CHAPTER 3
DISCUSSION QUESTIONS
Q3-1. The total dollar amount of a fixed cost is con- costs is expediency, i.e., it requires less time
stant at different levels of activity within the and is, therefore, less costly than the use of
relevant range, but fixed cost per unit of activ- any of the three computational methods. The
ity varies. In contrast, the total amount of a disadvantage is that the use of managerial
variable cost varies at different levels of activ- judgment to separate fixed and variable costs
ity, but the variable cost per unit remains con- often results in unreliable estimates of cost.
stant within the relevant range. A semivariable Cost behavior is not always readily apparent
cost contains both fixed and variable ele- from casual observation. As a consequence,
ments. Consequently, both total semivariable managers often err in determining whether a
cost and semivariable cost per unit vary with cost is fixed or variable and frequently ignore
changes in activity. the possibility that some costs are semivari-
Q3-2. The relevant range is the range of activity able.
over which a fixed cost remains constant in Q3-5. The three computational methods available
total or a variable cost remains constant per for separating the fixed and variable compo-
unit of activity. The underlying assumptions nents of semivariable costs are: (1) the high
about the relationship of the activity and the and low points method; (2) the statistical scat-
incurrence of cost change outside the rele- tergraph method; and (3) the method of least
vant range of activity. Consequently, the squares.
amount of fixed cost or the variable cost rate Q3-6. The high and low points method has the
must be recomputed for activity above or advantage of being simple to compute, but it
below the relevant range. has the disadvantage of using only two data
Q3-3. The fixed and variable components of a semi- points in the computation, thereby resulting in
variable cost should be segregated in order to a significant potential for bias and inaccuracy
plan, analyze, control, measure, and evaluate in cost estimates. The scattergraph has the
costs at different levels of activity. Separation advantage of using all of the available data,
of the fixed and variable components of semi- but it has the disadvantage of determining the
variable cost is necessary to: fixed and variable components on the basis of
(a) compute predetermined factory overhead a line drawn by visual inspection through a
rates and analyze variances; plot of the data, thereby resulting in bias and
(b) prepare flexible budgets and analyze vari- inaccuracy in cost estimates. The method of
ances; least squares has the advantage of accu-
(c) analyze direct cost and the contribution rately describing a line through all the avail-
margin; able data, thereby resulting in unbiased
(d) determine the break-even point and ana- estimates of the fixed and variable elements
lyze the effect of volume on cost and of cost, but it has the increased disadvantage
profit; of computational complexity.
(e) compute differential cost and make com- Q3-7. The $200 in the equation, referred to as the
parative cost analyses; y intercept, is an estimate of the fixed portion
(f) maximize short-run profits and minimize of indirect supplies cost. The $4 in the equa-
short-run costs; tion, referred to as the slope of the regres-
(g) budget capital expenditures; sion equation, is an estimate of the variable
(h) analyze marketing profitability by territo- cost associated with a unit change in
ries, products, and customers. machine hours. These estimates may not be
Q3-4. The obvious advantage to using managerial perfectly accurate because they were derived
judgement to separate fixed and variable from a sample of data that may not be entirely
3-1
,3-2 Chapter 3
representative of the universe population, good fit. A standard error of zero would indi-
and because activities not included in the cate a perfect fit, i.e., all actual observations
regression equation may have some influ- would be on the regression fine.
ence on the cost being predicted. Q3-10. Heteroscedasticity means that the distribution
Q3-8. The coefficient of correlation, denoted r, is a of observations around the regression line is
measure of the extent to which two variables not uniform for all values of the independent
are related linearly. It is a measure of the variable. If heteroscedasticity is present, the
covariation of the dependent and independ- standard error of the estimate and confidence
ent variables, and its sign indicates whether interval estimates, based on the standard
the independent variable has a positive or error, are unreliable measures.
negative relationship to the dependent vari- Q3-11. Serial correlation means that rather than
able. The coefficient of determination is the being random, the observations around the
square of the coefficient of correlation and is regression line are correlated with one
denoted r 2. The coefficient of determination is another. If serial correlation is present, the
a more easily interpreted measure of the standard error of the estimate and confidence
covariation than is the coefficient of correla- interval estimates, based on the standard
tion, because it represents the percentage of error, are unreliable measures.
variation in the dependent variable explained Q3-12. Multicollinearity means that two or more of
by the independent variable. the independent variables in a multiple
Q3-9. The standard error of the estimate is defined regression analysis are correlated with one
as the standard deviation about the regres- another. When the degree of multicollinearity
sion line. It is essentially a measure of the is high, the relationship between one or more
variability of the actual observations of the of the correlated independent variables and
dependent variable from the points predicted the dependent variable may be obscured.
on the regression line. A small value for the However, this circumstance would normally
standard error of the estimate indicates a not affect the estimate of cost.
,Chapter 3 3-3
EXERCISES
E3-1
Activity Level Cost
High............................................ 2,600 hours $1,300
Low............................................. 2,100 1,100
Difference .................................. 500 hours $ 200
Variable rate: $200 ÷ 500 machine hours = $.40 per machine hour
High Low
Total cost ...................................
$1,300 $1,100
Variable cost:
$.40 × 2,600 hours........ 1,040
$.40 × 2,100 hours........ 840
Fixed cost.................................. $ 260 $ 260
E3-2
$1,000
$900
$800
$700
SUPPLIES COST
$600
$500
$400
$300
$200
$100
$0
0 200 400 600 800
DIRECT LABOR HOURS
Average cost ($7,575 total ÷ 10 months).................... $757.50
Fixed cost per month ................................................... 350.00
Average total variable cost .......................................... $407.50
$407.50 average total variable cost $.6936 variable cost
=
5,875 total direct labor hours ÷ 10 months per direct labor hour
, 3-4 Chapter 3
E3-3
Σ( x i − x )(y i − y ) 87, 000
b= = = $60
Σ( x i − x )2 1, 450
a = y– – bx– = $10,000 – ($60 × 125) = $2,500
Travel and entertainment expense for 200 sales calls would be:
yi = a + bxi = $2,500 + ($60 × 200 calls) = $14,500
E3-4
(1) (2) (3) (4) (5) (6)
y (y – y–) x (x – x–) (x – x–)2 – –)
(x – x )(y – y
Electricity Cost Machine Activity
Month Cost Deviation Hours Deviation (4) Squared (4) × (2)
January...... $1,600 100 2,790 190 36,100 19,000
February .... 1,510 10 2,680 80 6,400 800
March ......... 1,500 0 2,600 0 0 0
April ........... 1,450 (50) 2,500 (100) 10,000 5,000
May............. 1,460 (40) 2,510 (90) 8,100 3,600
June ........... 1,520 20 2,610 10 100 200
July ............ 1,570 70 2,750 150 22,500 10,500
August ....... 1,530 30 2,700 100 10,000 3,000
September . 1,480 (20) 2,530 (70) 4,900 1,400
October...... 1,470 (30) 2,520 (80) 6,400 2,400
November .. 1,450 (50) 2,490 (110) 12,100 5,500
December .. 1,460 (40) 2,520 (80) 6,400 3,200
Total $18,000 0 31,200 0 123,000 54,600
–
y = Σy = n = $18,000 ÷ 12 = $1,500
x– = Σx = n = 31,200 ÷ 12 = 2,600
Σ( x − x )(y − y ) Column 6 total 54, 600
Variable rate (b ) = = = = $.44
Σ( x − x ) 2
Column 5 total 123, 000
– – bx–
Fixed cost (a) = y
= $1,500 – ($.44)(2,600)
= $356
DISCUSSION QUESTIONS
Q3-1. The total dollar amount of a fixed cost is con- costs is expediency, i.e., it requires less time
stant at different levels of activity within the and is, therefore, less costly than the use of
relevant range, but fixed cost per unit of activ- any of the three computational methods. The
ity varies. In contrast, the total amount of a disadvantage is that the use of managerial
variable cost varies at different levels of activ- judgment to separate fixed and variable costs
ity, but the variable cost per unit remains con- often results in unreliable estimates of cost.
stant within the relevant range. A semivariable Cost behavior is not always readily apparent
cost contains both fixed and variable ele- from casual observation. As a consequence,
ments. Consequently, both total semivariable managers often err in determining whether a
cost and semivariable cost per unit vary with cost is fixed or variable and frequently ignore
changes in activity. the possibility that some costs are semivari-
Q3-2. The relevant range is the range of activity able.
over which a fixed cost remains constant in Q3-5. The three computational methods available
total or a variable cost remains constant per for separating the fixed and variable compo-
unit of activity. The underlying assumptions nents of semivariable costs are: (1) the high
about the relationship of the activity and the and low points method; (2) the statistical scat-
incurrence of cost change outside the rele- tergraph method; and (3) the method of least
vant range of activity. Consequently, the squares.
amount of fixed cost or the variable cost rate Q3-6. The high and low points method has the
must be recomputed for activity above or advantage of being simple to compute, but it
below the relevant range. has the disadvantage of using only two data
Q3-3. The fixed and variable components of a semi- points in the computation, thereby resulting in
variable cost should be segregated in order to a significant potential for bias and inaccuracy
plan, analyze, control, measure, and evaluate in cost estimates. The scattergraph has the
costs at different levels of activity. Separation advantage of using all of the available data,
of the fixed and variable components of semi- but it has the disadvantage of determining the
variable cost is necessary to: fixed and variable components on the basis of
(a) compute predetermined factory overhead a line drawn by visual inspection through a
rates and analyze variances; plot of the data, thereby resulting in bias and
(b) prepare flexible budgets and analyze vari- inaccuracy in cost estimates. The method of
ances; least squares has the advantage of accu-
(c) analyze direct cost and the contribution rately describing a line through all the avail-
margin; able data, thereby resulting in unbiased
(d) determine the break-even point and ana- estimates of the fixed and variable elements
lyze the effect of volume on cost and of cost, but it has the increased disadvantage
profit; of computational complexity.
(e) compute differential cost and make com- Q3-7. The $200 in the equation, referred to as the
parative cost analyses; y intercept, is an estimate of the fixed portion
(f) maximize short-run profits and minimize of indirect supplies cost. The $4 in the equa-
short-run costs; tion, referred to as the slope of the regres-
(g) budget capital expenditures; sion equation, is an estimate of the variable
(h) analyze marketing profitability by territo- cost associated with a unit change in
ries, products, and customers. machine hours. These estimates may not be
Q3-4. The obvious advantage to using managerial perfectly accurate because they were derived
judgement to separate fixed and variable from a sample of data that may not be entirely
3-1
,3-2 Chapter 3
representative of the universe population, good fit. A standard error of zero would indi-
and because activities not included in the cate a perfect fit, i.e., all actual observations
regression equation may have some influ- would be on the regression fine.
ence on the cost being predicted. Q3-10. Heteroscedasticity means that the distribution
Q3-8. The coefficient of correlation, denoted r, is a of observations around the regression line is
measure of the extent to which two variables not uniform for all values of the independent
are related linearly. It is a measure of the variable. If heteroscedasticity is present, the
covariation of the dependent and independ- standard error of the estimate and confidence
ent variables, and its sign indicates whether interval estimates, based on the standard
the independent variable has a positive or error, are unreliable measures.
negative relationship to the dependent vari- Q3-11. Serial correlation means that rather than
able. The coefficient of determination is the being random, the observations around the
square of the coefficient of correlation and is regression line are correlated with one
denoted r 2. The coefficient of determination is another. If serial correlation is present, the
a more easily interpreted measure of the standard error of the estimate and confidence
covariation than is the coefficient of correla- interval estimates, based on the standard
tion, because it represents the percentage of error, are unreliable measures.
variation in the dependent variable explained Q3-12. Multicollinearity means that two or more of
by the independent variable. the independent variables in a multiple
Q3-9. The standard error of the estimate is defined regression analysis are correlated with one
as the standard deviation about the regres- another. When the degree of multicollinearity
sion line. It is essentially a measure of the is high, the relationship between one or more
variability of the actual observations of the of the correlated independent variables and
dependent variable from the points predicted the dependent variable may be obscured.
on the regression line. A small value for the However, this circumstance would normally
standard error of the estimate indicates a not affect the estimate of cost.
,Chapter 3 3-3
EXERCISES
E3-1
Activity Level Cost
High............................................ 2,600 hours $1,300
Low............................................. 2,100 1,100
Difference .................................. 500 hours $ 200
Variable rate: $200 ÷ 500 machine hours = $.40 per machine hour
High Low
Total cost ...................................
$1,300 $1,100
Variable cost:
$.40 × 2,600 hours........ 1,040
$.40 × 2,100 hours........ 840
Fixed cost.................................. $ 260 $ 260
E3-2
$1,000
$900
$800
$700
SUPPLIES COST
$600
$500
$400
$300
$200
$100
$0
0 200 400 600 800
DIRECT LABOR HOURS
Average cost ($7,575 total ÷ 10 months).................... $757.50
Fixed cost per month ................................................... 350.00
Average total variable cost .......................................... $407.50
$407.50 average total variable cost $.6936 variable cost
=
5,875 total direct labor hours ÷ 10 months per direct labor hour
, 3-4 Chapter 3
E3-3
Σ( x i − x )(y i − y ) 87, 000
b= = = $60
Σ( x i − x )2 1, 450
a = y– – bx– = $10,000 – ($60 × 125) = $2,500
Travel and entertainment expense for 200 sales calls would be:
yi = a + bxi = $2,500 + ($60 × 200 calls) = $14,500
E3-4
(1) (2) (3) (4) (5) (6)
y (y – y–) x (x – x–) (x – x–)2 – –)
(x – x )(y – y
Electricity Cost Machine Activity
Month Cost Deviation Hours Deviation (4) Squared (4) × (2)
January...... $1,600 100 2,790 190 36,100 19,000
February .... 1,510 10 2,680 80 6,400 800
March ......... 1,500 0 2,600 0 0 0
April ........... 1,450 (50) 2,500 (100) 10,000 5,000
May............. 1,460 (40) 2,510 (90) 8,100 3,600
June ........... 1,520 20 2,610 10 100 200
July ............ 1,570 70 2,750 150 22,500 10,500
August ....... 1,530 30 2,700 100 10,000 3,000
September . 1,480 (20) 2,530 (70) 4,900 1,400
October...... 1,470 (30) 2,520 (80) 6,400 2,400
November .. 1,450 (50) 2,490 (110) 12,100 5,500
December .. 1,460 (40) 2,520 (80) 6,400 3,200
Total $18,000 0 31,200 0 123,000 54,600
–
y = Σy = n = $18,000 ÷ 12 = $1,500
x– = Σx = n = 31,200 ÷ 12 = 2,600
Σ( x − x )(y − y ) Column 6 total 54, 600
Variable rate (b ) = = = = $.44
Σ( x − x ) 2
Column 5 total 123, 000
– – bx–
Fixed cost (a) = y
= $1,500 – ($.44)(2,600)
= $356
