Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
Chapter 10 Quantitative Analyses of Cost Functions
10.1 Use standard mathematical notation to specify a cost function that can be graphed
as a straight line.
1) There is a homogeneous relationship between the individual cost items in the dependent variable pool
and the cost driver when each activity whose costs are included in the dependent variable has the same
cost driver.
2) A single cost pool that includes many different costs is a heterogeneous cost pool.
3) A nonlinear cost function adequately describes the changes in the levels of the cost driver due to
changes in the behaviour of various costs.
4) A linear cost function is a function in which the graph of total costs versus a single cost driver forms a
straight line, within the relevant range.
5) When estimating cost functions, it is assumed that variations in total cost of a cost object cannot be
explained by variations in a single cost driver.
6) A mixed cost has a fixed element.
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
7) A cost-benefit relationship, relative to cost drivers and resulting costs, may develop because of physical
relationships, contractual relationships, or implicit relationships.
8) The selection of the best measure of benefit will depend upon the corresponding change in the cost
pool.
9) There is poor correlation if the predicted values do not match actual cost observation.
10) Correctly identifying the cost driver and separating fixed from variable costs are important inputs for
many management decisions.
11) The coefficient of determination (r2) measures the percentage of variation in Y explained by X (the
predictor variable).
12) Which of the following is an equation of a variable cost function?
A) Y = ax + bx
B) Y = a + bx
C) Y = b
D) Y = a
E) Y = bx
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
13) Which of the following describes the intercept in a linear cost function?
A) the component of fixed costs that, within the relevant range, does not vary with changes in the level of
the cost driver
B) the component of fixed costs that, within the relevant range, does vary with changes in the level of the
cost driver
C) the component of variable costs that, within the relevant range, does not vary with changes in the level
of the cost driver
D) the component of variable costs that, within the relevant range, does vary with changes in the level of
the cost driver
E) the sum of the components of both fixed and variable costs that, within the relevant range, do not vary
with changes in the level of the cost driver
14) For April, the month just ended, the cost components to make tapes were $2 per tape plus fixed costs
of $10,000. One thousand tapes were produced. For May the cost to make tapes will be $2.20 per tape plus
fixed costs of $10,000. Fifteen hundred tapes are expected to be produced. What are the estimates for the
intercept and slope coefficient for May, respectively?
A) $2.00 and $10,000.00
B) $2.20 and $10,000.00
C) $10,000.00 and $2.00
D) $10,000.00 and $2.20
E) $22,000 and $10,000
15) The cost function y = 1,000 + 5X
A) has a slope coefficient of 1,000.
B) has an intercept of 5.
C) is a straight line.
D) represents a fixed cost.
E) is missing the slope coefficient.
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
16) Which of the following statements related to assumptions about estimating linear cost functions is
true?
A) Variations in a single cost driver explain variations in total costs.
B) A cost object is anything for which a separate measurement of costs is desired.
C) A linear function approximates cost behaviour at all ranges of production.
D) Correlation refers to the relationship between fixed and variable costs.
E) The graph of total costs does not form a straight line within the relevant range because of variable
costs.
17) Which of the following statements regarding a linear cost function is true?
A) When there are only fixed costs, total material costs increase as the number of units produced
increases.
B) The slope coefficient of a mixed cost line intersects the vertical axis at zero.
C) The relationship between the cost driver and the fixed cost is represented by the cost-benefit
relationship.
D) It is easier to identify a single measure of benefit in a more heterogeneous cost pool.
E) A linear cost function for manufacturing overhead can be graphed when the reported benefit received
can be paired with the corresponding dollar value of the cost pool.
18) Brandt Cheque Encoders employs 30 individuals. Ten employees are paid $10 per hour for 173 hours
a month and the rest are salaried employees paid $6,000 a month. How would total costs of personnel be
classified?
A) variable and fixed
B) a fixed cost within a relevant range
C) a variable cost within a relevant range
D) a mixed cost
E) a fixed cost
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
Use the information below to answer the following question(s).
Raymaster is a small computer software company which uses the account analysis method and has hired
you to perform some management advisory services. The company sold 2,500 high quality payroll
programs last year.
Cost of goods sold
$600,000
Store manager’s salary
80,000
Secretary’s salary
40,000
Operating costs (Store)
120,000
Sales Personnel 4 employees
Salary
$29,000 each
Commissions of 15% of sales
?
Advertising and promotion per year
20,000
Sales
1,200,000
19) What is the variable cost per unit sold?
A) $180,000
B) $320
C) $312
D) $240
E) $72
20) What is the total budgeted cost per unit sold?
A) $240.00
B) $288.00
C) $358.40
D) $362.40
E) $462.40
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
21) What would be their estimated cost per unit if Raymaster expects to sell 2,000 units next year?
A) $300
B) $312
C) $370
D) $498
E) $500
22) What is the predicted indirect manufacturing labour cost if 160 machine–hours are budgeted and 170
are actually worked, assuming the estimated cost function is y = $81.04 + 5.32x?
A) $985.44
B) $932.24
C) $904.40
D) $851.20
E) $81.04
23) A nonlinear cost function
A) has two constants and a single slope.
B) does not effectively describe the behaviour of costs all of the time.
C) never describes the behaviour of costs in relation to the cost driver.
D) always describes the behaviour of costs in relation to the cost drivers.
E) means the relevant range cannot be determined for that cost.
24) Time-series data analysis includes
A) using a variety of time periods to measure the predictor variable.
B) using the highest and lowest observation.
C) observing different entities during the same time period.
D) comparing information in different cost pools.
E) analyzing cost drivers at different levels of production.
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
Answer the following question(s) using the information below.
Penny’s TV and Appliance Store is a small company that has the following information pertaining to 2012
operations.
Sales (2,000 televisions)
$900,000
Cost of goods sold
400,000
Store manager’s salary per year
70,000
Operating costs per year
157,000
Advertising and promotion per year
15,000
Commissions (4% of sales)
36,000
25) What was the variable cost per unit sold for 2012?
A) $18
B) $235
C) $339
D) $200
E) $218
26) What were total fixed costs for 2012?
A) $242,000
B) $436,000
C) $678,000
D) $227,000
E) $278,000
27) What are the estimated total costs if Penny’s expects to sell 3,000 units next year?
A) $896,000
B) $678,000
C) $1,259,000
D) $269,000
E) $542,000
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
28) Which cost estimation method is being used by Penny’s TV and Appliance Store?
A) the industrial engineering method
B) the conference method
C) the high-low method
D) the quantitative analysis method
E) the account analysis method
29) Write a linear cost function equation for each of the following conditions. Use y for estimated costs
and X for activity of the cost driver.
a. Direct manufacturing labour is $10 per hour.
b. Direct materials cost $9.20 per cubic metre.
c. Utilities have a minimum charge of $1,000, plus a charge of $0.05 per kilowatt-hour.
d. Machine operating costs include $200,000 of machine amortization per year, plus $75 of utility costs
for each day the machinery is in operation.
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
30) Compute the estimated costs for each of the following equations assuming the following costs for
July:
Fixed manufacturing cost $80,000
Variable cost per machine-hour 6
Number of hours used 2,000
In addition, state whether each is for a variable, fixed, or mixed cost.
a. Total estimated costs = intercept
b. Total estimated costs = constant
c. Total estimated costs = constant + (slope × cost driver)
d. Total estimated costs = slope coefficient × cost driver
In addition, state whether each is for a variable, fixed, or mixed cost.
31) Compute the estimated costs for each of the following equations, assuming the following costs for
July:
Fixed manufacturing cost $40,000
Variable cost per machine-hour 6
Number of hours used 1,000
In addition, state whether each is for a variable, fixed, or mixed cost.
a. Total estimated costs = intercept
b. Total estimated costs = constant
c. Total estimated costs = constant + (slope × cost driver)
d. Total estimated costs = slope coefficient × cost driver
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
32) Write a cost estimating equation for each of the following conditions. Use y for estimated costs and X
for activity of the cost driver.
a. Direct manufacturing labour is $20 per hour.
b. Direct materials cost $8.00 per cubic metre.
c. Utilities have a minimum charge of $2,000 plus a charge of $0.05 per kilowatt hour.
d. Factory supplies average $10 per day plus $1.00 for each machine-hour per day.
e. Total manufacturing amortization includes $5,000 for straight-line plant amortization plus machinery
amortization of $100 for each day operated.
Use the information below to answer the following question(s).
Miller’s Good Value Appliance Store is a small company that has hired you to perform some
management advisory services. The following information pertains to 2012 operations.
Sales (5,000 microwave ovens)
$1,350,000
Cost of goods sold
540,000
Store manager’s salary per year
75,000
Operating costs per year
225,000
Advertising and promotion per year
25,000
Commissions (4% of sales)
67,500
33) What was the variable cost per unit sold for 2012?
34) What were total fixed costs for 2012?
35) What are the estimated total costs if Miller’s expects to sell 6,500 units next year?
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
36) Which cost estimation method is being used by Miller’s Good Value Appliance Store?
37) What are two of the assumptions against which data should be evaluated when used to develop a
linear cost function? Briefly explain the three ways that a linear cost function may behave?
38) List and briefly describe the five steps in estimating a cost function under quantitative analysis.
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
39) Discuss the potential use of nonlinear curves in cost functions and cost analysis. Give some examples.
40) Write a linear cost function equation for each of the following conditions. Use y for estimated costs
and X for activity of the cost driver.
a. Direct manufacturing labour is $10 per hour.
b. Direct materials cost $9.20 per cubic yard.
c. Utilities have a minimum charge of $1,000, plus a charge of $0.05 per kilowatt-hour.
d. Machine operating costs include $200,000 of machine depreciation per year, plus $75 of utility costs
for each day the machinery is in operation.
41) Write a linear cost function equation for each of the following conditions. Use y for estimated costs
and X for activity of the cost driver.
a. Direct materials cost is $.75 per pound.
b. Direct labour cost is $16.75 per hour.
c. Auto rental has a fixed fee of $75.00 per day plus $.50 per mile driven.
d. Machine operating costs include $350 of maintenance per month, and $5.00 of coolant usage costs for
each day the machinery is in operation.
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
10.2 Understand the various methods of cost estimation and use historical data to
predict future costs.
1) The account analysis method classifies cost accounts with respect to the identified cost driver.
2) All of the following are approaches to cost estimation EXCEPT
A) the account analysis method.
B) the conference method.
C) the flexible cost analysis method.
D) the industrial engineering method.
E) quantitative analysis.
3) Which of the following statements about the cost estimation methods is FALSE?
A) With the conference method, the accuracy of the cost estimates largely depends on the accuracy and
details of the inputs.
B) The methods require more historical data than most quantitative analyses.
C) The methods are not mutually exclusive.
D) There are four methods generally used for cost estimation.
E) Many organizations use a combination of the approaches.
4) The industrial-engineering method is
A) for analyzing relationships between inputs and outputs in physical terms.
B) for significant costs which cannot be easily traced.
C) used only for governmental contracts which are cost plus based.
D) used with qualitative rather than quantitative information.
E) used with both qualitative and quantitative information.
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
5) The collection of information on costs and their drivers, gathered through observations and interviews,
from departments within an organization is known as
A) the account analysis method.
B) the conference method.
C) the industrial-engineering method.
D) the quantitative analysis method.
E) the departmental analysis method.
6) Which cost estimation method typically uses qualitative analysis rather than quantitative analysis?
A) the account analysis method
B) the conference method
C) the industrial-engineering method
D) the quantitative analysis method
E) the departmental analysis method
7) Which cost estimation method would be described as a formal method to fit linear cost functions to
past data observations?
A) the account analysis method
B) the conference method
C) the industrial-engineering method
D) the quantitative analysis method
E) the departmental analysis method
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
Use the information below to answer the following question(s).
Presented below is the production data for the last six months of the year for the mixed costs incurred by
Wagner Company.
Month
Cost
Units
July
$24,450
8,200
August
20,120
6,400
September
32,400
10,600
October
44,200
15,000
November
29,000
9,600
December
36,680
13,200
8) Using the high-low method, the cost function would be stated as
A) Y = $2,200 + $2.80X.
B) Y = $17,816 + $0.36X.
C) Y = $536 + $3.06X.
D) Y = $24,450 + $0.33X.
E) Y = $39,250 + $0.33X.
9) The total cost at an operating level of 10,000 units would be
A) $31,136.
B) $30,200.
C) $21,416
D) $42,550
E) $46,625
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
Use the information below to answer the following question(s).
The Skip Corporation has assembled the following data pertaining to certain costs which cannot be easily
identified as either fixed or variable. Skip Corporation has heard about a method of measuring cost
functions called the high-low method and has decided to use it in this situation.
Cost
Hours
$20,000
7,000
12,200
4,000
17,000
5,200
15,640
4,900
18,200
6,000
22,080
7,800
21,200
7,480
18,600
6,760
10) The cost function would be stated as
A) Y = $13,386 + $0.46X.
B) Y = $10,680 + $0.38X.
C) Y = $5,056 + $2.16X.
D) Y = $1,800 + $2.16X.
E) Y = $1,800 + $2.60X.
11) The total cost at an operating level of 2,850 hours would be
A) $19,210.
B) $11,763.
C) $14,697.
D) $11,212.
E) $9,210.
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
Use the information below to answer the following question(s).
The Monroe Company uses the high-low method to estimate the cost function. The information for 2002
is provided below.
Machine
Hours
Labour
Costs
240
$4,000
110
2,960
12) What is Monroe Company’s slope coefficient per machine hour?
A) $26.91
B) $18.00
C) $16.67
D) $10.00
E) $8.00
13) What is the constant for the estimating cost equation?
A) $2,080
B) $2,960
C) $3,970
D) $4,000
E) $8,000
14) What is the estimate of Monroe’s cost function when 200 machine hours are used?
A) $1,840.00
B) $1,997.50
C) $2,280.00
D) $3,333.33
E) $3,680.00
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
Use the information below to answer the following question(s).
At the high point of the relevant range, labour hours at Bradco Restoration were 10,000 and wages were
$22,500. At the low point of the relevant range, labour hours were 7,500 and wages were $17,500.
15) Using the high-low method determine the slope coefficient per labour hour at Bradco Restoration?
A) $5.25
B) $4.00
C) $2.00
D) $0.50
E) $0.25
16) Using the high-low method determine the constant at Bradco Restoration?
A) $17,500
B) $13,750
C) $2,500
D) $1,250
E) $750
17) What is the high-low estimate of the labour costs at Bradco Restoration when 8,000 hours are used?
A) $21,500
B) $18,500
C) $17,750
D) $17,250
E) $17,125
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
18) When using the high-low method, the denominator in the equation that determines the slope is the
A) outcome variable.
B) predictor variable.
C) difference between the high and low observations of the cost driver.
D) difference between the high and low observations of the outcome variables.
E) the intercept.
19) When using the high-low method, the two observations used are the high and low observations of the
A) cost driver.
B) outcome variables.
C) outliers.
D) mixed costs.
E) total pool cost.
Answer the following question(s) using the information below.
The Taranto Company uses the high-low method to estimate it’s cost function. The information for 2012 is
provided below:
Machine-hours
Costs
2,000
$225,000
1,000
$125,000
20) What is the slope coefficient per machine-hour?
A) $125.00
B) $12.50
C) $10.00
D) $100.00
E) $0.50
Cost Accounting: A Managerial Emphasis, 6e
Chapter 10 – Quantitative Analyses of Cost Functions
21) What is the constant for the estimating cost equation?
A) $125,000
B) $225,000
C) $25,000
D) $0
E) $12,500
22) What is the estimate of the total cost when 1,100 machine-hours are used?
A) $125,000
B) $135,000
C) $150,000
D) $200,000
E) $136,000