©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Determining How Costs Behave Chapter 10 2/07/05

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Learning Objective 1 Explain the two assumptions frequently used in cost-behavior estimation. Costs are driven by activities called cost drivers and are linear within the relevant range

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Assumptions in Cost-Behavior Estimation Changes in total costs can be explained by changes in the level of a single activity, i.e., a cost driver. Cost behavior can adequately be approximated by a linear function of the activity level within the relevant range. For example, fixed costs are fixed and variable costs are constant per unit of activity.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Learning Objective 2 Describe linear cost functions and three common ways in which they behave. (Variable, Fixed and Mixed)

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Cost Function What is a cost function? It is a mathematical expression describing how costs change with changes in the level of an activity.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Cost Function La Playa Hotel offers an airline three alternative cost structures to accommodate its crew overnight: 1. $60 per night per room usage y = $60x The slope of the cost function is $60, because all costs are variable in this case.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Cost Function

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Cost Function 2. $8,000 per month y = $8,000 $8,000 is called a constant or intercept. The slope of the cost function is zero, because fixed costs don’t change with the level of activity.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Cost Function

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Cost Function 3. $3,000 per month plus $24 per room This is an example of a mixed cost. Part of the total cost is fixed, and part of the cost varies with the level of activity (x). y = $3,000 + $24x y = a + bx

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Cost Function

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Cost Classification (fixed or variable) determined by: Choice of cost object (Fleet of Vans vs. one Van) Time span (the longer the time the more likely the cost will vary) Relevant range of activity (Within which cost behavior patterns hold true)

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Choice of Cost Object Example If the number of taxis owned by a taxi company is the cost object, annual taxi registration and license fees would be variable costs. If miles driven during a year on a particular taxi is the cost object, registration and license fees for that taxi are fixed costs.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Time Span Whether a cost is variable or fixed with respect to a particular activity depends on the time span. More costs are variable with longer time spans.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Relevant Range Variable and fixed cost behavior patterns are valid for linear cost functions only within the given relevant range. Costs may behave nonlinear outside the range.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Cost Estimation What is cost estimation? It is the attempt to measure a past cost relationship between costs and the level of an activity. Past cost-behavior functions can help managers make more accurate cost predictions.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster The Cause-and-Effect Criterion In Choosing Cost Drivers Physical relationship (between the cost and the driver) Contractual agreements (x amount of cost per unit of activity) Implicitly established by logic (the more the units, the more the cost)

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Learning Objective 3 Understand various approaches to cost estimation.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Cost Estimation Approaches Industrial engineering method Conference method Account analysis method Quantitative analysis methods

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Account Analysis Example The cost analyst uses experience and judgment to separate total costs into fixed and variable. Avisha & Co. sells software programs. Total sales = $390,000 The company sold 1,000 programs.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Account Analysis Example Cost of goods sold = $130,000 Manager’s salary = $60,000 Secretary’s salary = $29,000 Commissions = 12% of sales What is the total fixed cost? $60,000 + $29,000 = $89,000 What is the fixed cost per unit sold?

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Account Analysis Example $89,000 ÷ 1,000 = $89.00 What is the variable cost per unit sold? Cost of goods sold: $130,000 Commissions: $390,000 ×.12 = $46,800 ($130,000 + $46,800) ÷ 1,000 = $176.80

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Learning Objective 4 Outline steps in estimating a cost function on the basis of past cost relationships.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Steps In Estimating A Cost Function Step 1: Choose the dependent variable (the cost to be estimated). Step 2: Identify the independent variable (cost driver). Step 3: Collect data on the dependent variable and the cost driver(s).

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Steps In Estimating A Cost Function Step 5: Estimate the cost function, (using High-Low or Regression analysis). Step 6: Evaluate the estimated cost function. Step 4: Plot the data on a graph.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster High-Low Method Example High capacity December: 55,000 machine-hours Cost of electricity: $80,450 Low capacity September: 30,000 machine-hours Cost of electricity: $64,200 What is the variable rate? Solving for b in general formula Y = a + b (X), Where Y is total cost, a is fixed cost, and b is variable cost per activity (X)

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster High-Low Method Example ($80,450 – $64,200) ÷ (55,000 – 30,000) $16,250 ÷ 25,000 = $0.65 Variable cost per unit of activity (b) What is the fixed cost (a)?

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster High-Low Method Example Using the high level of activity, $80,450 = Fixed cost + (55,000 × $0.65) Fixed cost = $80,450 – $35,750 = $44,700 Or, using the low level of activity, $64,200 = Fixed cost + (30,000 × $0.65) Fixed cost = $64,200 – $19,500 = $44,700 General Formula: y = a + bx y = $44,700 + $0.65 × (X) Machine-hours

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Regression Analysis It is used to measure the average amount of change in a dependent variable, such as Electricity cost, that is associated with unit increases in the amounts of one or more independent variables, such as machine-hours. Regression analysis uses all available data to estimate the cost function.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Regression Analysis Simple regression analysis estimates the relationship between the dependent variable and one independent variable. Regression analysis also provides R 2, which is an indication of the ‘goodness of fit’ of the general formula for estimating purposes.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Regression Analysis The regression equation and regression line are derived using the least-squares technique. See appendix : Regression Analysis The objective of least-squares is to develop estimates of the parameters a and b.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Regression Analysis The regression method is more accurate than the high-low method, because it uses information from all observations. A possible downside would be “outliers” which are non-representative observations.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Learning Objective 5 Describe criteria used to evaluate and choose cost drivers.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Goodness of Fit The coefficient of determination (r 2 ) expresses the extent to which the changes in (x) explain the variation in (y). An (r 2 ) of 0.80 indicates that more than 80% of the change in the dependent variable can be explained by the change in the independent variable.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Slope of Regression Line A relatively steep slope indicates a strong relationship between the cost driver and costs. (Good for accurately estimating costs) A relatively flat regression line indicates a weak relationship between the cost driver and costs.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Slope of Regression Line The closer the value of the correlation coefficient (r) to ±1, the stronger the statistical relation between the variables. As (r) approaches +1, a positive relationship is implied, meaning the dependent variable (y) increases as the independent variable (x) increases.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Learning Objective 6 Explain and give examples of nonlinear cost functions. (These would negate the linear assumption we make for Cost Behavior within the Relevant range)

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Nonlinearity and Cost Functions A nonlinear cost function is a cost function in which the graph of total costs versus the level of a single activity is not a straight line within the relevant range. Economies of scale Quantity discounts Step cost functions

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Nonlinearity and Cost Functions Economies of scale in advertising may enable an advertising agency to double the number of advertisements for less than double the cost. Quantity discounts on direct materials purchases produce a lower cost per unit purchased with larger orders.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Nonlinearity and Cost Functions A step function is a cost function in which the cost is constant over various ranges of the level of activity, but the cost increases by discrete amounts as the level of activity changes from one range to the next.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Learning Curves A learning curve is a function that shows how labor-hours per unit decline as units of output increase.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Experience Curve This is a function that shows how the costs per unit in various value chain areas decline as units produced and sold increase.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Learning Objective 8 Be aware of data problems encountered in estimating cost functions.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Data Collection and Adjustment Issues Time periods do not match between recording dependent variable cost and cost driver activity. Fixed costs are allocated as if they were variable. i.e., rent cost allocated to products Data are either not available or not reliable. Inflation may change relationship between cost and driver.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Data Collection and Adjustment Issues Extreme values of observations occur from mechanical errors in recording costs. Analysts should adjust or eliminate unusual observations before estimating a cost relationship. There is no homogeneous relationship. The relationship between the cost driver and the cost is not stationary.

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Data Collection and Adjustment Issues The most difficult task in cost estimation is collecting high-quality, reliably measured data on the dependent variable and the cost driver(s).

©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster End of Chapter 10