1. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury Part Six: The application of quantitative methods to management accounting Chapter Twenty-three: Cost estimation and behaviour

2. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.1a 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 + b 1 x 1 + b 2 x 2 Resulting cost functions must make sense and be economically plausible.

3. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.1b Cost estimation methods 1.Engineering methods 2.Inspection of accounts method 3.Graphical or scattergraph method 4.High-low method 5.Least squares method.

4. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.2 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 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.

5. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.3 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 Y = £240 + £2x

6. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.4a 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

7. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.4b Figure 23.2 High–low method.

8. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.5a The least squares regression formula

9. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.5b 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. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.6a Multiple regression analysis

11. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.6b Multiple regression analysis contd

12. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.7 Factors to be considered when using past data to estimate cost functions Identify the potential activity bases (i.e. cost drivers) 1.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). 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.

13. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.8 *Be aware of the dangers of predicting costs outside the relevant range. 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.

14. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.9a 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. A more simplistic approach is to compute the coefficient of variation (known as r 2 ). See slide 23.9b for the calculation of r 2 from the data shown on sheet 23.5a.

15. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury r so that r 2 = (0.941) 2 = 0.8861 r 2 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. 23.9b

16. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.10a

17. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.10b

18. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.11a Mathematical method

19. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury 23.11b Mathematical method contd