Formulae Used in Shares and Dividends: Formulas, Examples

Formulae Used in Shares and Dividends: A substantial volume of money is necessary to start a large corporation. An individual may not always be able to invest such a large sum. Then a group of people that are interested in the company join. They break down the anticipated value into smaller pieces ranging from \(₹1\) to \(₹100\). Each of these parts is referred to as a share, and the value assigned to each share is referred to as its original or nominal value \((N.V.)\). Shareholders are those who buy shares in a company.

In this article, we shall learn about formulae to calculate the number of shares, dividends on the number of shares, income and returns.

Terms Related to Shares and Dividends

Introduction: A substantial sum of money is required to start or establish a company, and it is often not possible for a single/few people to raise such a large sum of money on their own. Thus, the firm raises its capital from the public through the issue of shares. A ‘share’ is one of the units in which a company’s capital is divided. Let’s see some terms related to shares and dividends.

Nominal value: A share’s nominal value \((N.V.)\) is also known as its Register value, Printed value, Face value \((F.V.)\), and so on. A share’s nominal value does not vary over time.

Market value: Market value \((M.V.)\) or cash value refers to the price of a stock in the market at any given time. A share’s market value might fluctuate (drop or grow) over time.

Depending on the company’s performance and profits, the market value of a share can be the same, higher, or less than its nominal value.

1. A share is at par if its market value is the same as its nominal value.
2. A share is above par or at a premium if its market value is more than its nominal value.
3. A share is below par or at a discount if its market value is less than its nominal value.

Thus,

1. At par means: Market value \(=\) Nominal value, i.e., \(M . V .=N . V\).
2. Above par or at a premium means: \(M . V .>N . V\).
3. Below par or at a discount means: \(M . V .<N . V\).

The dividend is the profit that a shareholder receives (from the firm’s profits) because of his investment in the company.

1. Dividends are always expressed as a percentage of the share’s nominal value.
2. The dividend is not affected by the stock’s market value.

Learn All Concepts on Taxation

Shares and Dividends Formulas

1. Sum invested \(=\) the number of shares bought \(\times M.V.\) of \(1\) share.
If the shares are available at par
\(M.V.\) of each share \(=N.V.\) of it.
2. Number of shares bought \(=\frac{\text { the sum invested in buying the shares }}{M . V . \text { of } 1 \text { share }}\)
Also, number of shares bought \(=\frac{\text { total dividend from these shares }}{\text { dividend on } 1 \text { share }}\) \(=\frac{\text { total income }(\text {profit})}{\text { income }(\text {profit}) \text { on } 1 \text { share }}\)
Total dividend earned \(=\) number of shares \(\times\) rate of dividend \(\times N.V.\) of a share
3. \({\rm{Return}}\,\% = {\rm{income}}\left( {{\rm{profit}}} \right)\% \)
4. For a shareholder:
Income \(=\) return \(=\) profit
\(=\) dividend paid by the company

Note: 
“\(15 \%\,₹\,100\) shares at \(₹ \,145\)” means that

1. The face value of \(1\) share \(=₹100\)
2. The market value of \(1\) share \(=₹145\)
3. The dividend (profit) on \(1\) share \(=15 \%\) of \(₹100=₹15 p.a.\)
4. The income on \(₹145\) is \(₹15\) for one year.
5. The rate of return (or yield) \(p . a .=\left(\frac{15}{145} \times 100\right) \%=\frac{300}{29} \%=10 \frac{10}{29} \%\)

Computation of Income and Return

Computation of Income is the process of determining the various sources of income.

Dividend: The profit, which a shareholder gets for their investment from the company, is called the dividend. 

1. The dividend is always expressed as the percentage of the face value of the share.
2. The dividend is always paid (by the firm) on the face value of the share, regardless of the share’s market value.

Income and Returns

Annual income (total dividend) \(=\) number of shares \( \times \) rate of dividend \( \times \) face value of one share

Example: Rajan has \(450\) shares of \(₹200\) of a company paying a dividend of \(16\%\). Find his net income after paying an income tax of \(20\%\).

Solution: We know that annual income (total dividend) \(=\) number of shares \( \times \) rate of dividend \( \times \) face value of one share.
\(=450 \times \frac{16}{100} \times ₹200=₹14400\)
Income tax \(=20 \%\) of \(₹14400=₹\left(\frac{20}{100} \times 14400\right)\)
\(=₹2880\)
Therefore, net income \(=\) total dividend \(-\) income tax
\(=₹14400-₹2880\)
\(=₹11520\)
Hence, the net income is \(₹11520\).

Dividend Yield Ratio Across Industries

Yield Percentage:  The percentage return a shareholder receives on an investment made by purchasing the business shares for the dividend declared by the firm is referred to as yield percentage.

Dividend yield ratios should only be compared between companies in the same industry because industry average yields differ significantly. The following are the average dividend yields for specific industries on an average over the last few years:

1. Basic materials industry: \(4.92\% \)
2. Financial services industry: \(4.17\% \)
3. Healthcare industry: \(2.28\% \)
4. Industrial industry: \(1.76\% \)
5. Services industry: \(2.37\% \)
6. Technology industry: \(3.2\% \)
7. Utility industry: \(3.96\% \)

Solved Examples – Formulae Used in Shares and Dividends

Q.1. Keerthi invested \(₹12,500\) in shares of a company paying \(6\%\) dividend per annum. If she bought \(₹50\) shares for \(₹62.50\) each, find her income from the investment.
Ans: Since the market value of each share \(=₹62.50\) and the sum invested is \(₹12,500\)
Number of shares bought \(=\frac{\text { sum invested }}{M . V . \text { of } 1 \text { share }}\)
Therefore, the number of shares bought by Keerthi \(=\frac{12,500}{62.25}=200\)
Income (dividend) on one share \(=6 \%\) of \(N.V.=\frac{6}{100} \times ₹50=₹3\)
Therefore, her total income \(=200 \times ₹3=₹600\).

Q.2. Ravindra buys \(₹100\) shares at \(₹20\) premium in a company paying \(15\% \) dividend. Find:
1. The market value of \(600\) shares,
2. His annual income,
3. His percentage income
Ans:
The market value of \(1\) share \(=₹100+₹20=₹120\)
\(⟹\)The market value of \(600\) shares \(=600×₹120=₹72000\)
Annual income \(=\) Number of shares \( \times \) Rate of dividend \( \times N.V. (F.V)\). of \(1\) share
\(=600 \times \frac{15}{100} \times ₹100=₹9000\)
\(₹9000\) is the income obtained on investing \(₹72000\)
Therefore, percentage income \(=\frac{9000}{72000} \times 100 \%=12.5 \%\)

Q.3. A man bought \(500\) shares, each of face value \(₹10\), of a certain business concern and during the first year after purchase received \(₹400\) as dividend on his shares. Find the rate of dividend on shares.
Ans: Let the rate of dividend be \(r\%\) per annum.
Annual dividend \(=\) number of shares \( \times \) rate of dividend \( \times \) face value of one share
\(=500 \times \frac{r}{100} \times ₹10=₹50 r\)
Given that, the dividend received after one year of purchase of shares is \(₹400\).
Therefore, \(₹50r= ₹400\)
\(⟹50r= 400\)
\(⟹r=8\)
Hence, the rate of dividend is \(8\%\).

Q.4. A man invests \(₹22500\) in \(₹50\) shares available at \(10\%\) discount. If the dividend paid by the company is \(12\%\), calculate:
i. The number of shares purchased.
ii. The annual dividend received.
Ans:
i. Since the man invests in \(₹50\) shares available at \(10\%\) discount, the market value of one share
\(=\left(1-\frac{10}{100}\right)\) of \(₹50= ₹\left(50 \times \frac{9}{10}\right)=₹45\).
As the investment is \(₹22500\),
Therefore, the number of shares purchased \(=\frac{₹22500}{₹45}=500\).
ii. Annual dividend received \(=\) number of shares \( \times \) rate of dividend \( \times \) face value of one share
\(=500 \times \frac{12}{100} \times ₹50\)
\(₹(5 \times 12 \times 50)=₹3000\)
Hence, the annual dividend is \(₹3000\).

Q.5. A man purchases \(600\) shares of the face value of \(₹40\) at par. If a dividend of \(₹1680\) was received at the end of the year, find the dividend rate.
Ans: Total value of all the shares (investment) \(=₹(40×600)=₹24000\).
The dividend received at the end of the year \(=₹1680\).
Therefore, the rate of dividend \(=\left(\frac{1680}{24000} \times 100\right) \%=7 \% \).

Summary

In this article, we learnt about shares and dividends introduction, shares and dividends formulas, computation of income and return, dividend yield ratio across industries, solved examples on formulae used in shares and dividends, FAQs on formulae used in shares and dividends.

The learning outcome of this article is to learn how people funding to start the company by selling the shares and how the people are getting income from those shares.

FAQs

Q.1. What is the formula for dividends per share?
Ans: The formula for dividend per share is \(\frac{\text { total dividend from these shares }}{\text { number of shares bought }}\)

Q.2. How are shares calculated?
Ans: The number of shares bought is calculated using the following formula:
Number of shares bought \(=\frac{\text { sum invested to buy the shares }}{M . V \cdot \text { of } 1 \text { share }}\)
Also, number of shares bought \(=\frac{\text { total dividend from these shares }}{\text { dividend on } 1 \text { share }}\)
\(=\frac{\text { total income }(\text { profit })}{\text { income (profit) on } 1 \text { share }}\)

Q.3. What is the dividend per share, for example?
Ans: Dividend: The profit, which a shareholder gets for their investment from the company, is called the dividend.
1. The dividend is always expressed as the percentage of the face value of the share.
2. The dividend is always given (by the company) on the face value of the share irrespective of the market value of the share.
Example: A man buys \(₹10\) shares at a premium of \(₹5\) per share. If the company pays \(9\%\) dividend, find the percentage return on his investment in buying \(200\) shares.
Solution: Given, the face value of one share \(=₹10\) and premium \(=₹5\)
Investment on one share \(=10+5=₹15\)
Therefore, investment in buying \(200\) shares \(=200×15=₹3000\)
Also, given rate of dividend \(=9\%\)
Now, annual income on \(1\) share \(=9\%\) of \(₹10\)
\(=\frac{9}{100} \times 10=₹\frac{9}{10}\)
Hence, the dividend on one share is \(₹\frac{9}{{10}}.\)

Q.4. What is a good dividend per share ratio?
Ans: From a dividend investor’s perspective, a range of \(35\%\) to \(55\%\) is regarded as healthy and reasonable. A company expected to share around half of its earnings in dividends is well-established and a market leader.

Q.5. Is a high dividend per share good?
Ans: Dividends per share (DPS) is a crucial financial ratio for determining a company’s financial health and long-term growth potential. A company’s consistent or increasing dividend payment can be an indication of stability and growth.

We hope this detailed article on the formulae used in shares and dividends helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!