Chapter 2
The Cost Function
Key Topics:
•
•
•
•
Cost Behavior
Cost Function and Assumptions
Cost Plots and Regression Analysis
Using Cost Information for Decisions
Chapter 2
1
Example: Total Versus
Average Cost
Lari’s Leather produces customized motorcycle jackets. The leather
for one jacket costs $50, and Lari rents a shop for $450/month.
Compute the total costs per month and the average cost per jacket if
she makes:
– One jacket per month
– 10 jackets per month
1 Jacket
TC/Mo
10 Jackets
AC/Jkt
TC/Mo
Leather
Leather
Rent
Rent
Total
Total
Chapter 2
AC/Jkt
2
Total Versus Average Cost
Behavior
• Graphs of total cost
• Graphs of average (per unit) cost
Chapter 2
3
Cost Function
Refer to the Lari’s Leather Example:
• Write the Cost Function
• Using the Cost Function, Calculate Total Monthly
Costs, Assuming the Company Makes:
– 1 Jacket
– 10 Jackets
Chapter 2
4
Cost Estimation Techniques
Our Focus in This Chapter:
• Cost Plots
• Regression Analysis:
– Simple Regression
– Multiple Regression
Other Methods:
• Analysis at the Account Level
• Engineered Estimate of Cost
• Activity Based Costing
• High-Low Method
Chapter 2
5
From Accounting Records
Scott Manufacturing
Schedule of Expenditures
Expenditure
Actual
Direct materials
$500,000
Direct labor
300,000
Rent
25,000
Insurance
15,000
Commissions
200,000
Property tax
20,000
Telephone
10,000
Depreciation
85,000
Power & light
30,000
Admin salaries
100,000
Total
$1,285,000
Note: 100,000 units were produced and sold.
Chapter 2
6
Developing a cost function
In margin
1. Separate fixed from variable costs
2. Total the fixed costs
3. Total the variable costs
4. Calculate a variable cost per unit
5. Write out the cost function
Chapter 2
7
When There Are No Units
Given
Need to use variable cost as a percentage
of revenues in cost function
TC = F + (VC/Revenue) *New Revenue
Chapter 2
8
Exercise: Creating a Cost
Function
Chapter 2
9
Cost Function Assumptions
Refer to the Wildcat Club Example:
If you use the cost function to estimate next month’s
costs, what assumptions are you making?
Chapter 2
10
Analyzing Cost Functions
Chapter 2
11
High-Low Method
• Pick highest and lowest points of either
cost or cost driver
• Solve for variable cost by analyzing
change in cost divided by change in
volume
• Solve for fixed cost using highest or lowest
point observations in TC = F + VC*Q
Chapter 2
12
A.Administrative Costs
Scatter Plot of Potential Cost
Driver
A.Scatter Plot With Trend Line
A.$80,000
A.$60,000
A.$40,000
A.$20,000
Chapter 2
A.$0
A.$0
A.$300,000
A.$600,000
A.$900,000
A.$1,200,000
A.Sales
13
Regression Output
A.SUMMARY OUTPUT
A.Regression Statistics
A.Multiple R
A.R Square
A.Adjusted R Square
A.0.9680477
A.0.93711636
A.0.90567454
A.Standard Error
A.Observations
A.3293.4038
A.4
A.ANOVA
A.df
A.SS
A.Regression
A.1
A.323277737
A.323277737
A.Residual
A.2
A.21693017.2
A.10846508.6
A.Total
A.3
A.344970754
A.Coefficients
A.Intercept
A.X Variable 1
Chapter 2
A.16800.2444
A.0.04466925
A.Standard Error
A.7734.73545
A.0.00818212
A.MS
A.t Stat
A.2.17205158
A.5.45937486
A.F
A.Significance F
A.29.8047739
A.P-value
A.0.16197623
A.0.0319523
A.0.0319523
A.Lower 95%
A.-16479.6594
A.0.00946441
14
Regression Output
•
•
•
•
Intercept coefficient = fixed cost
Slope coefficient = variable cost
R-square - goodness of fit statistic
T-statistic - compares coefficient with its
standard error
• P-value - the statistical significance of the
T-statistic
Chapter 2
15
Cost Function for Big Jack
• High Low
• TC = $11,728 + 0.050*Sales
• Regression
• TC = $16,800(?) + 0.045*Sales
Chapter 2
16
Positive Correlation
≠ Cost Driver
Chapter 2
17
Other Types of Cost
Functions
• Activity Outside the Relevant Range:
– Fixed costs (step function)
– Variable costs
•
•
•
•
No Apparent Cost Driver
Discretionary Costs
Economies of Scale
Learning Curves
Chapter 2
18
Using Cost Information for
Decision Making
• Keep in Mind: Management Decision Making
Framework
• Uncertainties
• Information Quality
• Quality of Estimation Techniques
• Reliability of Cost Estimates
Chapter 2
19