1. B313F Management and Cost Accounting
Lecture 6
Cost Estimation
By Charles Chiu, PhD, CFA

2. Relationship between cost and activity.
Introduction
Cost estimation
Cost behavior
Relationship between cost and activity.
Cost prediction
Using knowledge of cost behavior to forecast level of cost at a particular activity. Focus is on the future.
Process of determining cost behavior, often focusing on historical data.

3. Cost Terminology
Variable Costs – costs that change in total in relation to some chosen activity or output
Fixed Costs – costs that do not change in total in relation to some chosen activity or output
Mixed Costs – costs that have both fixed and variable components; also called semivariable costs

4. Cost Behavior Patterns

5. Unit Variable Cost
Total Variable Cost
Unit Fixed Cost
Total Fixed Cost

6. Examples of variable costs Examples of fixed costs
Merchandisers
Cost of Goods Sold
Service Organizations
Supplies and travel
Manufacturers
Direct Material, Direct Labor, and Variable Manufacturing Overhead
Merchandisers and Manufacturers
Sales commissions and shipping costs
Examples of fixed costs
Merchandisers, manufacturers, and service organizations
Real estate taxes, Insurance, Sales salaries Depreciation, Advertising

7. Types of Fixed Costs Committed Discretionary Examples Examples
Long-term, cannot be reduced in the short term.
Discretionary
May be altered in the short-term by current managerial decisions
Examples
Depreciation on Buildings and Equipment
Examples
Advertising and Research and Development

8. Trends in Cost Structure
A trend toward more fixed costs because of
Increased automation.
Stable workforce.
Implications
Managers are more “locked-in” with fewer decision alternatives.
Planning becomes more crucial: fixed costs are difficult to change with current operating decisions.

9. Cost Functions
A cost function is a mathematical representation of how a cost changes with changes in the level of an activity relating to that cost (cost driver)

10. Identifying Cost Drivers

11. Criteria for Evaluating Alternative Cost Drivers
Economic Plausibility
Economic significance
Goodness of Fit
Significance of the Independent Variable
Statistical significance

12. The Linear Cost Function
y = a + bX
The Dependent
Variable:
The cost that is
being predicted
The Independent
Variable:
The cost driver
The Slope of
the Line:
Variable cost
per unit
The Intercept:
Fixed costs

13. Y Total Cost Y = a + bX X Cost Variable Cost Fixed Cost
Number of Units Produced

14. The Linearity Assumption and the Relevant Range
Variations in the level of a single activity (the cost driver) explain the variations in the related total costs
Cost behavior is approximated by a linear cost function within the relevant range
Graphically, the total cost versus the level of a single activity related to that cost is a straight line within the relevant rage

15. Economist’s Curvilinear Cost Function
Relevant Range
A straight line closely approximates a curvilinear variable cost line within the relevant range.
Economist’s Curvilinear Cost Function
Total Cost
Accountant’s Straight-Line Approximation (constant unit variable cost)
Activity

16. Fixed Costs and Relevant Range
Example: Office space is available at a rental rate of $30,000 per year in increments of 1,000 square feet. As the business grows more space is rented, increasing the total cost.
Continue

17. Rent Cost in Thousands of Dollars90
Total cost doesn’t change for a wide range of activity, and then jumps to a new higher cost for the next higher range of activity.
Relevant Range 60
Rent Cost in Thousands of Dollars 30
, , , Rented Area (Square Feet)

18. Criteria for Classifying Variable and Fixed Components of a Cost
Choice of Cost Object – different objects may result in different classification of the same cost
Time Horizon – the longer the period, the more likely the cost will be variable
Relevant Range – behavior is predictable only within this band of activity

19. Cause-and-Effect Relationship for Cost Drivers
The most important issue in estimating a cost function is determining whether a cause-and-effect relationship exists between the level of an activity and the costs related to that level of activity.
A cause-and-effect relationship might arise as a result of:
A physical relationship between the level of activity and costs
A contractual agreement
Knowledge of operations
Note: a high correlation (connection) between activities and costs does not necessarily mean causality

20. Question for Discussion 1 
Which of the following statements about cost behavior are true?
Fixed costs per unit vary with the level of activity.
Variable costs per unit are constant within the relevant range.
Total fixed costs are constant within the relevant range.
Total variable costs are constant within the relevant range.

21. Cost Estimation Methods
Industrial Engineering Method
Conference Method
Account Analysis Method
Quantitative Analysis Methods
High-Low Method
Regression Analysis

22. Industrial Engineering Method
Estimates cost functions by analyzing the relationship between inputs and outputs in physical terms
Includes time-and-motion studies
Very thorough and detailed, but also costly and time consuming
Also called the Work-Measurement Method

23. Direct Labor Direct Material
Analyze the kind of work performed.
Estimate the time required for each labor skill for each unit.
Use local wage rates to obtain labor cost per unit.
Material required for each unit is obtained from engineering drawings and specification sheets.
Material prices are determined from vendor bids.

24. Nonlinear Cost Functions
Economies of Scale
Quantity Discounts
Step Cost Functions – resources increase in “lot-sizes,” not individual units
Learning Curves – labor hours consumed decrease as workers learn their jobs and become better at them
Experience Curve – broader application of learning curve that includes downstream activities including marketing and distribution

25. There is often a systematic
Learning Curves
There is often a systematic
relationship between experience in performing a task and the time required to do it.
The average time per task declines by a constant percentage each time the quantity of tasks done doubles.

26. Types of Learning Curves
Cumulative Average-Time Learning Model – cumulative average time per unit declines by a constant percentage each time the cumulative quantity of units produced doubles
Incremental Unit-Time Learning Model – incremental time needed to produce the last unit declines by a constant percentage each time the cumulative quantity of units produced doubles

27. Effect of Learning on Cost Behavior
Berry Co. makes products requiring labor that follows an 80 percent learning rate. If the first unit of such a product requires 10 hours, what is the average time for 16 units of this product?
An 80 percent learning rate: the average time required to make 2 units is 80 percent of the time for 1 unit and the average time for 4 units is 80 percent of the time for 2 units, etc.

28. Cumulative Average-Time Learning Model
The graphic presentation of the learning phenomenon is called the learning curve.

29. Learning Curve Learning effects are large initially.
Learning effects become smaller, eventually reaching expected final time.
Average Labor Time per Unit
Cumulative Production Output

30. determine investment required.
This is used to help
determine investment required.
This is used to estimate
ongoing results.
Average Labor Time per Unit
Cumulative Production Output

31. Learning Curve Formula

32. Question for Discussion 2 
Time to produce the first unit = 100 minutes
Learning factor = ln(0.80)/ln2 =
What is the cumulative average time to produce 5 units?
What is the total time to produce 5 units?
What is the time it took to produce the 5th unit?

33. Incremental Unit-Time Learning Model
Using the example of Berry Co. and using
the incremental unit-time learning model

34. Conference Method
Estimates cost functions on the basis of analysis and opinions about costs and their drivers gathered from various departments of a company
Pools expert knowledge
Reliance on opinions still makes this method subjective

35. Account Analysis Method
Estimates cost functions by classifying various cost accounts as variable, fixed, or mixed with respect to the identified level of activity
Is reasonably accurate, cost-effective, and easy to use, but is subjective

36. Total Cost = $2 per unit + $1,650
Example
Total Cost = $2 per unit + $1,650

37. Problems what is the proper cost driver what is truly fixed
changes in price
is a history available

38. Quantitative Analysis
Uses a formal mathematical method to fit cost functions to past data observations
Advantage: results are objective

39. Steps in Estimating a Cost Function Using Quantitative Analysis
Choose the dependent variable (the cost to be predicted)
Identify the independent variable or cost driver
Collect data on the dependent variable and the cost driver
Plot the data
Estimate the cost function using the High-Low Method or Regression Analysis
Evaluate the cost driver of the estimated cost function

40. The High-Low Method
WiseCo recorded the following production activity and maintenance costs for two months:
Using these two levels of activity, compute:
the variable cost per unit;
the fixed cost; and then
express the costs in equation form Y = a + bX.

41. The High-Low Method
Variable cost = $2,400 ÷ 3,000 units = $0.80 per unit
Fixed cost = Total cost – Total variable cost
Fixed cost = $9,800 – ($0.80 per unit × 8,000 units)
Fixed cost = $9,800 – $6,400 = $3,400
Total cost = Fixed cost + Variable cost (Y = a + bX) Y = $3,400 + $0.80X

42. Question for Discussion 3 
Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the variable portion of sales salaries and commission?
a. $0.08 per unit
b. $0.10 per unit
c. $0.12 per unit
d. $0.125 per unit

43. Question for Discussion 4 
Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000

44. Regression Analysis
Regression analysis is a statistical method that measures the average amount of change in the dependent variable associated with a unit change in one or more independent variables
Is more accurate than the High-Low method because the regression equation estimates costs using information from all observations; the High-Low method uses only two observations

45. Types of Regression
Simple – estimates the relationship between the dependent variable and one independent variable
Multiple – estimates the relationship between the dependent variable and two or more independent variables

46. Terminology
Goodness of Fit – indicates the strength of the relationship between the cost driver and costs
Residual Term – measures the distance between actual cost and estimated cost for each observation

47. The simple cost model is actually a regression model: TC = F + VX
Caution: Before doing the analysis, take time to determine if a logical relationship between the variables exists.
This model will only be useful within a relevant range of activity.

48. Simple Regression Method
Software can be used to fit a regression line through the data points.
The cost analysis objective is the same: Y = a + bX
Least-squares regression also provides a statistic, called the R2, that is a measure of the goodness of fit of the regression line to the data points.

49. R2 is the percentage of the variation in total cost explained by the activity.20 * * * * * * * * * *
Total Cost 10
R2 for this relationship is near 100% since the data points are very close to the regression line. X
Activity

50. Multiple regression includes two or more independent variables:
Terms in the equation have the same meaning as in simple regression with only one independent variable.
TC = FC + V1X1 + V2X2

51. Data Problems
The time period for measuring the dependent variable does not match the period for measuring the cost driver
Fixed costs are allocated as if they are variable
Some data may be missing or are not uniformly reliable
Extreme values of observations occur from errors in recording costs

52. There is no homogeneous relationship between the cost driver and the individual cost items in the dependent variable-cost pool.
The relationship between the cost driver and the cost is not stationary (not stable)
Inflation has affected costs, the driver, or both

53. Data Adjustment
Corresponding numbers should be causally related (i.e., if relating supplies to production units, the figures should be usage of supplies per some number of units of production NOT supplies purchased in the same period).
Consider outliers carefully: the object is to find the relationship that will hold in the future.
Remember that cost relationships can change over time (a “nonstationary” relationship).

54. The Ideal Database
The database should contain numerous reliably measured observations of the cost driver and the costs
In relation to the cost driver, the database should consider many values spanning a wide range

55. End of Lecture 6