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Revision: Commercial Mathematics >> Shares and Dividends Maths (English Medium) ICSE Class 10 CISCE

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Definitions [7]

Definition: Dividend

The annual profit distributed among shareholders is called a dividend.

Definition: Shares

A share is the smallest unit of the capital of a company. The capital of a company is divided into small equal parts, each of which is called a share.

Definition: Capital

The total amount of money needed to run the company is called the capital.

Definition: Market Value of a Share (M.V.)

The shares of different companies can be bought or sold in the market through the stock exchange.

Definition: Face Value / Nominal Value / Par Value (F.V. / N.V.)

The value of a share printed on the share certificate is called its Nominal Value, or Face Value, or Par Value.

Definition: Stock Exchange

A stock exchange is a place where the buying and selling of shares takes place. It is also known as the share market or capital market.

Definition: Shareholder

A shareholder is a person who owns one or more shares of a company. A shareholder is a part owner of the company in proportion to the number of shares held.

Formulae [6]

Formula: Shares, Dividends and Rate of Return

Investment and Number of Shares

\[ \text{Investment} = \text{Number of Shares} \times \text{Market Value} \]

\[ \text{Number of Shares} = \frac{\text{Total Investment}}{\text{Market Value per Share}} \]

Dividend

\[ \text{Dividend per Share} = \frac{\text{Dividend } \%}{100} \times \text{Face Value} \]

\[ \text{Total Annual Dividend} = \text{Number of Shares} \times \text{Dividend per Share} \]

Rate of Return

\[ \text{Rate of Return} = \frac{\text{Total Annual Dividend}}{\text{Total Investment}} \times 100 \]

Formula: Dividend / Income

Dividend (Income) = Face Value × No. of shares × $$\frac{Rate\ of\ dividend}{100}$$

Formula: Investment (Amount Invested)

Formula: Number of Shares

$$\text{No. of shares} = \frac{\text{Investment}}{\text{Market Value of 1 share}}$$

$$
\text{No. of shares} = \frac{\text{Total Income}}{\text{Dividend on 1 share}}$$

Formula: Rate of Return

\[\text{Rate of Return}=\frac{\text{Annual Income}}{\text{Investment}}\times100\]

Formula: Total Dividend Earned

Total dividend earned = No. of shares × rate of dividend × N.V. of a share 

Key Points

Key Points: Important Facts of Share
Term Short Explanation
Share The smallest unit of a company’s capital.
Dividend Part of the company’s profit is distributed per share, calculated on Face Value.
Stock Exchange Market where shares are bought and sold (e.g. BSE, NSE).
Market Index Indicator of stock market performance (SENSEX – BSE, NIFTY – NSE).
Face Value (FV) Value printed on the share certificate (also called par value).
Market Value (MV) The price at which a share is bought/sold in the market.
MV > FV Shares issued at a premium.
MV = FV Share issued at Par.
MV < FV Shares issued at a discount.
Sum Invested Total amount spent to buy shares. Formula: Number of shares × MV
Rate of Return (RoR) Percentage return on investment. Formula: (Dividend ÷ MV) × 100

Concepts [3]

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