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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
2.
Variable-cost estimate based on the scatter diagram on the next page:
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.
Cost predictions at 300 hours of operation:
(a)
High-low method:
(b)
Visually-fitted line:
(c)
Regression:
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.
Least-square regression using manual calculations:
(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
(b)
Calculation of parameters:
a
=
))(( )(
))(( ))((
2
2
XXXn
XYXXY
−
−
(c)
Cost formula:
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.
Least-square regression using manual calculations:
(a)
Tabulation of data:
Month
Dependent
Variable
(cost in
thousands)
Y
Independent
Variable
(thousands
of
passengers)
X
X2
XY
July .............................
54
16
256
864
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:
Calculation and interpretation of R2 using manual calculations:
(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
(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:
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$710,4$
−
−
Cost formula:
3.
Cost prediction at 600 hours of activity:
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)
2. Total cost for 1,700 tons:
Depreciation…………………………………………...
$ 30,000
Charitable contributions…………………………….
----
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)
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:
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
$10,000
$9,500
$11,500
$12,500
Chapter 06 - Activity Analysis, Cost Behavior, and Cost Estimation
PROBLEM 6-40 (CONTINUED)
2.
See graph for requirement (1).
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
*Pounds (in hundreds) of equipment loaded or unloaded
Chapter 06 - Activity Analysis, Cost Behavior, and Cost Estimation
PROBLEM 6-40 (CONTINUED)
5.
High-low method:
*Pounds (in hundreds) of equipment loaded or unloaded
Total cost at 2,600 units of activity ..............................................................
$12,120
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
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.
7.
Predicted Material-Handling Costs
Using Visually-Fit
Cost Line*
Using
High-Low Method
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.
Least-squares regression equation:
3.
Cost prediction:
4.
The cost predictions differ because the cost formulas differ under the three cost-
estimation methods. The high-low method, while objective, uses only two data points.
Ten observations are excluded.
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
(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:
