Class 10 Exam > Class 10 Notes > Mathematics Class 10 ICSE > Chapter Notes: Shares and Dividend
Shares and Dividend Chapter Notes | Mathematics Class 10 ICSE PDF Download
| Table of contents |
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| Introduction |
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| Formulae |
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| Miscellaneous Problems |
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| Solved Examples |
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Introduction
Imagine you want to own a part of your favorite company, but buying the whole business is out of reach. What if you could join hands with others to invest smaller amounts and still share the profits? That’s where the exciting world of shares and dividends comes in! This chapter introduces you to the concept of shares, where a company’s value is split into tiny, affordable parts, and dividends, the profits shareholders earn. It’s like being a co-owner of a big venture, reaping rewards based on your investment. Let’s dive into the details of how shares work, their values, and how dividends bring returns to investors, all explained in simple steps to make you a pro at understanding this financial game!
- A large company needs a huge amount of money to start or run.
- It’s tough for one person to invest such a big sum alone.
- People come together, pool their money, and divide the company’s estimated value into small parts called shares.
- Each share has a fixed value, known as its nominal value (N.V.), ranging from ₹1 to ₹100.
- Those who buy these shares become shareholders, owning a part of the company.
- Nominal Value (N.V.): Also called face value, register value, or printed value, it’s the original value of a share and stays constant over time.
- Market Value (M.V.): The price of a share in the market at a given time, which can increase or decrease based on the company’s performance.
- Share Status:
- At Par: When M.V. equals N.V. (M.V. = N.V.).
- Above Par (Premium): When M.V. is greater than N.V. (M.V. > N.V.).
- Below Par (Discount): When M.V. is less than N.V. (M.V. < N.V.).
- Dividend: The profit a shareholder receives from the company’s earnings, expressed as a percentage of the nominal value.
- Dividend depends on N.V., not M.V., and is paid based on the company’s profits.
Example: Ramesh buys ₹100 shares at ₹20 premium in a company paying 15% dividend.
Find: (i) the market value of 600 shares; (ii) his annual income; (iii) his percentage income.
Solution:
(i) M.V. of 1 share = N.V. + Premium = ₹100 + ₹20 = ₹120
M.V. of 600 shares = 600 × ₹120 = ₹72,000
(ii) Annual income = No. of shares × Dividend% × N.V. = 600 × (15/100) × ₹100 = ₹9,000
(iii) Percentage income = (Income / Investment) × 100 = (9,000 / 72,000) × 100 = 12.5%
Alternative: Income% × M.V. = Dividend% × N.V. → Income% × 120 = 15 × 100 → Income% = 12.5%
Formulae
- Sum invested = Number of shares bought × Market Value of 1 share
- If shares are at par, M.V. = N.V.
- Number of shares bought = Sum invested / Market Value of 1 share
- Number of shares bought = Total dividend / Dividend on 1 share
- Number of shares bought = Total income (profit) / Income (profit) on 1 share
- Total dividend earned = Number of shares × Rate of dividend × Nominal Value of a share
- Return% = (Income / Investment) × 100%
- For a shareholder, Income = Return = Profit = Dividend paid by the company.
Example: Rakhee 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.
Solution:
- M.V. of each share = ₹62.50, Sum invested = ₹12,500
- No. of shares bought = Sum invested / M.V. = 12,500 / 62.50 = 200
- Dividend on 1 share = 6% of N.V. = (6/100) × ₹50 = ₹3
- Total income = 200 × ₹3 = ₹600
- Alternative: Total income = No. of shares × Dividend% × N.V. = 200 × (6/100) × ₹50 = ₹600
Miscellaneous Problems
- This section covers advanced problems combining concepts of shares and dividends, such as calculating market value based on return, changes in income after selling shares, or dividing investments for equal returns.
- Key focus is on applying formulas creatively to solve complex scenarios, often involving multiple companies or transactions.
- Alternate methods are used where applicable, especially when comparing returns or solving for unknown values like market price or number of shares.
Example: A man buys a ₹80 share in a company, which pays 20% dividend. He buys the share at such a price that his profit is 16% on his investment. At what price did he buy the share?
Solution:
- Dividend on 1 share = 20% of ₹80 = ₹16
- Let M.V. = ₹x, Profit = 16% of ₹x = (16/100) × x
- Profit = Dividend → (16/100) × x = 16 → x = ₹100
- Alternative: Dividend% × N.V. = Profit% × M.V. → (20/100) × 80 = (16/100) × M.V. → M.V. = ₹100
Solved Examples
Example 1: Calculate the money required to buy: (i) 350, ₹20 shares at a premium of ₹7; (ii) 275, ₹60 shares at a discount of ₹10; (iii) 50, ₹40 shares quoted at ₹38.50.
Solution:
(i) M.V. = ₹20 + ₹7 = ₹27, Money required = 350 × ₹27 = ₹9,450
(ii) M.V. = ₹60 - ₹10 = ₹50, Money required = 275 × ₹50 = ₹13,750
(iii) M.V. = ₹38.50, Money required = 50 × ₹38.50 = ₹1,925
Example 2: Rupees 67,200 are invested in ₹100 shares which are quoted at ₹120. Find the income if 12% dividend is declared on the shares.
Solution:
- Sum invested = ₹67,200, M.V. = ₹120
- No. of shares = 67,200 / 120 = 560
- Dividend on 1 share = 12% of ₹100 = ₹12
- Total income = 560 × ₹12 = ₹6,720
- Alternative: Total income = No. of shares × Dividend% × N.V. = 560 × (12/100) × 100 = ₹6,720
Example 3: A man wants to buy 62 shares available at ₹132 (par value being ₹100).
(i) How much he will have to invest?
(ii) If the dividend is 7.5%, what will be his annual income?
(iii) If he wants to increase his annual income by ₹150, how many extra shares should he buy?
Solution:
(i) Investment = 62 × ₹132 = ₹8,184
(ii) Dividend on 1 share = 7.5% of ₹100 = ₹7.50, Annual income = 62 × ₹7.50 = ₹465
(iii) Income per share = ₹7.50, Extra shares needed = 150 / 7.50 = 20
Example 4: Which is a better investment: 12% ₹100 shares at 120 or 8% ₹100 shares at 90?
Solution:
- First case: Profit% × M.V. = Dividend% × N.V. → Profit% × 120 = 12 × 100 → Profit% = 10%
- Second case: Profit% × 90 = 8 × 100 → Profit% = 8.9%
- Since 10% > 8.9%, the first investment (12% ₹100 shares at 120) is better.
The document Shares and Dividend Chapter Notes | Mathematics Class 10 ICSE is a part of the Class 10 Course Mathematics Class 10 ICSE.
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FAQs on Shares and Dividend Chapter Notes - Mathematics Class 10 ICSE
| 1. What are shares and how do they function in a company? |  |
Ans. Shares represent ownership in a company. When an individual buys shares, they are purchasing a small part of the company and become a shareholder. Shares can provide dividends, which are a portion of the company's profits distributed to shareholders, and can also appreciate in value, offering potential capital gains when sold.
| 2. What is a dividend and how is it calculated? | |
Ans. A dividend is a payment made by a corporation to its shareholders, typically from its profits. The dividend amount is usually expressed as a percentage of the share's face value or as a fixed amount per share. It can be calculated using the formula: Dividend = (Total Dividend Declared / Number of Shares Outstanding).
| 3. What are the different types of shares available in the market? | |
Ans. The main types of shares are equity shares and preference shares. Equity shares give shareholders voting rights and the potential to earn dividends, while preference shares usually provide fixed dividends and have priority over equity shares in asset distribution during liquidation but typically do not carry voting rights.
| 4. How does the concept of face value relate to shares? | |
Ans. The face value of a share is its nominal value as stated in the company's charter. It does not necessarily reflect the market value, which can fluctuate based on supply and demand. The face value is important for calculating dividends and for determining the amount of capital that shareholders invest in the company.
| 5. Why is it important for investors to understand the risks associated with buying shares? | |
Ans. Understanding the risks associated with buying shares is crucial for investors because the stock market can be volatile, and share prices can fluctuate widely. Factors such as company performance, market conditions, and economic indicators can affect share values. Being aware of these risks helps investors make informed decisions and manage their investment portfolios effectively.
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