1.167399635 0.287338538 -7562.413284 21361.98225 -7562.413284 21361.98225
Machine Hours 1.209051724 0.248267693 4.869951909 0.002794513 0.601562566 1.816540883 0.601562566 1.816540883
Total Power Cost = $6,900 + ($1.21 × Number of Machine Hours)
R² is 0.798, or 79.8%. This is not bad; however, a little more than 20% of the variance in the dependent variable
(power cost) is not explained by the independent variable (machine hours).
3-43
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CHAPTER 3 Cost Behavior and Forecasting
P 3-68 (Concluded)
4. The output of a regression program after Quarter 1 (20,000, $26,000) has been dropped.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.957883502
R Square 0.917540803
Adjusted R Square 0.901048964
Standard Error 1367.284823
Observations 7
ANOVA
df SS MS F Significance F
Regression 1 104009803.9 104009803.9 55.63605034 0.000683462
Residual 5 9347338.936 1869467.787
Total 6 113357142.9
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 12407.56303 3289.994132 3.771302479 0.013005506 3950.363873 20864.76218 3950.363873 20864.76218
Machine Hours 1.009803922 0.135381371 7.458957725 0.000683462 0.661795029 1.357812814 0.661795029 1.357812814
Total Power Cost = $12,408 + ($1.01 × Number of Machine Hours)
This regression looks better in terms of R². The R² for this regression is 0.92, or 92%. By dropping the outlier, the
explanatory power of machine hours is much improved. However, the controller should first carefully examine Quarter 1
to see what the reason was for the lower than expected power cost. If the explanation is that something occurred that is
not expected to reoccur, then the point can be dropped. If the reason is one that is expected to reoccur, then that needs
to be factored into the controller’s judgment about power costs.
3-44
© 2018 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
CHAPTER 3 Cost Behavior and Forecasting
P 3-69
1. The scattergraph provides evidence for a linear relationship, but the observation for
300 moves may be an outlier.
2. High (800, $14,560); Low (100, $3,000)
Variable Rate = ($14,560 – $3,000)/(800 – 100)
= $11,560/700 moves
= $16.514
* Variable rate rounded to three decimal places.
Fixed Rate Cost = $3,000 – ($16.514 × 100)
= $3,000 – $1,651.40
= $1,349
** Total fixed cost rounded to the nearest dollar.
Total Cost = $1,349 + ($16.514 × Number of Moves)
= $1,349 + ($16.514 × 550)
= $10,432
*** Total cost rounded to the nearest dollar.
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
$16,000
0 500 1,000
Cost
Number of Moves
Cost of Moving Materials
*
**
***
3-45
© 2018 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
CHAPTER 3 Cost Behavior and Forecasting
P 3-69 (Continued)
3. Output of the regression routine calculated by a spreadsheet:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.96785846
R Square 0.936749999
Adjusted R Square 0.926208332
Standard Error 1266.703399
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 142581862.5 142581862.5 88.86165795 8.10236E-05
Residual 6 9627225 1604537.5
Total 7 152209087.5
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 497.5 987.0073364 0.504048938 0.63219637 -1917.619944 2912.619944 -1917.619944 2912.619944
Number of Moves 18.425 1.954565778 9.426646167 8.10236E-05 13.64234984 23.20765016 13.64234984 23.20765016
Rounding the coefficients:
Variable Rate = $18.43 per move
Fixed Rate = $498
Total Cost = $498 + ($18.43 × Number of Moves)
= $498 + ($18.43 × 550) = $10,635
R² = 0.94 (rounded)
This says that 94% of the variability in the cost of moving materials is explained by the number of moves.
3-46
© 2018 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
CHAPTER 3 Cost Behavior and Forecasting
P 3-69 (Concluded)
4. Normally, we would prefer the least squares method since the data appear to be linear.
However, the third observation may be an outlier. If the third observation (300 moves
and $3,400 of cost) is dropped, the R² rises to 99%. The new cost formula would be:
Total Cost = $1,411 + ($17.28 × Number of Moves)
The higher fixed cost is much more in keeping with what we observed with the
scattergraph in Requirement 1.
3-47
© 2018 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
CHAPTER 3 Cost Behavior and Forecasting
Case 3-70
1. The order should cover the variable costs described in the cost formulas.
These variable costs represent flexible resources.
Materials ($94 × 20,000)……………………………………………………… $1,880,000
Labor ($16 × 20,000)…………………………………………………………… 320,000
Variable overhead ($80 × 20,000)…………………………………………… 1,600,000
Variable selling ($7 × 20,000)………………………………………………… 140,000
Total additional resource spending……………………………….……… $3,940,000
Divided by units produced…………………………………….…………… 2 0,000
Total unit variable cost…………………………………………………… $ 197
Garner should accept the order because it would cover total variable costs
and increase income by $15 per unit ($212 – $197) for a total increase of
$300,000.
2. The coefficients of determination indicate the reliability of the cost formulas.
Of the four formulas, overhead activity may be a problem. A coefficient of
determination of 0.56 means that only about 56% of the variability of
overhead cost is explained by direct labor hours. This should have a bearing
on the answer to Requirement 1 because if the percentage is low, there are
activity drivers other than direct labor hours that are affecting variability in
overhead cost. What these drivers are and how resource spending would
change need to be known before a sound decision can be made.
3. Resource spending attributable to order:
Materials ($94 × 20,000)…………………………………………….………… $1,880,000
Labor ($16 × 20,000)…….…………………………………….…..…………… 320,000
Variable overhead:
($85 × 20,000)……………….……………………………….……………… 1,700,000
($5,000 × 12)…………………………….…………………………………… 60,000
($300 × 600)……………………………..……………………..…………… 180,000
Variable selling ($7 × 20,000)…………………………………….………… 140,000
Total additional resource spending………………………………………… $4,280,000
Divided by units produced…………………………………………………… 2 0,000
Total unit variable cost………………………………………..………… $ 214
The order would not be accepted now because it does not cover the variable
activity costs. Each unit would lose $2 ($214 – $212).
CASES
3-48
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CHAPTER 3 Cost Behavior and Forecasting
Case 3-70 (Concluded)
It would also be useful to know the step-cost functions for any activities that have
resources acquired in advance of usage on a short-term basis. It is possible that
there may not be enough unused activity capacity to handle the special order, and
resource spending may also be affected by a need (which, in this case, would be
unexpected) to expand activity capacity.
Case 3-71
1. Carl’s behavior is definitely unethical. He is stealing confidential information from
Kilborn and using it for unethical advantages. Kilborn would not approve of Carl’s
actions and would have a potential lawsuit against him for theft of information.
2. Assuming that the data were acquired illicitly, Bill’s instincts were on target. To hire
Carl in implicit exchange for the confidential information would be a violation of
integrity. As soon as Carl joined Brindon’s staff, Kilborn could have legal standing
to include the Thomas Electronics Division in any suit against Carl. Not only are
Carl’s actions in violation of Kilborn’s code of conduct, but they should also be
against the Thomas Electronics Division’s code of conduct. Finally, Bill should
remember that Carl is basically a disloyal employee. If he is willing to act against
the best interests of his former employer, he will certainly be willing to act against
the best interests of his current and future employers.
3-49
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