1. Cost Estimation & Cost Behaviour

2. Outcomes Calculate and interpret the coefficient of determination
Compute the correlation coefficient
Implement the steps in estimating cost functions
Estimate hourly-driven costs when there is a learning curve effect present using tabular and mathematical method

3. General principles
A regression equation (or cost function) measures past relationships
between a dependent variable (total cost)and potential independent
variables (i.e. cost drivers/activity measures).
Simple regression y = a + bx
Where y = Total cost
a = Total fixed cost for the period
b = Average unit variable cost
x = Volume of activity or cost driver for the period
Multiple regression y = a + b1 x1 + b2 x2
Resulting cost functions must make sense and be economically plausible.

4. Cost estimation methods
Engineering methods
Inspection of accounts method
Graphical or scattergraph method
High-low method
Least squares method.

5. Cost estimation methods
Engineering methods
Analysis based on direct observations of physical quantities required for an activity and then converted into cost estimates.
Useful for estimating the costs of repetitive processes where input-output relationships are clearly defined.
Appropriate for estimating the costs associated with direct labour, materials and machine time.
Inspection of accounts method
Departmental manager and accountant inspect each item of expenditure within the accounts for a particular period and classify each item as fixed, variable or semi-variable.

6. Cost estimation methods
Graphical or scattergraph method
Past observations are plotted on a graph and a line of best fit is drawn.
Unit VC =
Difference in cost = £720 – £560 = £2 per hour Difference in activity 240 hours – 160 hours

7. Cost estimation methods
High-low method
Involves selecting the periods of highest and lowest activity levels and comparing changes in costs that result from the two levels.
Example
Lowest activity 5,000 units £22,000
Highest activity 10,000 units £32,000
Cost per unit = £10,000/5,000 units = £2 per unit
Fixed costs = £22,000 – (5,000 × £2) = £12,000
Major limitation = Reliance on two extreme observations

8. Least squares method

9. Cost estimation methods - Least squares method.
The simple regression equation y = a + bx can be found from the following two equations and solving for a and b
The above equation can be used to predict costs at different output levels.

10. Least squares method Revision activity 23.14 High-low method

11. Multiple regression analysis

12. Multiple regression analysis

13. Factors to be considered when using past data to estimate cost functions
Identify the potential activity bases (i.e. cost drivers)
The objective is to find the cost driver that has the greatest effect on cost.
Ensure that the cost data and activity measures relate to the same period.
Some costs lag behind the associated activity measures (e.g. wages paid for the output of a previous period).

14. Factors to be considered when using past data to estimate cost functions
Ensure that a sufficient number of observations are obtained.
Ensure that accounting policies do not lead to distorted cost functions.
Adjust for past changes so that all data relates to the circumstances of the planning horizon.
Adjust for inflation, technological changes and observations based on abnormal situations.

15. Summary 1. Select the dependent variable (y) to be predicted.
2. Select the potential cost drivers.
3. Plot the observations on a graph.*
4. Estimate the cost function.
5.Test the reliability of the cost function.
*Be aware of the dangers of predicting costs outside the relevant range.

16. Tests of reliability
Tests of reliability indicate how reliable potential cost drivers are in predicting the dependent variable.
The most simplistic approach is to plot the data for each potential cost driver and examine the distances from the straight line derived from the visual fit.
An alternative approach is to compute the coefficient of variation (known as r2).
See slide 17 for the calculation of r2 from the data shown on sheet 8.

17. coefficient of determination.
Tests of reliability R=
r2 = (0.941)2 =
r2 indicates that 88.61% of the variation in total cost is explained by the variation in the activity base and the remaining 11.39% by other factors. Therefore the higher the coefficient of variation the stronger the relationship between the dependent and independent variable.
The coefficient of variation is also known as the
coefficient of determination.

18. Learning curve theory
When doing a job for the first time, the workforce involved will probably not immediately achieve maximum efficiency.
Through repetition of the task, workers become increasingly knowledgeable, labour efficiency increases and the labour cost per unit declines.
At a certain point, the learning process will cease and the time taken to complete the task will stabilise.
The learning curve equation:
Yx = aXb

19. Learning curve theory X Number of units produced
The learning curve equation:
Yx = aXb
Yx Cumulative average time required to produce X units
X Number of units produced
a Time required to produce the first unit of output
b Logorithm of learning curve improvement rate divided by the logarithm of 2 i.e.
log (learning %)
log 2

20. 3.10a

22. Learning curve – mathematical method
Using the mathematical method for an 80% learning curve:
Yx = aXb
a = 32
b = log 0.80/ log 2 =
Y32 = 2000 x
Y32 = 655

23. Learning curve – mathematical method
Using the mathematical method for an 80% learning curve:
a = 32
b = log 0.80/ log 2 =
Y10 = 2000 x
Y10 = ~ 953
Y20 = 2000 x
Y20 = ~ 762

24. Learning curve – incremental cost
Incremental hours can be derived by examining the differences between total hours for various combinations of cumulative hours.
Assume the company has completed four units cumulative production.
To calculate the incremental hours for 6 more:
Total hours for 10 units (10 x 953hrs) 9 530
Total hours for 4 units (4 x 1280hrs) 5 120
4 410

25. Learning curve – incremental cost
Incremental hours can be derived by Note learning effect only applies to direct labour-related variable costs.
Learning curve applications
Pricing decisions
Work scheduling
Standard setting

26. Learning Curve- activity 3.6 P31
= Cumulative average time per unit X 100
Previous cumulative average time per unit
= ( )/2 x 100
= %

27. Learning Curve- activity 3.6 P31
The total weekdays needed to complete the roof trusses of the complex.
Tabular method
Cumulative units
Doubling
Hours of cumulative average time per roof 1 -
16 hrs 2
15.52 hrs 4
15.05 hrs 8 3
14.60 hrs 16
14.16 hrs 32 5
13.74 hrs

28. Learning Curve- activity 3.6 P31
The total weekdays needed to complete the roof trusses of the complex.
Formula method
Cumulative average time per roof
= time for 1st unit x total number of units(log learning curve/log 2)
= 16 x 32(log (0.97))/(log 2)) = hours
Days required = (13.74 x 32) /8 = 55days

29. Learning Curve- activity 3.6 P31
Cost to complete the roof trusses
Expected total hours for the whole complex 32 x
Less: First 2 units already completed
Expected hours to complete the complex
Days required for completeing the work = / 8 = ~ 52days
Total trusses cost = R950 x 85 = R49 400