**FORMULA AND DERIVATION**

Before one can learn the formula to find the theoretical ex-rights price, it is necessary to know the concept ‘market capitalisation’.

\[Market\ Capitalisation=Price\ per\ share\times Number\ of\ shares\ outstanding\ \]

It is the total market value of all shares outstanding of a company. Using this, the price of a share can be calculated as follows:-

\[Price=\frac{Market\ capitalisation}{Number\ of\ shares}\]

After a right issue, the number of shares increases and obviously the market capitalisation would increase too. So, the price of a share after a rights issue can be calculated as follows:-

\[TERP=\frac{Original\ market\ capitalisation+Extra\ market\ capitalisation}{Original\ number\ of\ shares+Extra\ number\ of\ shares}\]

Now, let us suppose the following:

The current price of a company’s share is \(P\), and there are \(N\) number of shares.

This means the market capitalisation is \(N\times P\) .

The company makes an \(n-for-m\) rights issue, i.e. \(n\) number of new shares for every \(m\) number of shares held. So the number of additional shares raised through the rights issue would be \(\frac{n}{m}N\)

The rights issue price is \(Q\).

So, the extra market capitalisation would be

\[\frac{n}{m}N\times Q\]

The total market capitalisation \(\ (original+extra)\) would now be

\[\left(N\times P\right)+\left(\frac{n}{m}N\times Q\right)\]

The total number of shares \(\ original+extra\) would now be

\[N+\frac{n}{m}N\]

Thus, the price of the share immediately after the rights issue would be (as stated earlier):

\[TERP=\ \frac{Original\ market\ capitalisation+Extra\ market\ capitalisation}{Original\ number\ of\ shares+Extra\ number\ of\ shares}\]
\[\ \ \ \ \ \ \ \ \ \ \ \ =\frac{\left(N\times P\right)+\left(\frac{n}{m}N\times Q\right)}{N+\frac{n}{m}N}\]
\[\ \ \ \ \ \ \ \ \ \ \ \ =\frac{mP+nQ}{m+n}\]

TERP is therefore the weighted average of the share price before rights issue and the rights issue prices.

**EXAMPLES**

Example 1

The current price of a company’s share is \(\$200\). 1 for 1 rights issue will be made (1 new share for every 1 share held), at a rights issue price of \(\$100\). The TERP needs to be ascertained.

Using notations from the formula,

\[P=200(current\ share\ price)\]
\[Q=100(rights\ issue\ price)\]
\[n=1\]
\[m=1\]

\[TERP=\frac{mP+nQ}{m+n}\]
\[\ \ \ \ \ \ \ \ \ \ \ \ =\frac{\left(1\times 200\right)+\left(1\times 100\right)}{1+1}\]
\[\ \ \ \ \ \ \ \ \ \ \ \ =\frac{300}{2}=150\]

Example 2

Consider the same prices as in example 1 (current price\(\$200\) and rights issue price \(\$100\) ). Now, 1 for 5 rights issue is made. (1 new share is given for 5 shares held).

Here,

\[P=200(current\ share\ price)\]
\[Q=100(rights\ issue\ price)\]
\[n=1\]
\[m=5\]

\[TERP=\frac{mP+nQ}{m+n}\]
\[\ \ \ \ \ \ \ \ \ \ \ \ =\frac{\left(5\times 200\right)+\left(1\times 100\right)}{5+1}\]
\[\ \ \ \ \ \ \ \ \ \ \ \ =\frac{1100}{6}=183.33\]

Example 3

Consider the same prices as in example 1 (current price\(\$200\) and rights issue price\(\$100\) ). Now, 1 for 10 rights issue is made. (1 new share is given for 10 shares held).

Here,

\[P=200(current\ share\ price)\]
\[Q=100(rights\ issue\ price)\]
\[n=1\]
\[m=10\]

\[TERP=\frac{mP+nQ}{m+n}\]
\[\ \ \ \ \ \ \ \ \ \ \ \ =\frac{\left(10\times 200\right)+\left(1\times 100\right)}{10+1}\]
\[\ \ \ \ \ \ \ \ \ \ \ \ =\frac{2100}{11}=190.91\]

Factors influencing TERP

All of the above given examples consider the same current share price and rights issue price (200 and 100 respectively). But still, all three examples give different values for TERP. This difference is due to the basis of rights issue.

In example 1, a \(1-for-1\) rights issue was made. So, the number of new shares is \(100\%\) of the existing number of shares. This pushed the price down to a greater extent, i.e. the share price fell from \(\$200\) to \(\$150\).

In example 2, a
\(1-for-5\) rights issue was made. The number of new shares was only\(20\%\) of the existing number of shares. So, the price dropped to a lesser extent compared to example 1, i.e. the share price dropped from \(\$200\) to \(\$183.33\) .

In example 3, a \(1-for-10\) rights issue was made, which means the number of additional shares raised was only \(10\%\) of the existing number of shares. So, the drop in share price was the lowest (\(\$200\) to \(\$190.91\) ) compared to examples 1 and 2.

So, the additional number of shares issued through the rights issue would influence the value of TERP.

Also, the amount of discount given on the rights issue will influence the value of TERP. Higher the discount on the rights issue price, lower the TERP would be.