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# Sample of the articles of the foundation

By Lawrence Morris,2014-11-11 22:30
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Sample of the articles of the foundation

INDEX NUMBERS

In business, managers are often concerned with the way in which values change over time:

prices paid for raw materials;

numbers of employees and customers,

annual income and profits, etc.

Index numbers are used to describe such changes. They are often concerned with money or

manpower.

It is necessary in business to be able to understand and manipulate the different published index series, and to construct your own index series.

Index numbers measure the changing value of a variable over time in relation to its value at some fixed point in time, the base period, when it is

given the value of 100.

Indexes are often used to show overall changes in:

a market,

an industry

the economy.

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For example, a graph of the two indexes can be used to illustrate a company's performance within the sector compared to the volume of sales for the overall market.

Company

Market

100

Time

Base period Parity

Constructing an Index

valueinperiodn

100Index for any time period n =

valueinbaseperiod

Example 1 Year Value Calculation Index (Base year 1 12380 12380/12380 x 100 100.00

is year 1) 2 12490 12490/12380 x 100 100.88

3 12730 12730/12380 x 100

4 13145

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Finding values from Indexes

For index linked values, if we know all the index numbers and one of the index linked values we can find all the other values by scaling accordingly.

Example 2

Table showing monthly price index for an item: Month 1 2 3 4 5 6 7 8 9 10 11 12

Index 121 112 98 81 63 57 89 109 131 147 132 126

If the prices are index linked and if the price in month 3 is ?240, what is it in the other months?

Price in month 3 is ?240

121

?240?296.3 Price in month 1 is

98

112

?240?274.3 Price in month 2 is

98

Month 4: Month 5:

Month 1 2 3 4 5 6 7 8 9 10 11 12

Index 121 112 98 81 63 57 89 109 131 147 132 126

Price (?) 296 274 240 140 218 267 320 360 323 309

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Price indexes

The most commonly quoted index is the Retail

Price Index, the RPI.

is a monthly index indicating The Retail Price Index

the amount spent by a 'typical household'.

It gives an aggregate value based upon the price of a representative selection of many hundred products and services with weightings produced by the

'Family expenditure survey' as a measure of their importance.

The RPI shows price changes clearly and is applied when considering inflation for:

wage bargaining,

insurance values, etc.

The RPI is used as a benchmark against which other indexes are compared to show how the price of a product changes over time, due to:

changing costs of raw materials;

variable supply and demand;

general inflation; etc.

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Other Indexes

We can measure the way any variable changes

over time:

unemployment figures;

car registrations;

gross national product; etc.

Indexes can be calculated with any convenient

frequency: yearly, monthly, daily, etc.

Examples of each are:

Yearly G.N.P. Gross National Product

Monthly Unemployment figures

Daily Stock market prices, etc.

Index values are measured in percentage points

since the base value is always 100.

Changes over time are measured as either a percentage point change by subtraction

or as a percentage change.

changeinindexnumber

100percentage change = .

originalindexnumber

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Example 3

Month Price(?) Price index

(Base period Jan.)

Jan. 20 100 Feb. 22 22/20 100 = 110

Mar. 25 25/20 100 = 125

Apr. 26 26/20 100 = 130

May 27

Month Price Index Percentage

(?) Change

Jan. 20 100

Feb. 22 110 (110-100)/100 100 = 10.0

Mar. 25 125 (125-110)/110 100 = 13.6

Apr. 26 130

May 27 135

Month Price Index Percentage

(?) Point Change

Jan. 20 100

Feb. 22 110 110-100 = 10.0

Mar. 25 125 125-110 = 15.0

Apr. 26 130

May 27 135

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Changing the base period

The choice of base period can be any convenient

time - it is periodically adjusted.

It is usual to update the base period when: Any significant change which makes

comparison with earlier figures meaningless. The numbers are growing so large that the size

of a points change is many times that of a

percentage change.

We need to know how to change a base period.

Published index numbers may include base changes: a series 470, 478, 485 continues 100, 103, 105, etc.

A common base year is needed before analysis as a continuous series can be undertaken.

In order to change from one index series to another we need values for both indexes in one period.

The ratio of these two values forms the basis of any conversion between them.

NewOld

NewOldandOldNew

OldNew

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Example 3

The advertising expenditure by a supermarket is index linked and is described by the following indexes:

Year 1 2 3 4 5 6 7 8

Index 1 100 138 162 196 220

Index 2 100 125 140 165

Complete each index series, then, given the expenditure for year 3, calculate the expenditure for the other years.

a) Base year for each index:

Index 1 = Index 2 =

b) Missing values for Index 1 and Index 2:

(Both values known for year 5)

Index1220

allvaluesincreased

Index2100

Index2100

allvaluesreduced

Index1220

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Index 1 for Year 6

220220

125275.0Index 1 = Index 2

100100

Index 2 for Year 1

100100

10045.45Index 2 = Index 1

220220

c) Advertising expenditure is calculated for all years

from the known year using the ratio of the relevant

index numbers from both series. If advertising cost ?4860 in year 3, that for:

Year 1 =

10045.45

48603000or48603000

16273.64

Year 2 =

13862.73

48604140or48604140

16273.64

1 2 3 4 5 6 7 8 Year

100 138 162 196 220 275 308 363 Index 1

45.5 62.7 73.6 89.1 100 125 140 165 Index 2

3000 4140 4860 5880 6600 8250 9240 10890 Adverts (?)

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Simple aggregate and Weighted aggregate

indexes

Most published price indexes are produced from many items rather than single ones as used by us previously.

Simple aggregate indexes add together the prices

of all items included in the 'basket of goods', ignoring the quantity bought.

Weighted aggregate indexes, such as the RPI,

weight each price according to the quantity bought in a particular time period which is:

the base period (a Laspeyres Index)

the current period ( a Paasche Index). The weightings to be applied are usually arrived at by discussion and mutual agreement or, as with the RPI, from the Family Expenditure Survey.

A simple illustration of the principle of these aggregate indexes follows but the use of them in the 'real world' is far more complex and needs to be studied further before being used in a business context.

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