cost accounting dr. baldwin university of arkansas – fort smith fall 2010

Cost Accounting

Dr. BaldwinUniversity of Arkansas – Fort

SmithFall 2010

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Chapter 10

Determining How Costs Behave

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Why understand cost behavior?

• Managers need to understand cost behavior in order to make decisions about strategy and about operations.

• For example– Product decisions

• Apple iPod, iPhone, iPad• Amazon Kindle

– Other decisions• Fort Smith administration enrollment

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What do we already know about the nature of costs?

Variable Cost

Fixed Cost

Mixed Cost

Cost

Volume of Activity

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Assumptions

• Costs are linear– or approximated by linear functions

• Each cost has a single cost driver

• Are these always true? Not always!• We generally assume they are true

within the relevant range.

• Exercise 18.

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Relevant Range

• The range of the activity in which total cost and the level of activity are related.

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How to understand cost behavior?

A cost function is • a mathematical description of how

a cost changes with changes in the volume of its cost driver activity.

Variable Cost

Fixed Cost

Mixed Cost

Cost

Volume of Activity

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Linear Cost Functions example

• Let’s assume you are a spin class instructor and you have to provide your own music for class. You spend a lot of time and money downloading songs to use in class. uTunes is providing three different payment options.– Let’s look at the options and identify

the cost function for each.

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Linear Cost Functions example

• Option A– Pay $5 per song downloaded

• Option B– Pay $100 per month for unlimited

downloads• Option C

– Pay $50 per month plus $0.50 per download

• Create a cost function for each option using the generic linear cost function formula.

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Create a Linear Cost Function

Formula: Y = a + bX• Where:

– Y = total costs– a = fixed costs– b = variable cost per unit of cost driver– X = cost driver

• Option A: Y = $0 + $5X• Option B: Y = $100 + $0X• Option C: Y = $50 + $0.50X

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Variable Cost

Fixed Cost

Mixed Cost

Cost

Volume of Activity (downloads)

A

B

C

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Calculate Total Cost of Each Option

Which option is least expensive?• Assuming 40 downloads a month, what

is the total cost per month for each option?

• Option A: Y = $0 + $5 * 40 = $200

• Option B: Y = $100 + $0*40 = $100

• Option C: Y = $50 + $0.50*40 = $70

• What happens if you download more or less than 40? 100? 200?

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Variable Cost

Fixed Cost

Mixed Cost

Cost

Volume of Activity (downloads)

A

B

C

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100

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Cost Estimation Methods• Many methods to estimate costs• Potential problems in cost

estimation– Availability of historical data– Accuracy of data– The estimates are only as good as the

data on which they are based.

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Cost Estimation Methods• Industrial Engineering

– Time and motion studies• Conference

– Consensus of estimates

• Account Analysis• Quantitative Analysis

– High-Low Method– Regression

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Account Analysis Method

Use knowledge of operations to• Classify cost accounts according to

their relationship with the cost driver activity:– variable, fixed, or mixed

• Estimate the cost/driver relationship

• Example: Lorenzo’s Car Wash (Exercise 20)

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Lorenzo’s Car Wash example

• Incoming cars are put on a conveyor belt.

• Cars are washed as they are carried by the conveyor belt from start to finish.

• The cars are then dried manually. • Workers clean and vacuum car

inside.• They are managed by a single

supervisor.• Lorenzo serviced 80,000 cars in

2009, for which he reports the following costs:

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Accounts Total CostsCar Wash Labor $260,000Soap and Supplies $42,000Water $38,000Power $72,000Salaries $46,000Depreciation $64,000

Use knowledge of operations to• Classify cost accounts according to their

relationship with the cost driver activity:– variable, fixed, or mixed

• Estimate the costs if 90,000 cars are washed in 2010.

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• Classify: variable, fixed, or mixed

Accounts Total CostsCar Wash Labor $260,000Soap and Supplies $42,000Water $38,000Power $72,000Salaries $46,000Depreciation $64,000

Variable

Fixed

$412,000

$110,000

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• Variable Costs for 2009$ 412,000 80,000 cars = $5.15 per car

• Fixed Costs$110,000

• Total average cost per car =(412,000 + 110,000)

80,000 cars = $6.53 per car

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Estimate Lorenzo’s 2010 costs (90,000 washes)

• Variable Costs90,000 cars * $5.15 per car = $463,500

• Fixed Costs$110,000

• Total costs =$463,500 + $110,000 = $573,500

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Cost Estimation Methods• Industrial Engineering

– Time and motion studies• Conference

– Consensus of estimates• Account Analysis• Quantitative Analysis


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Quantitative Analysis

• Uses formal mathematical methods to fit cost functions to past data observations.

• Remember, a cost function is a mathematical description of how a cost changes with changes in the level of its cost driver activity.– Total costs = FC + VCUNIT * activity– Lorenzo’s cost function:

• $110,000 + $5.15 per car * number of cars

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Estimate a Linear Cost Function

• Formula: Y = a + bX• Where:

– Y = total costs– a = fixed costs– b = variable cost per unit of cost driver– X = cost driver

• Two methods– High-Low Method– Regression Analysis

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High-Low Method• Uses two points (the high and the low)

to find the equation of the cost line y = a + bx– slope = b = change in y/change in x– intercept = a = y - bx

• Strengths– Simple to compute– Easy to understand

• Weaknesses– Only two points used - what if they are not

representative of normal relationship?• Exercise 16.

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Regression Analysis

• Uses all the observations to find the equation of the cost line y = a + bx– slope = change in y/change in x– intercept = a = y - bx

• Regression minimizes the sum of the squared differences between the observed data and the predicted line

• Strengths– More accurate than the high-low

method

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Statistical Output

Provides • estimates of the two parameters in the

cost function: Y = a + bX– a = intercept = fixed costs– b = slope = variable costs per unit

• Measures of goodness of fit– Co-efficient of determination = r2

• Measures the % variation in Y explained by X– T-statistic = b/standard error of estimated

co-efficient• t tells us if b is different from zero

Larger is better

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Statistical Output

What do we do with it?• Check goodness of fit measures

– Want r2 .3 (or perhaps even higher)– Want t 2

• Compare cost drivers to see which is best

• Estimate Y (total costs) for future period.

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Non-Linear Functions

Costs are not always linear!For example:• Quantity discounts

– Costs decrease as volume increases• Step cost functions

– Costs increase by discrete amounts over narrow ranges

• Step fixed-cost functions– Cost remain the same over wider intervals

• Learning curves

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Learning Curves

A learning curve is a function that measures how labor-hours per unit decline as unites of production increase because workers are learning and becoming better at their jobs. Two types:

• Cumulative average-time learning model– Average time per unit declines at a constant

rate• Incremental unit-time learning model

– Time to produce last unit decreases at a constant rate

Learning curves are given as a percentage

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Learning Curves

• Formula:Y = pXq

• Where:–Y = cumulative average time or

incremental time–p = labor hours on first unit–X = cumulative # of units–q reflects the learning rate (log

of learning curve)

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Learning Curves

• Learning is faster in which model? – (cumulative model)

• Which of these models will predict higher costs?– (incremental model)

• Which of these models is better?– It depends! Case by case basis

decision.

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Learning Curves• What are implications for product

costing?– Charge more initially and decrease price

as time to produce declines? • Will the customers put up with that?

– Price down the learning curve - set price based on what we expect costs to be in the future• Why might companies do this?

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Summary 1

• Managers have to understand cost behavior in order to make decisions about strategy and about operations.

• Most of the time we assume costs are linear and each has single cost driver.

• A cost function is a mathematical description of how a cost changes with changes in the level of its cost driver activity.– Formula: Y = a + bX

• Costs are not always linear (e.g. learning curves).

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Summary 2

Cost Estimation Methods help us understand cost behavior.

• Industrial Engineering (Time & motion studies)

• Conference (consenses)• Account Analysis• Quantitative Analysis


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Summary 3

• Many methods to estimate costs• Potential problems in cost

estimation– Availability of historical data– Accuracy of data– The estimates are only as good as the

data on which they are based.

• Don’t forget to read the appendix which discusses regression.

cost accounting dr. baldwin university of arkansas – fort smith fall 2010

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