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