MBA 502B Managerial Accounting University of Scranton, Dr. Robyn Lawrence Analyzing Cost Behavior Session Two

MBA 502B Managerial AccountingUniversity of Scranton, Dr. Robyn Lawrence

Analyzing Cost BehaviorAnalyzing Cost Behavior

Session Two

S-II: Analyzing Cost Behavior, MBA 502B,Univ. of Scranton, Dr. R. Lawrence2

Classifying CostsClassifying Costs

In GAAP system, costs are classified according to function– Cost of goods sold– Selling– Administrative

Another classification system generally improves internal (management) decisions—according to cost behavior.


Cost BehaviorCost Behavior

Activity Base: – Cost Driver: causes changes in the behavior of costs. – Cost Predictor: accompanied by consistent, observable changes in a cost

item (correlated with)--predicts but may not cause the cost to change

Activity Base Examples:– miles driven – in a trucking company,– room occupancy – in a hotel, – number of customers called on – by a salesperson, or– number of patients—in a hospital.

Relevant (Normal or Practical) Range: – the range of interest; or – the range over which a company expects to operate during a year.

The manner in which a cost changes as a related activity changes

Variable Fixed Mixed


Variable CostsVariable Costs

Vary in total directly and proportionately with changes in the activity level;

Remain the same per unit at every level of activity.

Number of Cost per TotalWeekday Minutes Minute Cost 200 .05 $10 400 .05 20 600 .05 30 800 .05 40

200

400

600

800

Number of Weekday Minutes

TotalCost

$20

$80

$60

$40

0

$100

. . . .


Fixed CostsFixed Costs Remain the same in total regardless of changes in the activity level (within

the relevant range).

Per unit cost varies inversely with the activity level.

Number of Cost per MonthlyUnits Produced Unit Rent 200 2.50 $500 400 1.25 500 600 .83 500 800 .625 500

200

400

600

800

Number of Units Produced

TotalCost

$200

$800

$600

$400

0

$1,000

. . . .

400

600

800

200

CostPerUnit

0

1.00

2.00

3.00

.

.. .


Variable versus Fixed CostsVariable versus Fixed Costs

Varies in direct proportion to

changes in activity

Remains constant throughout

the relevant range

Remains constant throughout the relevant range

Varies inversely with changes in

activity throughout the relevant range

VariableCost

FixedCost

Total Cost Unit Cost


Mixed CostsMixed Costs

Contain both variable and fixed cost elements.

Changes in total but not proportionately with changes in the activity level.

200

400

600

800

Number of Miles Driven per Day

Cost

$100

$800

$600

$400

0

$1,000

..

..

50

.Example: Assume that local rental terms for a 17-foot moving truck, including insurance, are $50 per day plus $.50 per mile. The per diem charge is a fixed cost with respect to miles driven in a day, while the mileage charge is a variable cost.

High-low method, Scattergraph method or OLS Regression can be used to identify/estimate the fixed and variable components.


Practice Classifying CostsPractice Classifying Costs

Below costs are given for two periods (and two levels of activity). Classify the costs as to variable, fixed, or mixed.

January February

1,000 units 1,200 units Classification

Rent $ 700 $ 700

Maintenance 200 240

Utilities 700 800

Insurance 500 500

Inspection 800 840

Supplies 100 120

Indirect Labor 220 250

Direct Materials 250 300

Fixed

Variable

Mixed

Fixed

Mixed

Variable

Mixed

Variable


High-Low Estimation MethodHigh-Low Estimation Method

EXAMPLE: Production Total cost

June 700 units 3,200

July 800 3,800

August 900 4,300

September 500 2,700

October 400 2,050

Essentially finding the slope (variable cost per activity unit)

and then the intercept (total fixed costs) for a line going through two points:

Difference in Total Cost Difference in Activity

= Variable Cost perUnit of Activity

900 – 400

4,300 – 2,050=

2,250 500 = $4.50/unit

Find the slope (variable cost per activity):

Find the intercept (total fixed costs):

Using the higher point: 4,300 – (900 x 4.50) = 4,300 – 4,050 = 250

Using the lower point: 2,050 – (400 x 4.50) = 2,050 – 1,800 = 250

Variable costs are $4.50 per unit and fixed costs are $250.

Cost formula: Total Costs = $250 + $4.50X


Graphing CostsGraphing Costs

100

600

700

800

900

400

500

200

3000

$2,000

$1,000

$3,000

$4,000

$5,000

TotalCosts

Units Produced

250FixedCosts

.

.(400, 2,050)

.(900, 4,300)

Total Variable Costs

Fixed Costs

Total Cost Line


Scattergraph EstimationScattergraph Estimation

100

600

700

800

900

400

500

200

3000

$2,000

$1,000

$3,000

$4,000

$5,000

TotalCosts

Units Produced

.(700, 3,200)

.(900, 4,300)

.(800, 3,800)

.(400, 2,050)

.(500, 2,700)

1. Plot all of the observations

2. Draw the most representative line.

3. Pick two points on the line & use high-low method to determine variable and fixed costs

$4,250 - $3,000 900 - 600

= 1,250/300 = 4.1667 variable cost per unit

$3,000 – 4.1667 x 600= 3,000 – 2,500 = 500Total Fixed Costs

Total Cost = 4.17X + 500


OLS Regression MethodOLS Regression Method

MS Excel Ordinary Least Squares Output: For slope (variable cost per unit) use =INDEX(LINEST(known_y's,known_x's)1) For the intercept (total fixed costs) use =INDEX(LINEST(known_y's,known_x's)2) For the full regression output use =LINEST(known_y's,known_x's,const,stats)

m = 4.227

(Variable cost per unit)

b = 420.349

(Total fixed costs)

Total Cost =

4.227X + 420.349

X Y700 3200800 3800900 4300500 2700400 2050

Slope = 4.227 420.349 = InterceptSE X = 0.366 250.982 = SE intercept

R2 = 0.978 151.830 = SE YF = 133.299 3.000 = degrees of freedom

SS Regresssion = 3072843.02 69156.98 = SS Residual

The formula must be entered as an array formula. After copying the example to a blank worksheet, select the range A14:E18 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER.

For Example:


Comparison of Methods to Calculate Mixed Cost

Components

Comparison of Methods to Calculate Mixed Cost

Components High-low method – Uses the total costs incurred at the high and low levels of activity to calculate

the variable cost per unit and the total fixed costs using the line formula. – Advantage: easy to calculate.– Disadvantages:

relies on the representativeness of the high point and the low point. does examine whether a line (linear model) is appropriate.

Scattergraph Method– Plots observations, draws in the “best” line and calculates the line’s values.– Advantage: examines whether there is a linear relationship.– Disadvantage: the line drawn might be different from person to person.

Ordinary Least Squares Regression– Estimates a line that minimizes sum of the squared differences between the

actual y-values and the average of the y-values.– Advantages:

uses all of the points—efficient estimator; provides more information about how much of the variability is explained by the line.

– Disadvantages: harder to use and explain overly affected by outliers.


Nonlinear Cost BehaviorNonlinear Cost Behavior

Total Mixed costs are fixed over some range then vary over the succeeding range.

Total Cost

Example: Monthly phone fee plus per call fee if number of calls exceed a preset number.

Step-Fixed are fixed for a range, then jump and remain fixed for a range…

Example: A salaried supervisor for every ten employees

Total Cost

Curvilinear (variable) do not have a linear pattern

Example: Total cost of direct labor where overtime is sometimes involved.

Total Cost


Linear Estimation of Nonlinear Cost

Behavior

Linear Estimation of Nonlinear Cost

Behavior

Total Mixed

Total Cost

Step-Fixed

Total Cost

Curvilinear (variable)

Total Cost

Relevant Range is the range over which a company expects to operate during a year.

Within this range, a relationship approximating a straight-line might exist.


Why Does Cost Behavior Matter?

Why Does Cost Behavior Matter?

Determining Cost Behavior: Improves cost forecasts at different levels of activity.

Management’s volume response differs for variable versus fixed costs. For example:

– If fixed costs are $1,000 for the relevant range of 1 to 100 units, then if 10 units are produced, the unit cost is $100; if 100 units are produced, the unit cost is $10.

With fixed costs, unit costs change proportionately--there is incentive to produce more units with fixed costs to lower unit costs.

– If variable costs are $1 per unit, then the unit cost will be $1 per unit whether 1 or 100 are produced. Unit costs will not decline if more units are produced.


Session 2:

Analyzing Cost Behavior

This EndsThis Ends


Concluding ActivitiesConcluding Activities Read Chapter 11: pp. 417-423 Suggested homework:

– E11-1 [Classify costs]– E11-2 [Identify cost graphs]– E11-3 [Identify activity bases]– E11-6 [Relevant range; calculating variable & fixed costs]– E11-7 [High-low method; making an estimate]– E11-8 [High-low method]– P11-1 [Classify costs]

Submit to the Session Two Dropbox your solutions to the following:Required: For each of the different costs given below, indicate whether it is a variable, fixed, or mixed cost. Use the high-low technique to estimate the variable cost per unit and the total fixed costs for each.

Cost 400 hours 550 hours A $ 875 $ 875 B 360 480

C 1,440 1,980 D 3,900 5,250 E 1,000 1,000 F 785 845 G 171.6 172.2 H 120 165

Documents

MBA 502B Managerial Accounting University of Scranton, Dr. Robyn Lawrence Analyzing Cost Behavior Session Two