1. Module 14 Cost Behavior and Cost Estimation

2. What is the nature of costs and how are they used in decision making?
Introduction
What is the nature of costs and how are they used in decision making?
Do they increase or decrease as production volume changes?
Do they remain stable?
How can we use cost behavior to predict future costs?

3. The Behavior of Fixed Costs
Fixed Costs remain the same in total, but may vary per unit when production volume changes.
Examples: Rent, Depreciation, Salary of a Plant Manager, Insurance, Property Taxes
Fixed Cost Per Unit $ $
Total Fixed Costs 4
100 2
1.33 25 50 75 25 50 75
Volume
Volume

4. The Behavior of Variable Costs
Variable Costs vary in direct proportion to changes in production volume, but are fixed when expressed as per-unit amounts.Examples: Direct material, some direct labor, and other unit-level costs like factory supplies. $
Total Variable Costs
Variable Cost Per Unit $
150
100 2 50 25 50 75 25 50 75
Volume
Volume

5. Curvilinear Costs and the Relevant Range Straight-Line Approximation
Curvilinear Function
Straight-Line Approximation
Volume

6. Costs Within the Relevant Range
Total fixed costs are constant.
Fixed cost per unit decreases as units increase.
Total variable costs increase as units increase.
Variable cost per unit is constant.
Use the constant measures to create a linear relationship.

7. Mixed Costs (Fixed and Variable)00
Volume

8. The Cost Equation (for mixed costs)
Y = a + bX
Y = total costs.
a = total fixed costs (intercept of line).
b = variable cost per unit (slope of line).
X = units produced.

9. Cost Behavior and Decision Making
For Pizza Pete’s:
Assume that direct materials were $2 per pizza, direct labor was $1.50 per pizza, and variable overhead was $1.00 per pizza, and that $6,300 is fixed overhead.
What would be the cost of goods sold
(1) for 2,600 pizzas?
(2) for 1,000 pizzas?

10. Cost Behavior and Decision Making
2,600
1,000
Direct materials
Direct labor
Variable OH
Fixed OH
Total COGS
COGS per Unit
$2.00
$1.50
$1.00
$5,200
3,900
2,600
6,300
$18,000
$ 2,000
1,500
1,000
6,300
$10,800
$6.92
$10.80
Alternative – use formula: Y = a + bX

11. Mixed Costs Fixed and Variable Components of Pizza Pete’s:
Fixed: lease payment each month.
Variable: pizza components, wages, electricity, etc., that vary with the number of deliveries made (and miles driven).

12. Separating Mixed Costs into their Fixed and Variable Components
High-Low Method: an algebraic technique of solving for the slope (variable cost per unit) and intercept (fixed costs) of a line, by using the high and low observations (coordinates) of the line.
Regression Analysis: A statistical technique used to estimate the slope (VCU) and intercept (FC) components of a mixed cost is called least squares regression. Regression analysis uses statistical methods to fit a cost line (regression line) through a set of points which minimizes the sum of the squared distance from each data point to the line (hence the name least squares regression).

13. Estimating Slope and Intercept Using the High-Low Method
1. Use only two data points, the high and low levels of activity and their related total overhead costs.
2. Subtract the smallest from the largest for each and use the changes in the following formula. 3.
Change in Cost
= Variable cost per unit
Change in volume

14. Estimating Slope and Intercept Using the High-Low Method
4. Substitute the total cost and activity of one of the points for “y” and “x” in the equation y = a + bx .
5. Substitute the variable cost found using high-low for “b” .
6. Solve for fixed costs “a” .
7. Determine the formula to use in estimating the mixed costs at various levels .

15. Estimating Slope and Intercept Using the High-Low Method
Example:
1. High Point = 2,500 units at $12,450
Low Point = 1,950 units at $10,525
2. 2, ,950 = 550 units (change in units)
$12,450 - $10,525 = $1,925 (change in cost)
3. $1,925 / 550 units = $3.50 variable cost/unit

16. Estimating Slope and Intercept Using the High-Low Method
Steps 4,5,6
Y =
$12,450 =
$3,700 =
a + bx
a + $3.50 (2,500)
a + $8,750 a
$3,700 + $3.50x
Volume at high pt
Cost at high pt
Variable Costs
Fixed Costs
7. Y = $3,700 + $3.50 (X)
(formula to use to estimate costs)

17. Least Squares Regression Analysis
Regression Line =
Total Overhead Cost
Slope represents the
change in $ for a 1
unit change in volume
Total
Costs
? $
Slope of Regression Line = Variable Cost
per unit
Fixed
Cost
1 unit
Volume

18. Regression Statistics
Benefits of regression:
Uses all of the observations, not just high and low.
Resulting measures offer insight into the quality of the output.
R2 (r-squared) indicates the goodness of fit for the model. Range between 0 and 1, a high R2 indicates that the relationship between the independent variable and the dependent variable explains most of the change in cost.
Problem: output may indicate a relationship, even when there is no relationship.

19. Using a Spreadsheet Program to Perform Regression Analysis
Using the actual values of the mixed costs (dependent variable) and the volume of production (independent variable) and a spreadsheet program such as Excel, you can compute a regression line using least squares regression.