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Arithmetic I

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CAT 2025 Lesson : Percentages - Index & Inflation

6. Index and Inflation

Index is the representation of the value of a group of items relative to it's base value. The common indexes we come across are inflation index and stock index.

A particular year is decided as the base year for an index. For this base year, the index is assigned a value, typically 100.

Where

100

is the index value in the base year,

Index value in year

x = \dfrac{\text{Price of goods/stock in year} \space x}{\text{Price of goods/stock in base year}} \times 100

Therefore, percentage change in index value in a year will be the same as the percentage change in price of items in that year.

6.1 Inflation Index

In India, inflation is measured with Consumer Price Index (CPI) and Wholesale Price Index (WPI). As the names suggest, they track the rise in prices for consumers and wholesalers respectively. Any additional detail such as computing the index value or determining the basket of goods is outside the purview of CAT.

Example 20

Increase in Consumer Price Index (CPI) is considered inflation. CPI in

2016

and

2017

were

127

and

132

respectively, wherein the CPI in the base year of

2012

was

100

. What was the annual inflation rate and

5

-year inflation rate for

2017

Solution

CPI

_{2012}

= 100, CPI

_{2017}

132

Inflation over

5

years to

2017

\dfrac{132 - 100}{100} \times 100\% = 32\%

CPI

_{2016}

127

Inflation over

1

year to

2016

\dfrac{132 - 127}{127} \times 100 \% = 3.94\%

In the above example, note that the consumer price of the basket of goods could be numbers like

15789

and

16541

2016

and

2017

respectively. For a lay man without a calculator, these numbers are difficult to deal with.

As we are only concerned with the inflation or increase rate, dealing with simpler numbers with a base of

100

makes understanding easy. And, this is the primary reason for using indexes.

6.2 Stock Index

Companies require capital (or investment) to operate. These investments are made by the promoters or founders of the company. In several cases, they seek outside help and raise capital from other investors.

Big companies raise capital (or investments) from the public. This is done by issuing shares (also called stock, equity, equity shares, etc.) to the public in exchange for money paid as capital. This or these shares indicate a certain ownership in the company.

Stock exchanges have been setup for the public to buy and sell shares in companies that are listed with the respective stock exchanges. The two major stock exchanges in India are National Stock Exchange (NSE) and Bombay Stock Exchange (BSE).

Their respective stock indexes are NIFTY and Sensex. These indexes have different basket of stocks and different weights assigned to them (which is outside the purview of CAT). Now, you should be able to understand the details of Sensex written below.

Sensex uses the base year as the financial year of 1978-79, wherein Sensex = 100 on April

1

1979

.
Sensex on April

1

2018 = 33030

Increase in Sensex over

39

years =

\dfrac{33030 - 100}{100} \times 100\% = 32930 \%

Example 21

Share price of Company X was Rs.

85

2010

. If the company's price has always followed the NIFTY, then what was share price of X in

2018

if the NIFTY stood at

5100

and

10500

2010

and

2018

respectively?

Solution

Let the price of stock X and value of NIFTY in year

n

be X

_{n}

and NIFTY

_{n}

respectively.

As X has followed the NIFTY,

\dfrac{\text{X}_{2018}}{\text{X}_{2010}} = \dfrac{\text{NIFTY}_{2018}}{\text{NIFTY}_{2010}}

⇒

\dfrac{\text{X}_{2018}}{85} = \dfrac{10500}{5100}

⇒

X_{2018} = 175

Answer: Rs.

175

Note that questions with inflation or indexes in the entrance will explain these concepts. However, a good understanding of these will give you an edge. You could also have a Data Interpretation case around these.

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