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

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.

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

Cost Behavior Patterns

Unit Variable Cost Total Variable Cost Unit Fixed Cost Total Fixed Cost

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

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

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.

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)

Identifying Cost Drivers

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

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

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

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

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

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

Rent Cost in Thousands of Dollars 90 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 0 1,000 2,000 3,000 Rented Area (Square Feet)

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

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

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.

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

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

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.

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

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.

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

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.

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

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

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

Learning Curve Formula

Question for Discussion 2  Time to produce the first unit = 100 minutes Learning factor = ln(0.80)/ln2 = -0.32193 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?

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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.

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.

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 0 1 2 3 4 Activity

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

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

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

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).

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

End of Lecture 6