ACCA PM Syllabus D. Budgeting And Control - Fixed and Variable Cost elements - Notes ^{3 / 10}

There are two main methods which analyse semi-variable costs into their fixed and variable elements: -

* High/low method

* Least squares regression (this will not be directly examined in F5 from 2013 onwards)

High-low method

The main steps are

1. Review records of costs in previous periods.

   • Select the period with the highest activity level.

   • Select the period with the lowest activity level.

2. Find the variable cost per unit

   Total cost at high activity level - total cost at low activity level
   --------------------------------------------------------------------------
   Total units at high activity level - total units at low activity level

3. Find the fixed costs

   Total cost at high activity level – (Total units at high activity level × Variable cost per unit)

Advantages of the High-Low Method

1. Easy to use

2. Easy to understand

3. Quick method

Limitations of the High-Low Method

1. It relies on historical cost data – predictions of future costs may not be reliable.

2. It assumes that the activity level is the only factor affecting costs.

3. It uses only two values to predict costs – all data falling between the highest and lowest values are ignored.

4. Bulk discounts may be available at large quantities.

Even though it will not be directly examinable from 2013 onwards, let’s have a look at the main points: -

Two variables are said to be correlated if a change in the value of one variable is accompanied by a change in the value of another variable. Examples of variables which might be correlated are:

* A person's height and weight

* The distance of a journey and the time it takes to make it

One way of showing the correlation between two related variables is on a scattergraph or scatter chart, plotting a number of pairs of data on the graph.

E.g. a scattergraph showing total costs incurred at various output levels

A scattergraph can be used to make an estimate of fixed and variable costs by drawing a ‘line of best fit’ through the points which represents all the points plotted.

The line of best fit will be of the form

y = a + bx

where a = fixed costs
           b = variable costs

Regression analysis can be used to establish the equation of the line of best fit.

where x is the independent variable and y is the dependent variable. This means that changing x should cause a change in y, not the other way round. When establishing a relationship between volume and costs, volume should be x, because making more units causes more costs.

When establishing a relationship between price and quantity sold, x should be price, because charging less will cause more units to be sold. N is the number of pairs of readings.

These formulae are given in the exam. Remember always start working ‘b’, then move to ‘a’.

Correlation measures the strength of the relationship between two variables.

One way of measuring ‘how correlated’ two variables are, is by drawing the ‘line of best fit’ on a scattergraph.

Another way of measuring ‘how correlated’ two variables are, is to calculate a correlation coefficient, r.

The correlation coefficient measures the strength of a linear relationship between two variables.  It can only take on values between -1 and +1.

r = +1 indicates perfect positive correlation (all points fit on the regression line) and as one variable increases, so does the other

r = 0 indicates no correlation

r = -1 indicates perfect negative correlation (all points fit on the regression line) and as one variable increases, the other decreases

The correlation coefficient is calculated as follows: -

The coefficient of determination is the square of the correlation coefficient. It measures how much of the variation in the dependent variable is ‘explained’ by the variation of the independent variable.

For example, if r = 0.97, r2 = 0.94 or 94%.

94% of the variation in the dependent variable(y) is due to variations in the independent variable (x). 6% of the variation is due to random fluctuations. Therefore, there is high correlation between the two variables.

This formula is also given in the exam.