Chapter 3: Cost Behavior
Lower 95% -378.386986 Upper 95% 1219.08466
95% confidence interval includes zero
Adjusted R Square 0.970652673
97% of variation in cost is explained by the regression equation (production units).
P-value 0.00139517
99% confident the units coefficient is not zero 1.00 - .001 = .999 or 99%
Total costs
= total fixed costs + total variable costs
t Stat
Coefficients divided by Standard Error
Account Analysis Method of Estimating a Cost Function
Cost Function on Units: TC = FC + (VC/Unit ×Qty) Cost Function on Dollars: TC = FC + (VC/Sales $ ×Sales $)
Hypothesis test of cost parameters
The "t Stat" tests the hypothesis that the parameters are different from zero. The "P-value" is the level of significance achieved (based upon the t-statistic) Probability that the true coefficient being estimated is zero If p-value < 5% → more than 95% confident that the true coefficient is not zero
Cost driver is
a measure of activity or volume level; increases in a cost driver cause (is correlated with) increases in total costs
Resources
economic elements that enable one to perform activities
Fixed Cost
A cost that does not change as output changes
Industrial Engineering Method
A forward-looking method of determining, through physical observation and analysis, what activities and in what amounts, are needed to complete a process. Doesn't rely on past costs; Expensive; seldom up-dated; Can be used for new products & services; Less useful for services that changes from customer to customer.
Goodness of fit
Adjusted R-square(Coefficient of Determination) statistic shows the percentage of variation in the Y variable that is explained by the regression equation (the independent variable). Has a value between 0 and 1.00. Typically use Adjusted R Square—adjusted for the number of variables included in the equation.
Two forms of learning curve
Cumulative Average-Time Learning Curve Assumes cumulative average time per unit decreases by a constant percentage Learning rate is expressed as a percent Incremental Unit-Time Learning Curve Assumes incremental unit-time decreases by a constant percentage each time the cumulative quantity of units produced doubles
High-Low Estimation Example
EXAMPLE: STEP 1: Find the slope (variable cost per activity): Difference in Total Cost/Difference in Activity = Variable Cost per Unit of Activity STEP 2: Find the intercept (total fixed costs) using TC ‒ (V x Q) = F So when you know the total cost, the variable cost per unit, and the quantity, you can solve for F (the intercept--total fixed costs). This begins from the cost formula TC = F + (V x Q), and isolates F.
Mixed Linear Cost Behavior
Has both variable and fixed cost elements. Total cost changes but not proportionately with changes in activity level.
Methods to separate costs into their fixed and variable components
Industrial Engineering Method Account Analysis Method Two Point Method (including High-Low Method) Scattergraph Method Regression (Ordinary Least Squares & Multiple)
Coefficient of Correlation
It is the square root of the coefficient of determination when there is one independent variable Range between −1 (negative correlation--variables move oppositely) and +1 (positive correlation--variables move together) The higher the magnitude, the greater the correlation A coefficient of correlation value close to zero indicates no correlation
P-value 0.19256333
Only 81% (not 95%) confident that intercept is significantly different from zero 1.00 - .19 = .81 or 81%
Piecewise linear costs
Some variable costs per unit are constant at one level for one range of activity and constant at another level for another range of activity.
Account Analysis to Estimate Cost Functions
Steps: 1.Separate fixed and variable costs 2.Total the fixed costs 3.Total the variable costs 4.Calculate a variable cost per driver 5.Write out the cost function Spring
Total Cost function
TC = F+ (V×Q) where: F= total fixed cost V= variable cost per unit of the cost driver Q= the quantity of the cost driver
Two-Point Method of Estimating a Cost Function
Use the information contained in two past observations of cost and activity to separate mixed and variable costs. assumes a line between the two points. It is easier and less costly to use than most other methods, but: it is not very accurate, and it can grossly misrepresent costs if the data points are not representative. The high-low method is a two-point method uses the information from the highest and lowest activity levels to estimate cost functions. the highest and lowest points may not be representative of costs in the relevant range.
Activity Capacity
When a firm acquires the resources needed to perform an activity
Multiple Regression
When least squares is used to fit an equation involving two or more independent variables Linear equation is expanded to include the additional variable (X2) TC = F + β1X1 + β2X2 Adding another independent variable
Multiple regression: more than one independent variable. Y = α+βX + ε
Y is the actual total costs for data point α is the intercept term; total fixed costs ε is the difference between the predicted total cost for Xi and the actual total cost for observation I (error term) X is the actual quantity of the cost driver for data point β is the slope term; the variable cost per unit
Cost object
any thing or activity for which costs are measured the item for which managers want cost information
Total fixed costs
are costs that do not change (in total) as activity levels change.
Total variable costs (for linear costs)
are costs that increase (in total) in proportion to the increase in activity levels
Total fixed costs
do not change as the cost driver increases. Higher total fixed costs are higher above the x axis.
Regression Analysis
estimates the parameters for a linear relationship between a dependent variable (Y) and one or more independent (explanatory) variables (X). [Minimizes the sum of the square of the vertical deviation—finds the "line of best fit"]
The _______ relates cost to increased efficiency -the more you perform a task the lower the cost is of doing it
experience curve
Step-costs
fixed at one level for one range of activity and fixed at another level for another range of activity.
Confidence intervals
gives an estimated range of values which is likely to include an unknown population parameter based upon a given level of confidence.
Total variable costs
increase as the cost driver increases. A steeper slope represents higher variable costs per unit of the cost driver.
Variable Cost
increases in total with an increase in output and decreases in total with a decrease in output
Sometimes nonlinear costs exhibit _______ over a [relevant]range of the cost driver.
linear cost behavior
Multiple regression
more than one independent variable
Simple regression (ordinary least squares)
only one independent variable
Scatterplot
shows cost observations plotted against levels of a possible cost driver. can assist in determining which cost driver might be the best for analyzing total costs, and the cost behavior of the cost against the potential cost driver. Advantages Allows for visual inspection of the data Identifies nonlinearity, outliers, and shifts in the cost relationship Disadvantages It is subjective.
Learning curve
shows how labor hours per unit decreases as units produced increases
The terms fixed cost and variable cost only have meaning when related to
some output measure or driver. materials handling may be measured by the number of moves; shipping goods may be measured by the units sold; laundering hospital linen may be measured by the pounds of laundry.
Flexible Resources
supplied as needed and used --Quantity of resource supplied equals quantity demanded --No unused capacity
Committed Resources
supplied in advance of usage --A given quantity is obtained, whether or not that full amount is used --Unused capacity is possible
Practical Capacity
the activity level where the activity is performed efficiently
Relevant range
the span of activity levels for which the cost behavior patterns hold
Cost behavior
the term used to describe whether a cost changes when the level of output changes.
Intercept
the total fixed cost
Slope
the variable cost per unit of the cost driver