1. Activity Analysis, Cost Behavior, and Cost Estimation
Chapter 6
Activity Analysis, Cost Behavior, and Cost Estimation
Chapter 6: Activity Analysis, Cost Behavior, and Cost Estimation
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

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 focuses on historical data.
How does a managerial accountant determine the cost behavior pattern for a particular cost item?
The determination of cost behavior, which is often called cost estimation, can be accomplished in a number of ways.
One way is to analyze historical data concerning costs and activity levels.
The relationship between cost and activity, called cost behavior, is relevant to the management functions of planning, control, and decision making.
In order to plan operations and prepare a budget, managers need to predict the costs that will be incurred at different levels of activity.
Knowledge of cost behavior will help the manager to make the desired cost prediction.
A cost prediction is a forecast of cost at a particular level of activity. (LO1)
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3. Total Variable Cost Example
Your total Pay Per View bill is based on how many Pay Per View shows that you watch.
Total Pay Per View Bill
A variable cost changes in total in direct proportion to a change in the activity level (or cost driver).
For example, assume that you pay $4.95 for each Pay Per View show that you watch.
The more shows that you watch, the higher your Pay Per View bill will be.
The total cost of the Pay Per View bill increases in direct proportion to the number of shows watched.
Your text book describes the raw materials that goes into making donuts are also variable costs―the more donuts you make the higher the cost of raw materials. (LO2)
Number of Pay Per View shows watched
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4. Variable Cost Per Unit Example
The cost per Pay Per View show is constant. For example, $4.95 per show.
Cost per Pay Per View show
However, the variable cost per unit is constant as activity changes. In our Pay Per view example, the cost per show remains at $ To summarize, as activity changes, total variable cost increases in direct proportion to the change in activity level, but the variable cost per unit remains constant. (LO2).
Number of Pay Per View shows watched
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5. Total cost remains constant within a narrow range of activity.
Step-Variable Costs
Total cost remains constant within a narrow range of activity.
Some costs are nearly variable, but they increase in small steps instead of continuously.
Such costs, called step-variable costs, usually include inputs that are purchased and used in relatively small increments.
For a narrow range of activity, the total cost remains the same.
For example, the hourly rate for cashiers at a local grocery store is a set amount.
During hours when there are few customers only three cashiers are needed.
Therefore, at these low activity levels, the total cost for cashiers is the same. (LO2)
Cost
Activity
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6. Step-Variable Costs
Total cost increases to a new higher cost for the next higher range of activity.
But when the number of customers increases, the number of cashiers required increases.
The hourly rate, or cost per unit, stays the same but the total cost increases at the next higher range of activity. (LO2)
Cost
Activity
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7. Total Fixed Cost Example
Your monthly basic cable TV bill probably does not change no matter how many hours you watch.
Monthly Basic Cable Bill
A fixed cost remains unchanged in total as the activity level varies.
Examples of fixed costs include facilities costs, which include property taxes, depreciation on buildings and equipment, and the salaries of maintenance personnel.
The total cost of fixed costs remains constant, regardless of the level of activity. (LO2)
Number of hours watched
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8. Fixed Cost Per Unit Example
The average cost per hour decreases as more hours are spent watching cable television.
Monthly Basic cable Bill per hour watched
However, the fixed cost per unit does change as activity varies. The fixed cost per unit is calculated by dividing the total fixed costs by the number of units. Therefore, as the activity level increases, total fixed costs does not change, but unit fixed cost declines. For this reason, it is preferable in any cost analysis to work with total fixed cost rather than fixed cost per unit. (LO2)
Number of hours watched
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9. Rent Cost in Thousands of Dollars
Step-Fixed Costs
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. 90 60
Rent Cost in Thousands of Dollars
A company may rent office space at the cost of $30,000 per 1,000 square feet.
Extra space is only available in increments of 1,000 square feet.
The rent remains $30,000 regardless of activity.
As business increases, more square footage is needed.
The next 1,000 square feet costs another $30,000.
As the company expands, another 1,000 square feet is needed, costing another $30,000. (LO2) 30
0 1, , , Rented Area (Square Feet)
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10. A semivariable cost is partly fixed and partly variable.
A semivariable (or mixed) cost has both a fixed and a variable component.
Assume that a construction company leases a bulldozer and incurs a flat fee of $1500 per month, regardless of how many hours the bulldozer is used.
The company also incurs a cost of $35 per hour used. (LO2)
Consider the following example:.
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11. The slope is the variable cost per unit of activity.
Semivariable Cost
The slope is the variable cost per unit of activity.
Total semivariable cost
Variable Lease Charge Per Hour
Total Lease Cost
The company’s monthly bill would always be at least $1,500, the fixed portion of the lease.
The total cost would rise from $1,500, depending on how hours were used.
Therefore, the slope of a total cost line is the variable cost per unit of activity. (LO2)
Fixed Monthly Rental Charge
Rental Charge Per Hour
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12. Curvilinear Cost Total Cost Curvilinear Cost Function
A straight-line (constant unit variable cost) closely approximates a curvilinear line within the relevant range.
Relevant Range
The graphs of all of the cost behavior patterns examined so far consist of either straight lines or several straight-line sections.
A curvilinear cost behavior pattern has a curved graph.
Assume that a company groups its trash collection, telephone and electricity costs together as utility costs.
The company’s utilities cost may be a curvilinear cost. Recall that a marginal cost is the cost of producing the next unit.
For low levels of activity, the utilities cost would exhibit decreasing marginal costs because only the electricity costs would increase as production increased.
For high levels of activity the graph would exhibit increasing marginal costs.
If the demand for a particular month is at lower levels of activity, the company can use its modern, energy efficient equipment.
But at higher levels of activity, the older equipment must also be used.
This equipment is less energy-efficient.
As a result, the marginal utilities cost rises as monthly activity increases. (LO2)
Activity
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13. Curvilinear Cost Total Cost Curvilinear Cost Function
A straight-Line (constant unit variable cost) closely approximates a curvilinear line within the relevant range.
Management need not concern itself with extreme levels of activity if it is unlikely the company will operate at those activity levels.
Management is interested in cost behavior within the company’s relevant range, the range of activity within which management expects the company to operate. (LO3)
Relevant Range
Activity
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14. Engineered, Committed, and Discretionary Costs
Long-term, cannot be reduced in the short term.
Discretionary
May be altered in the short term by current managerial decisions.
Depreciation on Buildings and equipment
Advertising and Research and Development
Direct Materials
Engineered
Physical relationship with activity measure.
In the process of budgeting costs, it is often useful for management to make a distinction between engineered, committed, and discretionary costs.
An engineered cost bears a definitive physical relationship to the activity measure. Direct-material cost is an engineered cost.
A committed cost results from an organization’s ownership or use of facilities and its basic organization structure. Property taxes, depreciation on buildings and equipment, costs of renting facilities or equipment, and the salaries of management personnel are examples of committed fixed costs.
A discretionary cost arises as a result of a management decision to spend a particular amount of money for some purpose. Examples of discretionary costs include amounts spent on research and development, advertising and promotion, management development programs, and contributions to charitable organizations. (LO4)
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15. Visual-Fit Method
A scatter diagram of past cost behavior may be helpful in analyzing mixed costs.
When a cost has been classified as semi-variable, or when the analyst has no clear idea about the behavior of a cost item, it is helpful to use the visual-fit method to plot recent observations of the cost at various activity levels. (LO5)
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16. Plot the data points on a graph (total cost vs. activity).
Visual-Fit Method
Plot the data points on a graph (total cost vs. activity). *
Total Cost in 1,000’s of Dollars 10 20
Activity, 1,000’s of Units Produced
The resulting scatter diagram helps the analyst to visualize the relationship between cost and the level of activity (or cost driver). (LO5)
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17. Total Cost in 1,000’s of Dollars
Visual-Fit Method
Draw a line through the plotted data points so that about equal numbers of points fall above and below the line. *
Total Cost in 1,000’s of Dollars 10 20
Activity, 1,000’s of Units Produced
The cost analyst can visually fit a line to these data by laying a ruler on the plotted points. The line is positioned so that a roughly equal number of plotted points lie above and below the line. The scatter diagram provides little or no information about the cost relationship outside the relevant range. (LO5)
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18. Visual-Fit Method * Estimated fixed cost = $10,000 20
Vertical distance is total cost, approximately $16,000. *
Total Cost in 1,000’s of Dollars 10 20
Activity, 1,000’s of Units Produced
Estimated fixed cost = $10,000
The point where the line crosses the vertical axis is the estimated fixed costs.
The horizontal axis is the level of activity.
The vertical distance between the horizontal axis and the plotted line is the total cost at that level of activity. (LO5)
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19. The High-Low Method
Owl Co recorded the following production activity & maintenance costs for two months: Using these two levels of activity, compute: the variable cost per unit. the total fixed cost.
In the high-low method, the semi-variable cost approximation is computed using exactly two data points. The high and low activity levels are chosen from the available data set. These activity levels, together with their associated cost levels, are used to compute the variable cost per unit and the total fixed cost. (LO5)
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20. The High-Low Method
Before you can get started you must first calculate the change or difference in units and in cost. (LO5)
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21. The High-Low Method Unit variable cost = in cost in units
The first step of the high-low method is to divide the change in cost by the change in units. (LO5)
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22. The High-Low Method
Unit variable cost = $3,600 ÷ 4,000 units = $0.90 per unit
This will give you the variable cost per unit. (LO5)
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23. The High-Low Method
Unit variable cost = $3,600 ÷ 4,000 units = $0.90 per unit
Fixed cost = Total cost – Total variable cost
The next step is to determine the fixed costs. (LO5)
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24. The High-Low Method
Unit variable cost = $3,600 ÷ 4,000 units = $0.90 per unit
Fixed cost = Total cost – Total variable cost
Fixed cost = $9,700 – ($0.90 per unit × 9,000 units)
The total variable cost at either the high or low level is deducted from the total cost at the same level.
The total variable cost is calculated by multiplying the variable cost per unit (from step one) by the number of units. (LO5)
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25. The High-Low Method
Unit variable cost = $3,600 ÷ 4,000 units = $.90 per unit
Fixed cost = Total cost – Total variable cost
Fixed cost = $9,700 – ($.90 per unit × 9,000 units)
Fixed cost = $9,700 – $8,100 = $1,600
The total variable costs are deducted from the total cost to arrive at the fixed costs, $1,600. (LO5)
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26. Least-Squares Regression Method
Regression is a statistical procedure used to determine the relationship between variables such as activity and cost.
The objective of the regression method is the general cost equation:
Y = a + bX
Total Cost
Statistical techniques may be used to estimate objectively a cost behavior pattern using all of the available data.
The most common of these methods is called least-squares regression.
In the least-squares regression method, the objective is the general cost equation, Y = a + bX. (LO5)
Activity
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27. Equation Form of Least-Squares Regression Line
Y = a + bX
The intercept term (a) is the estimate of fixed costs.
Total Cost is the dependent variable.
The X term coefficient (b) is the estimate of variable cost per unit of activity, the slope of the cost line.
The activity (X) is the independent variable.
In the equation, X denotes the independent variable, such as activity level for a month, and Y denotes the estimated total utilities cost for that level of activity.
The intercept of the line on the vertical axis is denoted by a, and the slope of the line is denoted by b.
Within the relevant range, a is interpreted as an estimate of the fixed cost component, and b is interpreted as an estimate of the variable cost per unit of activity.
In regression analysis, X is referred to as the independent variable, since it is the variable upon which the estimate is based.
Y is called the dependent variable, since its estimate depends on the independent variable. (LO5)
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28. Least-Squares Regression Method
Statistics courses and computer courses deal with detailed regression computations using Microsoft Excel.
Accountants and managers must be able to interpret and use regression estimates.
The least-squares regression method does require considerably more computation than either the visual-fit or high-low method.
However, computer programs are readily available to perform least-squares regression.
In addition, accountants and managers must be trained to interpret and use regression estimates. (LO5)
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29. Multiple regression includes two or more independent variables:
Y = a + b1X1 + b2X2
Multiple regression is a statistical method that estimates a linear (straight-line) relationship between one dependent variable and two or more independent variables.
In a multiple regression equation, a denotes the regression estimate of the fixed-cost component, b1 denotes the regression estimate of the variable cost of variable 1 and b2 denotes the regression estimate of the variable cost of variable 2.
The multiple-regression equation will likely enable a controller to make more accurate cost predictions than could be made with the simple regression. (LO6)
Terms in the equation have the same meaning as in simple regression with only one independent variable.
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30. Engineering Method of Cost Estimation
A completely different method of cost estimation is to study the process that results in cost incurrence.
This approach is called the engineering method of cost estimation.
Engineering cost studies are time-consuming and expensive, but they often provide highly accurate estimates of cost behavior.
Moreover, in rapidly evolving, high-technology industries, there may not be any historical data on which to base cost estimates.
Such industries as genetic engineering, superconductivity, and electronics are evolving so rapidly that historical data are often irrelevant in estimating costs. (LO6)
Cost estimates are based on measurement and pricing of the work involved.
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31. Effect of Learning on Cost Behavior
I’ve noticed the same thing. And if you include all the variable overhead costs that are also declining, that must be the experience curve.
As I make more of these things it takes me less time for each one. It must be the learning curve effect that the boss was talking about.
In many production processes, production efficiency increases with experience. As cumulative production output increases, the average labor time required per unit declines. As the labor time declines, labor cost declines as well. This phenomenon is called the learning curve. When the learning-curve concept is applied to a broader set of costs than just labor costs, it is referred to as an experience curve. The learning curve and experience curve concepts have been applied primarily to complex, labor-intensive manufacturing operations, such as aircraft assembly and shipbuilding. Boeing and Airbus, for example, make extensive use of the learning and experience curve concepts when budgeting the cost for a new aircraft design. However, the learning curve also has seen limited application in the health care services industry, mainly focusing on complex surgical procedures. (LO6)
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32. Learning Curve Learning effects are large initially.
Learning effects become smaller, eventually reaching steady state.
Average Labor Time per Unit
A learning curve, then, is a graphical expression of the decline in the average labor cost required per unit as cumulative output increases.
Initially, the effects of learning are large. But eventually, these effects become smaller.
These cost predictions are then used in scheduling production, budgeting, setting product prices, and other managerial decisions. (LO6)
Cumulative Production Output
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33. Data Collection Problems
Missing data.
Outlier data points.
Mismatched time periods costs.
Trade-offs in choosing the time period.
Allocated and discretionary costs.
Inflation.
Regardless of the method used, the resulting cost estimation will be only as good as the data upon which it is based. The collection of data appropriate for cost estimation requires a skilled and experienced cost analyst. Six problems frequently complicate the process of data collection:
1. Missing data.
2. Outliers, which could represent errors or highly unusual circumstances.
3. Mismatched time periods.
4. Trade-offs in choosing the time period.
5. Allocated and discretionary costs.
6. Inflation.
(LO7)
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