1. Determining How Costs Behave
CHAPTER 10
Determining
How Costs Behave

2. Cost Functions
A cost function is a mathematical representation of how a cost changes with changes in the level of an activity relating to that cost

3. Cost Terminology
Variable Costs – costs that change in total in relation to some chosen activity or output
Fixed Costs – costs that do not change in total in relation to some chosen activity or output
Mixed Costs – costs that have both fixed and variable components; also called semivariable costs

4. Bridging Accounting & Statistical Terminology
Statistics
Variable Cost
Slope
Fixed Cost
Intercept
Mixed Cost
Linear Cost Function

5. The Linear Cost Function
y = a + bX
The Independent
Variable:
The cost driver
The Dependent
Variable:
The cost that is
being predicted
The slope of
the line:
variable cost
per unit
The Intercept:
Fixed Costs

6. Linear Cost Functions Illustrated

7. Cost Estimation Methods
Industrial Engineering Method
Conference Method
Account Analysis Method
Quantitative Analysis Methods
High-Low Method
Regression Analysis

8. Industrial Engineering Method
Estimates cost functions by analyzing the relationship between inputs and outputs in physical terms
Includes time-and-motion studies
Very thorough and detailed, but also costly and time-consuming
Also called the Work-Measurement Method

9. Conference Method
Estimates cost functions on the basis of analysis and opinions about costs and their drivers gathered from various departments of a company
Pools expert knowledge
Reliance on opinions still make this method subjective

10. Account Analysis Method
Estimates cost functions by classifying various cost accounts as variable, fixed or mixed with respect to the identified level of activity
Is reasonably accurate, cost-effective, and easy to use, but is subjective

11. Account Analysis Monthly Cost January Amount Fixed Variable
Supervisor’s salary and benefits
$5,000
Hourly workers’ wages and benefits
$10,000
Depreciation (based on time – monthly)
$20,000
Depreciation (based on unit produced)
$15,000
Equipment repairs
$3,000
Total
$52,000
The most plausible cost driver is the number of units produced.
The table above shows costs recorded in a month with 2,000 units produced.
Fixed
Variable
$5,000
$10,000
$20,000
$15,000
$3,000
$28,000
$35,000
02/12/2018 MK

12. Account Analysis Cost function: Fixed cost per month : $28,000
Variable cost per the unit produced: 35,000 / 2,000 = $17,5
The algebraic, mixed cost function, measured by account analysis, is
Y = $28,000 + ($17,5 * Q)
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13. Qualitative Analysis
Uses a formal mathematical method to fit cost functions to past data observations
Advantage: results are objective

14. High-Low Method Simplest method of quantitative analysis
Uses only the highest and lowest observed values

15. Steps in the High-Low Method
Calculate variable cost per unit of activity
TC (For highest level) – TC(For lowest level)
VCu =
Q (For highest level) - Q (For lowest level)

16. Steps in the High-Low Method
Calculate Total Fixed Costs
FC = TC – VCu*Q
Summarize by writing a linear equation

17. High-Low Method
Example: Flexible Manufacturing Company decided to relate total factory overhead costs to direct labor hours (DLH) to develop a cost-volume formula in the form of Y= FC + VCu*Q . Twelve monthly obsservations are collected. They are given as follows:
Month
DLH (000 ommitted)
Factory overhead (000 ommitted)
January
9 hours
$150
Fabruary 19
200
March 11
140
April 14
160
May 23
260
June 12
July
August 22
230
September 8
125
October 13
220
November 15
180
December 17
The high-low points selected from the monthly observations are
X Y
High 23 hours $25 (May pair)
Low (September pair)
Difference 16 hours $11
ΔY $11
Variable rate: : : $ per DHL
ΔX hours
The fixed cost portion is computed as
F = Total mixed cost – variable cost
F= $25- (0.6875*23) =
F= $14-(0.6875*7) =
Y= $ $0.6875*X
02/12/2018 MK
6-Okt-03

18. Steps in the High-Low Method–
VCu = = = $9 –
FC = * = $ per month.
Cost function (monthly);
Y = X
X: Units produced

19. Visual-fit method / Scattergraph method
Variable rate :$ 6000 /600 units = $10 per unit Fixed portion of... : – (10*1350) = $3500
Y = $3500 per period + $10 * X (units)
17000
ΔY = $6000
11000
ΔX = 600 Units
750
1350
02/12/2018 MK

20. Regression Analysis
Regression analysis is a statistical method that measures the average amount of change in the dependent variable associated with a unit change in one or more independent variables
Is more accurate than the High-Low method because the regression equation estimates costs using information from all observations; the High-Low method uses only two observations

21. Least Squares - Regression Analysis
∑y = b∑x + an
∑xy = b∑x2 + a∑x
n∑xy - (∑x) (∑y) b=
n∑x2 - (∑x)2
∑y -b∑x a= n
02/12/2018 MK

22. Least Squares - Regression Analysis
Months
Activity
(Unit) X
Factory Overhead Y XY X2 1
1150
14.000 2
1100
13.000 3
1000 4
1200
14.500 5
1250
15.000 6
1300
16.000
Toplam
7000
85.500 n ∑x ∑y
∑xy
∑ x2
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