PPT 3 -1

Don R. Hansen

Maryanne M. Mowen

COST MANAGEMENT

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Activity CostBehavior

Chapter Three

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Learning Objectives

Define and describe fixed, variable, and mixed costs.

Explain the use of resources and activities and their relationship to cost behavior.

Separate mixed costs into their fixed and variable components using the high-low method, the scatterplot method, and the method of least squares.

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Learning Objectives (continued)

Evaluate the reliability of the cost formula. Explain how multiple regression can be used to

assess cost behavior Discuss the use of managerial judgment in

determining cost behavior.

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Fixed Cost Behavior Variable Cost Behavior

$ $Relevant Range

Activity Activity

Cost Behavior

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Total Costs

$Cost

Number of Units Produced

Fixed Costs Variable Costs

Linearity Assumption

Y = F + VX

The Behavior of a Mixed Cost

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Basic Terms

Activity capacity is the ability to perform activities.

Practical capacity is the efficient level of activity performance.

Resources are economic inputs that are consumed in performing activities.

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Types of Fixed Resources

Flexible Resources Committed Resources Discretionary Fixed Costs

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Flexible Resources

Flexible resources are supplied as used and needed.They are acquired from outside sources, where the terms of acquisition do not require any long-term commitment for any given amount of the resource.

Example: Materials and energy

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Committed Resources

Committed resources are supplied in advance of usage.

They are acquired by the use of either an explicit or implicit contract to obtain a given quantity of resource, regardless of whether the amount of the resource available is fully used or not. Committed resources may have unused capacity.

Example: Buying or leasing a building or equipment

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Committed Resources (continued)

Committed fixed expenses are costs incurred for the acquisition of long-term capacity.

Example: Plant, equipment, warehouses, vehicles, and salaries of top employees

Discretionary fixed expenses are shorter-term committed resources.

Example: The hiring of new receiving clerks

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Resource Relationships

The relationship between resources supplied and resources used is expressed by the following equation:

Resources available = Resources used + Unused capacity

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Available orders = Orders used + Orders unused

7,500 orders = 6,000 orders + 1,500 orders

Fixed engineering rate = $150,000/7,500

= $20 per change order

Variable engineering rate = $90,000/6,000

= $15 per change order

Example

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Cost of orders supplied = Cost of orders used + Cost of unused orders

= [($20 + $15) x 6,000] + ($20 x 1,500)

= $240,000

Of course, the $240,000 is precisely equal to the $150,000 spent on engineers and the $90,000 spent on supplies.

The $30,000 of excess engineering capacity means that a new product could be introduced without increasing current spending on engineering.

Example (continued)

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$Cost

Number of Units Produced

Linearity Assumption

Narrow Width

Step-Variable Costs

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$Cost

Number of Units Produced

Linearity Assumption

Wider Width

Step-Fixed Costs

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Methods for Measuring the Fixed and Variable Components of a Mixed Cost

The High-Low Method Scatterplot Method The Method of Least Squares

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Month Utility Costs Units ProducedJanuary $2,000 200February 2,500 400March 4,500 600April 5,000 800May 7,500 1,000

High-Low Method: An Example

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Y = F + VX

Variable Cost Rate (V)= (Y2 - Y1)/(X2 - X1) V = ($7,500-$2,000)/(1,000-200) V = $5,500/800 V = $6.875 per unit

The High-Low Method (continued)

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Y = F + VX$7,500 = F + $6.875 (1,000)

F = $7,500 - $6,875 F = $625

The cost formula using the high-low method is:

Y = $625 + $6.875 (X)

The High-Low Method (continued)

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Units Produced

UtilityCost

$8,000

6,000

4,000

2,000

0200 400 600 800 1,000

..

. ..

Analyst can fit linebased on his or herexperience

Important: Cost function is onlyrelevant within relevant range

Scatterplot Method

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Nonlinear Relationship

ActivityCost

0 Activity Output

**

***

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Upward Shift in Cost Relationship

ActivityCost

0 Activity Output

* **

**

*

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Presence of Outliers

ActivityCost

0 Activity Output

* **

**

*

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Least Squares

Constant 250

Std Err of Y Est 299.304749934466

R squared 0.944300518134715

No. of Observations 5

Degrees of Freedom 3

X Coefficient(s) 6.75

Std Err of Coef. 0.9464847243

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Least Squares (continued)

The results gives rise to the following equation:

Utility Costs = $250 + ($6.75 x # of units produced)

R2 = .944, or 94.4 percent of the variation in setup costs is explained by the number of setup hours variable.

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Using Confidence Intervals:

Given:*T-value for sample size of 5 at 95% confidence level is 3.182 (two-tale

test and 3 degrees of freedom)*Standard error of estimate for this sample at the 95% confidence level

is 598.6

The confidence interval for 300 units is: TC = $250 + 6.75 (300) + (3.192 x $598.6) = $2275 + $1911

Least Squares (continued)

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TC = b0 + b1X1 + b2X2 + . . .

b0 = the fixed cost or intercept

bi = the variable rate for the ith independent variable

Xi = the ith independent variable

Multiple Regression

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Utility MonthMHrs SummerCostJanuary 1,3400 $1,688February 1,2980 1,636March 1,3760 1,734April 1,4050 1,770May1,500 12,390June 1,4321 2,304July 1,322 12,166August 1,4161 2,284September 1,3701 1,730October 1,5800 1,991November 1,4600 1,840December 1,4550 1,833

Multiple Regression (continued)

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Constant 243.1115

Std Err of Y Est 55.5083

R squared 0.9672

No. of Observations 12

Degrees of Freedom 9

X Coefficient(s) 1.0972 510.4907

Std Err of Coef. 0.2102 32.5490

Multiple Regression (continued)

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Multiple Regression (continued)

The results gives rise to the following equation:

Utilities cost = $243.11 + $1.097(MH) + $510.49(Summer)

R2 = 0.967, or 96.7 percent of the variation in utilities cost is explained by the machine hours and summer variables.

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Use past experience Try to confirm results with operating personal Use common sense to confirm statistical studies

Some Tips

Cost Behavior and Managerial Judgment

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End of Chapter 3