Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
EXERCISE 6-33 (45 MINUTES)
1.
Variable utility cost per hour
=
400 700
$2,600 $3,800
−
−
=
$4.00
Total utility cost at 700 hours …………………………………………………………….
Fixed cost per month ………………………………………………………………………..
2.
Variable-cost estimate based on the scatter diagram on the next page:
Cost at
……………………………………………………………..
Cost at
……………………………………………………………..
Difference
……………………………………………………………..
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
EXERCISE 6-33 (CONTINUED)
Scatter diagram and visually-fit line:
0
1000
4000
5000
0100 200 300 400 500 600 700
Utility cost
per month
Hours of
operation
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
EXERCISE 6-33 (CONTINUED)
3. Estimation of variable- and fixed-cost components of cost behavior using least-
squares regression:
4.
(a)
High-low method:
=
$1,000 + ($4.00)(300) = $2,200
(b)
Visually-fitted line:
=
$2,190
(c)
Regression:
=
$1,002 + ($4.04)(300) = $2,214
5. Calculation of R2:
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
EXERCISE 6-33 (CONTINUED)
The following alternative approach to calculating the regression parameters is not a
requirement in the problem.
(a)
Tabulation of data:
Month
Dependent
Variable
(cost)
Y
Independent
Variable
(hours)
X
X2
XY
January …………………..
3,240
550
302,500
1,782,000
February …………………
3,400
600
360,000
2,040,000
March ……………………..
3,800
700
490,000
2,660,000
April ……………………….
3,200
500
250,000
1,600,000
May ………………………..
2,700
450
202,500
1,215,000
June ……………………….
(b)
Calculation of parameters:
a
=
))(( )(
))(( ))((
2
2
XXXn
XYXXY
−
−
=
(c)
Cost formula:
$1,002 + $4.04X, where X denotes hours of operation.
Variable utility cost
=
$4.04 per hour of operation
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
EXERCISE 6-34 (45 MINUTES)
The following alternative approach to calculating the regression parameters and R2 is not a
requirement in the problem.
(a)
Tabulation of data:
Month
Dependent
Variable
(cost in
thousands)
Y
Independent
Variable
(thousands
of
passengers)
X
X2
XY
July ………………………..
54
16
256
864
August ……………………
54
17
289
918
September ………………
57
16
256
912
October …………………..
60
18
324
November ……………….
54
15
225
810
December ……………….
17
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
EXERCISE 6-34 (CONTINUED)
(b)
Calculation of parameters:
a
=
))(( )(
))(( ))((
2
2
XXXn
XYXXY
−
−
(c)
Cost formula:
(a)
Formula for calculation:
2
2
2
)(
)‘ (
1
YY
YY
R
−
−
−=
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
EXERCISE 6-34 (CONTINUED)
(b)
Tabulation of data:*
Month
Y
X
Predicted Cost (in
thousands)
Based on
Regression
Line Y’
[( Y – Y’)2]†
[(Y –
Y
)2]†
July …………….
54
16
55.176
1.383
4.000
August ………..
54
17
56.812
7.907
4.000
September …..
57
16
55.176
3.327
1.000
October ……….
60
18
58.448
2.409
November ……
54
15
53.540
4.000
December ……
57
17
56.812
=
($29,000 + $1,636X)/$1,000
(c)
Calculation of R2:
(d)
Interpretation of R2:
The coefficient of determination, R2, is a measure of the goodness of fit of the
least-squares regression line. An R2 of .49 means that 49% of the variability of
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
SOLUTIONS TO PROBLEMS
PROBLEM 6-35 (20 MINUTES)
Note that j was not used.
PROBLEM 6-36 (15 MINUTES)
An appropriate activity measure for the school would be hours of instruction. The costs are
classified as follows:
Variable
Variable
Semivariable (or mixed)*
Fixed
Fixed
Fixed
Fixed
Semivariable (or mixed)
Fixed
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
6-29
PROBLEM 6-37 (25 MINUTES)
1.
Variable maintenance cost per hour of service
=
310 525
990,2$710,4$
−
−
=
$8.00
Total maintenance cost at 310 hours of service ………………………………….
Fixed maintenance cost per month ……………………………………………………
Cost formula:
Monthly maintenance cost = $510 + $8.00X, where X denotes hours of
maintenance service.
3.
Cost prediction at 600 hours of activity:
Maintenance cost = $510 + ($8.00)(600) = $5,310
4.
Variable cost per hour [from requirement (2)] …………………………………….
$8.00
Fixed cost per hour at 610 hours of activity ($510/610) ……………………….
$ .84*
*Rounded.
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
PROBLEM 6-38 (25 MINUTES)
1. Straight-line depreciation—committed fixed
The per-ton mining labor/fringe benefit cost is constant at both volume levels
presented, which is characteristic of a variable cost.
Royalties have both a variable and a fixed component, making it a semivariable
(mixed) cost.
Variable royalty cost = difference in cost difference in tons
Fixed royalty cost:
June
(2,700 tons)
December
(1,400 tons)
Total royalty cost……………………….
Less: Variable cost at $65 per ton…..
Fixed royalty cost………………………
2. Total cost for 1,700 tons:
Depreciation……………………………………………
$ 30,000
Charitable contributions…………………………….
—-
Mining labor/fringe benefits at $225 per ton…….
Royalties:
49,000
Trucking and hauling………………………………..
$852,000
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
PROBLEM 6-38 (CONTINUED)
3. Hauling 1,400 tons is not particularly cost effective. Lone Mountain Extraction will
4. A committed fixed cost results from an entity’s ownership or use of facilities and its
In times of severe economic difficulties, a company’s management will often
operations that may be difficult to overturn when economic conditions rebound.
5. Lone Mountain Extraction uses a calendar year for tax-reporting purposes. At year-
end, it may have ample funds available and decide to make donations to charitable
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
PROBLEM 6-39 (25 MINUTES)
1. Machine supplies: $153,000 34,000 direct-labor hours = $4.50 per hour
2. Plant maintenance cost:
April
(23,000
hours)
June
(34,000
hours)
* Excludes supervisory labor cost
Variable maintenance cost = difference in cost difference in direct-labor hours
Fixed maintenance cost:
April
(23,000
hours)
Total maintenance cost ……………………….
Less: Variable cost at $13.50 per hour …
Fixed maintenance cost ………………………
June
(34,000
hours)
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
PROBLEM 6-39 (CONTINUED)
3. Manufacturing overhead at 29,500 labor hours:
Machine supplies at $4.50 per hour ……………
$132,750
Depreciation …………………………………………….
22,500
Plant maintenance cost:
Supervisory labor …………………………………….
$933,000
4. A fixed cost remains constant when a change occurs in the cost driver (or activity
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
PROBLEM 6-40 (40 MINUTES)
1.
Material-handling costs
$10,500
$11,000
$10,000
$9,500
$11,500
$12,500
$12,000
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
PROBLEM 6-40 (CONTINUED)
2.
3.
The estimate of the fixed cost is the intercept on the vertical axis.
Fixed-cost component = $9,700
To estimate the variable-cost component, choose any two points on the visually-fitted
cost line. For example, choose the following points:
Activity
Cost
0 ………………………………………………………………………………….
2,000 ……………………………………………………………………………
Then proceed as follows to estimate the variable-cost component:
=
$1.00
*Pounds (in hundreds) of equipment loaded or unloaded
4.
Cost equation:
Total material-handling cost = $9,700 + $1.00X, where X denotes the number pounds
(in hundreds) of equipment loaded or unloaded during the month.
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
PROBLEM 6-40 (CONTINUED)
5.
High-low method:
=
$1.20
*Pounds (in hundreds) of equipment loaded or unloaded
Total cost at 2,600 units of activity ……………………………………………………..
$12,120
Fixed cost …………………………………………………………………………………………
$ 9,000
Cost equation based on high-low method:
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
PROBLEM 6-40 (CONTINUED)
6.
Memorandum
Date:
Today
To:
President, Nantucket Marine Supply
From:
I.M. Student
Subject:
Material-handling cost estimates
On the basis of a scatter diagram and visually-fitted cost line, the Material-Handling
Department’s monthly cost behavior was estimated as follows:
Material-handling cost per month = $9,700 + $1.00 unit of activity
A unit of activity is defined in this department as 100 pounds of equipment loaded or
unloaded at the loading dock.
Using the high-low method, the following cost estimate was obtained:
Material-handling cost per month = $9,000 + $1.20 unit of activity
In this case, the two data points used by the high-low method do not appear to be
representative of the entire set of data.
7.
Predicted Material-Handling Costs
Using Visually-Fit
Cost Line*
Using
High-Low Method
$11,950 = $9,700 + ($1.00)(2,250)
*This method is preferable, because it uses all of the data
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
PROBLEM 6-41 (45 MINUTES)
1. Estimation of variable and fixed components of cost behavior using least-squares
regression:
2.
Total monthly cost = $9,943 + $.89 per unit of activity
Least-squares regression equation:
3.
Cost prediction:
4.
Ten observations are excluded.
Therefore, least-squares regression is the preferred method of cost estimation.
5. Calculation of R2:
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
The following alternative approach to calculating the regression parameters is not a
requirement in the problem.
Least-squares regression using manual calculations:
(a)
Tabulation of data:
Month
Dependent
Variable
(cost in
thousands)
Y
Independent
Variable
(units of
activity in
thousands)
X
X2
XY
January …………………..
11.70
1.8
3.24
21.060
February …………………
11.30
1.6
2.56
18.080
March ……………………..
11.25
1.3
1.69
14.625
April ……………………….
10.20
1.0
1.00
10.200
May ………………………..
11.10
2.2
4.84
24.420
June ……………………….
12.55
2.4
5.76
30.120
July ………………………..
12.00
2.0
4.00
24.000
August ……………………
11.40
1.8
3.24
20.520
12.12
2.6
6.76
31.512
October …………………..
11.05
1.1
1.21
12.155
November ……………….
11.35
1.2
1.44
13.620
December ……………….
(b)
Calculation of parameters:
a
=
))(( )(
))(( ))((
2
2
XXXn
XYXXY
−
−
Chapter 06 – Activity Analysis, Cost Behavior, and Cost Estimation
PROBLEM 6-41 (CONTINUED)
(c)
Fixed- and variable-cost components:
Monthly fixed cost = $9,943*
Variable cost = $.89 per unit of activity (rounded)†
*The intercept parameter (a) computed above is the cost per month in thousands.