**Index numbers are numbers applied to data that make costs or selling prices easier to compare over time. **

Index numbers take into account the effect of inflation on costs and when used correctly can make comparing data from different time periods much more efficient than simply comparing one with the other. Often you may hear people ask ‘how much is that in today’s money?’ when looking at how much something cost in the past. Index numbers allow us to answer that question.

Index numbers give us a simple means of comparing data from different time periods. A shift in index numbers indicates a shift in the cost or selling price in question. As an accountant it is important to not only recognise what a change in index number represents but also the driving factor behind the change. The price index for a raw material such as oil would be affected greatly if a new batch of oil was found, because the supply has increased it would be appropriate to assume the price globally may drop. This drop would be shown with a drop in index number. The opposite is also true, so if a supply of any material is becoming restricted then the price will be pushed up and so we would expect the index number to also increase.

# There are several versions of index numbers available

**Retail price index (RPI)**

Index calculated using the cost of a group of expenses typically incurred by households including the cost of housing (interest on mortgages, council tax). The expenses will be reflective of the time period they represent (mobile phone bills were not relevant in the 1960’s, the cost of coal is not as relevant today as in the 1960’s)

**Consumer price index (CPI)**

Similar to the RPI but doesn’t include the cost of housing. The CPI is calculated by adding up a ‘shopping basket’ of household goods which change year by year to represent what households are spending money on at that time. Examples of new additions in 2016 to the calculation of CPI are microwave rice and coffee pods. These obviously would not have been included in the CPI calculation for 1960 ** but** coffee beans and rice would have been.

**Specific market indexes**

For example the housing market or other specific products.

Whenever working with index numbers it is important to only compare ‘like for like’. This means that in order to calculate the difference in value of wheat from 1960 to 1990 we must compare the same quantity of wheat, for example price per kg or tonne (we will look at this in detail in the case studies later).

When dealing with index numbers it is important that we have a time period which we can have as an anchor point. We call this period the ** base period**. The base period will be given the index number 100. We use this base period in other calculations and it gives us an easy point for comparison.

# How to create an index number

The formula used to calculate an index number for a specific cost in a specific time period is as follows:

# Case study

The table given represents the average price (£) of 1kg of a unique raw material ‘Madeupium’ on an annual basis for 6 years.

Step one of this process is to pick a time period as a base period. It would seem logical to use 2000 as the base year. We therefore would use the index number 100 for this period.

By applying the formula above, we can convert the prices of Madeupium to index numbers.

**2001 =**

**253/250 x 100**

**= 101.2**

By using the same process for each year the completed table will look like this:

The index numbers here are representative of the prices from the different years. In 2002 we can see that the price has increased since the base year, this increase means the index must be over 100. In 2005 we can see the price is below £250 and therefore the index number must be below 100. This price movement could be because of a new supply of the material being made available (new mine opening perhaps). If supply increases then this would tend to push prices down (unless of course the demand is still exceeding this supply).

# How to compare historical prices to current using index numbers

The first step in comparing any historical prices to current prices is to see what the historical price would be in ‘today’s money’. The formula that we would apply in this sort of situation is:

# Case study

The house market price index, sourced on the nationwide website shows that the base period for the house market is Quarter 4 from 1952 when house prices were on average £1,891. The most recent index for this price market (at the time of writing Q2 2016) was 10802.

Using this data, a house purchased in 1952 for £3,000 can be given a modern day valuation (assuming the house valuation has increased in line with the index).

If we substitute our figures into the formula given above we can see that the price of the £3,000 house in the current climate (assuming the house was the same standard etc.) would have a very different valuation:

This increase from £3,000 to £324,060 (£321,060) represents a 10,702% increase from 1952 to 2016*.

*It is worth noting that the UK house price index does take into account the style of housing and area that the housing is located.

# Index numbers and their implications on variances

It is possible that price variances can be analysed further using index numbers.

# Case Study

A raw material has a standard cost of £3 per litre. This standard cost was set when the index for the material was 125. The production for the period required 12,000 litres of material with a total actual cost of £40,000. The price index at the end of the period is 130.

The material price variance for the period is calculated using the following:

Standard cost for actual usage – Actual cost of actual usage

Using our figures:

(£3 x 12,000) – £40,000 = __4,000 Adverse__

So now we can look into this a little further, how much of this variance can be blamed on the shift in price index? How much will be blamed on other causes?

If faced with this situation then we need three figures:

- The actual cost of the materials used
- The standard cost of the materials used (the total standard cost)
- The standard cost of the materials used if the price had increased in line with index movement (the revised standard)

- £40,000
- £36,000 (3 x 12,000)
- £37,440*

*this is calculated using this formula:

So by inputting our figures we can ‘flex’ the standard cost according to the index movement

The amount of variance that can be blamed on the shift in index numbers is calculated as follows:

Total standard cost – The revised standard cost

36,000 – 37,440 = __1,440 adverse__

This variance is considered to be an ‘uncontrollable’ variance as we, the management accountants, cannot alter the index movement in prices.

The amount of variance which must be blamed on other factors is calculated as follows:

The revised standard cost – actual cost

37,440 – 40,000 = __2,560 adverse__

This variance is considered to be a ‘controllable’ variance as we, the management accountants, can investigate the cause of this variance. The causes must be something internal within the business and therefore they must be found and where possible resolved.

By adding these variances we can see that they reconcile with the total material price variance:

**1440 adverse + 2560 adverse = 4000 adverse**

A diagram you may find useful for this analysis is shown below:

Hopefully this is easy to follow, always work right to left:

3 – 1 = Total Variance

3 – 2 = Variance blamed on index numbers

2 – 1 = Variance blamed on other factors

# Summary

Index numbers are used as a tool for comparing costs over time. Management accountants should have a good overall understanding of, plus know how to manipulate indexes where needed. Specifically they need to be able to:

- Create index numbers
- Use index numbers to compare costs from one period to another
- Use index numbers to explain price variances

There must be an understanding of the causes of movements in index numbers, this is essentially asking ‘why do prices change over time?’. This article has already suggested that supply/demand is a big factor in the movement in index numbers but there are far more causes which can be investigated. Trends can dictate a lot of what happens with prices of goods, think about how a mobile phone will be popular in one instance and then quickly becomes obsolete. There are lots of other factors which affect indexes.

The communication of index numbers to clients can be a fundamental part of the role of the accountant. The role of being an accountant is not simply being able to perform calculations but also giving an explanation as to the meaning and consequences of these calculations.

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**
Mathew Pickering is an AAT lecturer at The Sheffield College, part of the team which won Training Provider of the year (medium size provider) in 2015.
**