Cost estimation - Cost behavior What we really want to understand is how spending will vary in a variety of decision settings. Cause-effect relations and.

Cost estimation - Cost behavior

What we really want to understand is how spending will vary in a variety of decision settings.

Cause-effect relations and costs drivers.

Capacity and capacity costs:

• Theoretical = 100,000

• Practical = 90,000

• Normal = 85,000

• Budgeted = 80,000

• Suppose fixed overhead is budgeted at $1,000,000; variable overhead is $1 per unit; direct material costs = $3; and direct labor = $3. Overhead is applied based on units of product.

Capacity and capacity costs:

What does a unit of product cost if overhead is allocated based on theoretical capacity?

Practical capacity?

Normal capacity?

Budgeted capacity.

Which measure should the company use?

$17

$18.11

$18.76

$19.50

Capacity and capacity costs:

Suppose the company allocates overhead based on practical capacity and actual production is 70,000 units.

By how much is overhead underapplied?

What does that cost represent?

About $222,300

The cost of idleor excess capacity.

Capacity and capacity costs

• Who should pay for excess capacity?

• Who should pay for idle capacity?

• How is capacity measured?

What is the scarcest resource?

• Idle capacity and opportunity costs.

Cost estimation: overhead

• When is it important to understand how overhead behaves?

– When pricing, production, process and product design decisions are made.

– When bids and make or buy decisions are made.

– When we need to answer “what if” questions.

Cost estimation: overhead costs

• First week’s product costing exercises: applied overhead.– Valuing inventories & costs of sales.– Not for costing individual products– Not for predicting costs

What methods are available?

• Engineering estimates

• Account analysis

• Scattergraph and high-low estimates

• Statistical methods (typically regression)

Cost behavior: linear function by assumption.

TC = FC + VC*(level of cost driver)

where

TC = total cost

FC = fixed cost

VC = variable cost per unit of the cost driver,

and sometimes the cost driver is represented by X.

Volume

Overhead Costs

A B C D

Cost estimation: Account analysis

• Review each account

• Identify it as fixed or variable (or mixed)

• Attempt to determine the relationship between the activity of interest and the cost– Cost of building occupancy– Cost of quality inspections– Cost of materials handling

Example

Suppose management believes that the monthly overhead cost ($5000) in the factory is mixed. It is believed to be 50% fixed and 50% variable. The variable portion is believe to depend on machine hours, which average 10,000 per month. How would you show this as a linear equation?

TC = $2500 + $.25(machine hours)

Peterson Mfg. in Problem Set #1 will require account analysis.

Scattergraph

Suppose you have data on overhead costs and machine hours for the past 15 months. Can you easily determine whether the posited relationship exists?

Yes, plot the data and look for a relationship.

Plot of overhead costs vs.machine hours

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Machine Hours

Scattergram

High-Low cost estimation

Find the variable cost per unit of the cost driver (VC):

activityLowest - activityHighest

activitylowest at Overhead - activityhighest at Overhead VC

High-Low method: Example continued

mhr 50 -mhr 142$1,896 - $3,105

VC

mhr 92$1,209

VC

$13.14/mhr VC

High-Low cost estimation

$1,239

mhr) 142 * ($13.14 - $3,105 cost Fixed

$2,750 TC

mhr) 115 * ($13.14 $1,239 TC

mhr 115 * VC FC TC

Estimate the total overhead cost during amonths when 115 machine hours will be used:

Cost estimation using regression

• Y = the dependent variable (total O/H cost)• X = the explanatory variables

Y = X +

where X = machine hours and = random error.

TC = FC + VC*X +

Regression fits a line through these data points:

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Machine Hours

Scattergram

Simple linear regression

• One explanatory variable

• Cost estimation equation

• Coefficient of correlation (R)

• Coefficient of determination (R2)– Goodness of fit– Measure of importance

• F-statistic (hypothesis testing)

• p-value

Coefficient of determination

Measures the percentage of variation in thedependent variable explained by the independentvariable.

When the predicted values exactly equal theactual costs, R2 = 1.

A goodness of fit test: R2 > .3

The F statistic

• Goodness of fit hypothesis testing

• Compute a statistic for regression results

• Compute the associated p-value, or

• Look up a critical F-value and compare– 1 numerator degree of freedom– (n-2) denominator degrees of freedom– alpha = .05

The F test:

• The hypothesis is: The slope coefficient is zero.

• The F-statistic measures the loss of fit that results when we impose the restriction that the slope coefficient is zero.

• If F is large, the hypothesis is rejected.

The p-value

• This is the probability that the statistic we computed could have come from the population implied by our null hypothesis.

• Suppose we hypothesize that the slope coefficient is zero.

• If the p-value associated with the F-statistic is small, chances are the slope coefficient is not zero.

Regression result interpretation

15

0

.896

.802

.787

182.244

Count

Num. Missing

R

R Squared

Adjusted R Squared

RMS Residual

Regression Summary Overhead Costs vs. Machine Hours

1 1753772.049 1753772.049 52.804 <.0001

13 431765.285 33212.714

14 2185537.333

DF Sum of Squares Mean Square F-Value P-Value

Regression

Residual

Total

ANOVA Table Overhead Costs vs. Machine Hours

1334.293 162.913 1334.293 8.190 <.0001

12.373 1.703 .896 7.267 <.0001

Coefficient Std. Error Std. Coeff. t-Value P-Value

Intercept

Machine Hours

Regression Coefficients Overhead Costs vs. Machine Hours

Simple linear regression

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Machine Hours

Overhead Costs = 1334.293 + 12.373 * Machine Hours; R^2 = .802

Scattergram

Results using DM$15

0

.960

.921

.915

115.087

Count

Num. Missing

R

R Squared

Adjusted R Squared

RMS Residual

Regression Summary Overhead Costs vs. Direct Materials Cost

1 2013351.144 2013351.144 152.007 <.0001

13 172186.189 13245.091

14 2185537.333

DF Sum of Squares Mean Square F-Value P-Value

Regression

Residual

Total

ANOVA Table Overhead Costs vs. Direct Materials Cost

1456.586 87.225 1456.586 16.699 <.0001

.356 .029 .960 12.329 <.0001

Coefficient Std. Error Std. Coeff. t-Value P-Value

Intercept

Direct Materials Cost

Regression Coefficients Overhead Costs vs. Direct Materials Cost

Multiple regression15

0

.976

.952

.944

93.658

Count

Num. Missing

R

R Squared

Adjusted R Squared

RMS Residual

Regression Summary Overhead Costs vs. 2 Independents

2 2080274.802 1040137.401 118.576 <.0001

12 105262.531 8771.878

14 2185537.333

DF Sum of Squares Mean Square F-Value P-Value

Regression

Residual

Total

ANOVA Table Overhead Costs vs. 2 Independents

1333.960 83.724 1333.960 15.933 <.0001

4.359 1.578 .316 2.762 .0172

.258 .042 .697 6.101 <.0001

Coefficient Std. Error Std. Coeff. t-Value P-Value

Intercept

Machine Hours

Direct Materials Cost

Regression Coefficients Overhead Costs vs. 2 Independents

Forecasting overhead

• Predict monthly overhead when machine hours are expected to be 62 and direct materials costs are expected to be $1,900.

• Recall = $1,333.96– Coefficient for mhrs = $4.359– Coefficient for DM$ = $.258

Predicted overhead

$2,094.42

00)$.258($1,9 $4.359(62) $1,333.96 Overhead

Putting together a bid

• Calculate a minimum bid for a contract that would use 22 machine hours and $900 in direct materials. This would be a one-time-only job.

• What if there is no idle capacity?

• Would your bid change if there were potential for repeated business?

Problems with regression

• Nonlinear relationships• Outliers• Spurious relationships• Data problems

– Inaccurate accounting cut-offs

– Arbitrarily allocated costs

– Missing data

– Inflation

Thursday

• Cenex and Burd & Fletcher Cases.

• Use Excel for regression computations

• We will discuss the problems in class and

• Work a handout problem in groups.