Cost Behavior: Analysis and Use

Cost Behavior: Analysis and Use UAA – ACCT 202 Principles of Managerial Accounting Dr. Fred Barbee

$ How does the cost react? Volume (Activity Base) As the volume of activity goes up ? ? Graphically ? ?

Why do I need to know this information? Good question. Here are some examples of when you would want to know this.

? ? Graphically $ ? ? Volume (Activity Base) For decision making purposes, it’s important for a manager to know the cost behavior pattern and the relative proportion of each cost.

Knowledge of Cost Behavior Setting Sales Prices Make-or-Buy decisions Entering new markets Introducing new products Buying/Replacing Equipment

$ Volume (Activity Base) Total Variable Costs

$ Volume (Activity Base) Per Unit Variable Costs

Variable Costs - Example A company manufacturers microwave ovens. Each oven requires a timing device that costs $30. The per unit and total cost of the timing device at various levels of activity would be: # of Units Cost/Unit Total Cost 1 $30 $30 10 30 300 100 30 3,000 200 30 6,000 Linearity is assumed

Variable Costs The equation for total VC: TVC = VC x Activity Base Thus, a 50% increase in volume results in a 50% increase in total VC.

Step-Variable Costs Step Costs are constant within a range of activity. $ But different between ranges of activity Volume (Activity Base)

$ Volume (Activity Base) Total Fixed Costs

$ Volume (Activity Base) Per-Unit Fixed Costs

# of Units Monthly Cost Average Cost 1 $9,000 $9,000 10 9,000 900 100 9,000 90 200 9,000 45 Fixed Costs - Example A company manufacturers microwave ovens. The company pays $9,000 per month for rental of its factory building. The total and per unit cost of the rent at various levels of activity would be:

Relevant Range Curvilinear Costs & the Relevant Range Economist’s Curvilinear Cost Function $ Accountant’s Straight-Line Approximation Volume (Activity Base)

$ Volume (Activity Base) Mixed Costs Variable costs Fixed costs

The Analysis of . . . Mixed Costs

Slope Intercept y = a + bX This is probably how you learned this equation in algebra.

Total Costs VC Per Unit (Slope) y = a + bX Fixed Cost (Intercept) Level of Activity

Total Costs Dependent Variable VC Per Unit (Slope) y = a + bX Fixed Cost (Intercept) Level of Activity Independent Variable

Methods of Analysis • Account Analysis • Engineering Approach • High-Low Method • Scattergraph Plot • Regression Analysis

Account Analysis Each account is classified as either • variable or • fixed based on the analyst’s prior knowledge of how the cost in the account behaves.

Engineering Approach Detailed analysis of cost behavior based on an industrial engineer’s evaluation of required inputs for various activities and the cost of those inputs.

Y 20 * * * * * * * * Total Cost in1,000’s of Dollars * * 10 0 X 0 1 2 3 4 Activity, 1,000’s of Units Produced The Scattergraph Method Plot the data points on a graph (total cost vs. activity).

Quick-and-Dirty Method Draw a line through the data points with about anequal numbers of points above and below the line. Y 20 * * * * * * * * Total Cost in1,000’s of Dollars * * 10 Intercept is the estimated fixed cost = $10,000 0 X 0 1 2 3 4 Activity, 1,000’s of Units Produced

Quick-and-Dirty Method The slope is the estimated variable cost per unit. Slope = Change in cost ÷ Change in units Y 20 * * * * * * * * Total Cost in1,000’s of Dollars * * 10 Horizontal distance is the change in activity. Vertical distance is the change in cost. 0 X 0 1 2 3 4 Activity, 1,000’s of Units Produced

Advantages • One of the principal advantages of this method is that it lets us “see” the data. • What are the advantages of “seeing” the data?

Activity Cost * * * * * 0 Activity Output Nonlinear Relationship

Activity Cost * * * * * * 0 Activity Output Upward Shift in Cost Relationship

Activity Cost * * * * * * 0 Activity Output Presence of Outliers

Brentline Hospital Patient Data Textbook Example

From Algebra . . . • If we know any two points on a line, we can determine the slope of that line.

High-Low Method • A non-statistical method whereby we examine two points out of a set of data . . . • The high point; and • The low point

High-Low Method • Using these two points, we determine the equation for that line . . . • The intercept; and • The Slope parameters y = a + bX

High-Low Method • To get the variable costs . . . • We compare the difference in costs between the two periods to • The difference in activity between the two periods.

Brentline Hospital Patient Data Low High Textbook Example

High/ Low Month Patient Days Maint. Cost High June 8,000 $9,800 Low March 5,000 7,400 Difference 3,000 $2,400

Change in Cost V = ------------------ Change in Activity (Y2 - Y1) V = ------------ (X2 - X1)

High/ Low Month Patient Days Maint. Cost High June 8,000 $9,800 Low March 5,000 7,400 Difference 3,000 $2,400 Calculate the Variable Rate The Change in Cost Divided by the change in activity

Change in Cost V = ------------------ Change in Activity $2,400 V = ------------ 3,000 = $0.80 Per Unit

Calculate Fixed Costs Total Cost (TC) = FC + VC - FC = - TC + VC FC = TC - VC

Calculate Fixed Costs Using June FC = TC - VC FC = $9,800 - (8,000 x $0.80) = $3,400

Calculate Fixed Costs Using March FC = TC - VC FC = $7,400 - (5,000 x $0.80) = $3,400

The Cost Formula y = a + bx TC = $3,400 + $0.80X

We have taken “Total Costs” which is a mixed cost and we have separated it into its VC and FC components.

So what? You say! Thank you for asking! Now I can use this formula for planning purposes. For example, what if I believe my activity level will be 6,325 patient days in February. What would I expect my total maintenance cost to be?

What is the estimated total cost if the activity level for February is expected to be 6,325 patient days? Y = a + bx TC = $3,400 + 6,325 x $0.80 TC = $8,460

Cost Behavior: Analysis and Use