Cost Estimation & Cost Behaviour

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

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.

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

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.

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

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

Least squares method

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.

Least squares method Revision activity 23.14 High-low method

Multiple regression analysis

Multiple regression analysis

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).

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.

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.

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.

coefficient of determination. Tests of reliability R= r2 = (0.941)2 = 0.8861 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.

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

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

3.10a

Learning curve – mathematical method Using the mathematical method for an 80% learning curve: Yx = aXb a = 32 b = log 0.80/ log 2 = -0.3219 Y32 = 2000 x 32-0.322 Y32 = 655

Learning curve – mathematical method Using the mathematical method for an 80% learning curve: a = 32 b = log 0.80/ log 2 = -0.3219 Y10 = 2000 x 10-0.322 Y10 = 952.86 ~ 953 Y20 = 2000 x 20-0.322 Y20 = 762.42 ~ 762

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

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

Learning Curve- activity 3.6 P31 = Cumulative average time per unit . X 100 Previous cumulative average time per unit 1 = (15.04 + 16)/2 x 100 16 1 = 97%

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

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)) = 13.74 hours Days required = (13.74 x 32) /8 = 55days

Learning Curve- activity 3.6 P31 Cost to complete the roof trusses Expected total hours for the whole complex 32 x 13.74 439.68 Less: First 2 units already completed 16 + 15.05 31.04 Expected hours to complete the complex 408.64 Days required for completeing the work = 408.64 / 8 = 51.08 ~ 52days Total trusses cost = R950 x 85 = R49 400