The semi-variable cost behaviour pattern depicted in Figure 1.7 is most common in prac- tice and in examination situations.
Total cost, £
Fixed cost Variable cost
Activity level Figure 1.7 Semi-variable cost
Total cost, £
Fixed cost Variable cost
Activity level Figure 1.8 Semi-variable cost
A semi-variable cost is also referred to as a semi-fi xed or mixed cost. The CIMATerminology defi nes it as ‘ a cost containing both fi xed and variable com- ponents and which is thus partly affected by a change in the level of activity ’ .
REVISION OF BASIC ASPECTS, CLASSIFICATIONS AND APPROACHES TO COST ACCOUNTING
When managers have identifi ed a semi-variable cost they will need to know how much of it is fi xed and how much is variable. Only when they have determined this will they be able to estimate the cost to be incurred at relevant activity levels. Past records of costs and their associated activity levels are usually used to carry out the analysis. The three most common methods used to separate the fi xed and variable elements are as follows.
(a) The high–low method.
(b) The scattergraph method.
(c) The least squares method of regression analysis.
You will have learned about the least squares method in your earlier studies. If you do not recall the details of the method then you should refresh your memory. In this text we will look at methods (a) and (b) in more depth.
(a) The high–low method
This method picks out the highest and lowest activity levels from the available data and investigates the change in cost which has occurred between them. The highest and lowest points are selected to try to use the greatest possible range of data. This should improve the accuracy of the result.
We will demonstrate how the method works by using two examples. The fi rst example takes no account of infl ation. The second example demonstrates how index numbers can be used to eliminate the effects of infl ation.
Example: ignoring infl ation A company has recorded the following data for a semi- variable cost:
Month
Activity level units
Cost incurred
£
January 1,800 36,600
February 2,450 41,150
March 2,100 38,700
April 2,000 38,000
May 1,750 36,250
June 1,950 37,650
The highest activity level occurred in February and the lowest in May. Since the amount of fi xed cost incurred in each month is constant, the extra cost resulting from the activity increase must be the variable cost.
Activity level
units £
February 2,450 41,150
May 1,750 36,250
Increase 700 4,900
The extra variable cost for 700 units is £4,900. We can now calculate the variable cost per unit.
Variable cost £
£ per unit
4 900
700, 7
REVISION OF BASIC ASPECTS, CLASSIFICATIONS AND APPROACHES TO COST ACCOUNTING
Substituting back in the data for February, we can determine the amount of fi xed cost:
February £
– total cost 41,150
– variable cost (2,450 units £7) 17,150
Therefore, fi xed cost per month 24,000
Now that the fi xed and variable cost elements have been identifi ed, it is possible to esti- mate the total cost for any activity level within the range 1,750–2,450 units.
Example: taking account of infl ation A transport company has recorded the following data for a semi-variable cost, together with the relevant price index relating to each year.
Year
’000 miles travelled
Cost incurred
£ Price index
1 2,590 23,680 100
2 2,840 25,631 106
3 3,160 27,302 110
4 3,040 28,759 117
The managers wish to forecast the cost which will be incurred in year 5, when it is esti- mated that 3,100,000 miles will be travelled and the price index will be at 120.
The fi rst step is to select the highest and lowest activity levels and then use the index numbers to eliminate the effects of infl ation.
’000 miles £
Cost at year 1 prices, £ High – year 3 3,160 27,302 100/110 24,820
Low – year 1 2,590 23,680 23,680
Increase 570 1,140
Variable cost per ’000 miles at year 1 prices £1,140/570 £ 2
Fixed cost, substituting in year 1 £23,680 (2,590 £ 2) 18,500 at year 1 prices.
The cost for year 5 can now be estimated, using a price index of 120.
£ Variable cost 3,100 £ 2 120/100 7,440 Fixed cost £18,500 120/100 22,200
Total cost estimate 29,640
The major problem with the high–low method is that it takes account of only two sets of data. If these two measurements are not representative of the rest of the data then the estimate of fi xed and variable costs may be very inaccurate. It is a particular risk since it is results at the extremes of the range of activity levels that are most likely to be unrepresentative.
(b) The scattergraph method
This method takes account of all available historical data and it is very simple to use.
However, it is very prone to inaccuracies arising from subjectivity and the likelihood of human error.
1. First a scattergraph is drawn which plots all available pairs of data on a graph.
2. Then a line of best fi t is drawn by eye. This is the line which, in the judgement of the user, appears to be the best representation of the gradient of the sets of points on the graph. This is demonstrated in Figure 1.9 .
REVISION OF BASIC ASPECTS, CLASSIFICATIONS AND APPROACHES TO COST ACCOUNTING
3. The point where the extrapolation of this line cuts the vertical axis (the intercept) is then read off as the total fi xed cost element. The variable cost per unit is given by the gradient of the line.
From Figure 1.9 , the fi xed cost contained within this set of data is adjudged to be £200.
The variable cost is calculated as follows.
Cost for zero units £ Cost for units £ Gradient (i
200
150 500
..e. variable cost) £ per unit
500 200
150 0 2