ICSE Class 10 Maths Chapter 03 Shares and Dividend

Shares and Dividend

Introduction

To establish a big company, a large sum of money is required. It is sometimes not possible for an individual to invest such a big amount. Then some persons, interested in the company, join together. They divide the estimated value into small parts ranging from ₹ 1 to ₹ 100. Each part so obtained is called a share and the value fixed for each share is called its original or nominal value (N.V.). The persons who purchase shares are called share-holders.

1. The nominal value (N.V.) of a share is also called its Register value, Printed value, Face value (F.V.), etc. The nominal value of a share does not change with time.

2. The price of a share in the market, at any particular time, is called its Market value (M.V.) or cash value. The market value of a share may change (decrease or increase) with time.

3. The market value of a share can be the same, more or less than the nominal value of the share depending upon the performance and profits of the company.

(i) If the market value of a share is the same as its nominal value, the share is said to be at par.

(ii) If the market value of a share is more than its nominal value, the share is said to be above par or at a premium.

(iii) If the market value of a share is less than its nominal value, the share is said to be below par or at a discount.

Thus, (i) At par means - Market value = Nominal value i.e. M.V. = N.V.

(ii) Above par or at a premium means - M.V. > N.V.

(iii) Below par or at a discount means - M.V. < N.V.

4. The profit, which a share-holder gets (out of the profits of the company) from his investment in the company, is called dividend.

(i) The dividend is always expressed as a percentage of the nominal value of the share.

(ii) The dividend does not depend on the market value of the share.

Formulae

1. Sum invested = No. of shares bought × M.V. of 1 share.

If the shares are available at par

⟹ M.V. of each share = N.V. of it

2. No. of shares bought = (Sum invested to buy the shares) / (M.V. of 1 share)

Also, no. of shares bought = (Total dividend from these shares) / (Dividend on 1 share)

= (Total income (profit)) / (Income (profit) on 1 share)

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

4. Return % = Income (profit) % = (Income / Investment) × 100%

5. For a share holder:

Income = Return = Profit = Dividend paid by the company

Worked Examples

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) No. of shares to be bought = 350

₹ 20 shares at a premium of ₹ 7 means; nominal value of the share is ₹ 20 and its market value = ₹ 20 + ₹ 7 = ₹ 27.

∴ Money required to buy 1 share = ₹ 27

⟹ Money required to buy 350 shares = 350 × ₹ 27 = ₹ 9,450 Ans.

(ii) Money required to buy 1 share = ₹ 60 - ₹ 10 = ₹ 50

⟹ Money required to buy 275 shares = 275 × ₹ 50 = ₹ 13,750 Ans.

(iii) Quoted price of a share means its market value.

∴ Money required to buy 1 share = ₹ 38.50

⟹ Money required to buy 50 shares = 50 × ₹ 38.50 = ₹ 1,925 Ans.

Teacher's Note

Understanding shares helps students grasp how businesses grow by pooling resources from many investors - just like a group of friends pooling money to buy sports equipment.

2 - 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:

Since, the market value of each share = ₹ 62.50 and the sum invested is ₹ 12,500

∴ No. of shares bought by Rakhee = 12,500 / 62.50 = 200

No. of shares bought = (Sum invested) / (M.V. of 1 share)

Income (dividend) on one share = 6% of N.V. = (6 / 100) × ₹ 50 = ₹ 3

Therefore, her total income = 200 × ₹ 3 = ₹ 600 Ans.

or, directly:

Income = No. of shares × Rate of div. × Face value (N.V.) of each share

= 200 × 6% × ₹ 50 = ₹ 600 Ans.

Teacher's Note

Dividends are like rewards investors receive for believing in a company - similar to earning interest on money saved in a bank account.

3 - 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) Market value of 1 share = ₹ 100 + ₹ 20 = ₹ 120

⟹ Market value of 600 shares = 600 × ₹ 120 = ₹ 72,000 Ans.

(ii) Annual income = No. of shares × Rate of div. × N.V. (F.V.) of 1 share

= 600 × (15 / 100) × ₹ 100 = ₹ 9,000 Ans.

(iii) ₹ 9,000 is the income obtained on investing ₹ 72,000

∴ Percentage income = (9,000 / 72,000) × 100% = 12.5% Ans.

Income % on M.V. = Dividend % on N.V.

⟹ Income % × 120 = 15% × 100

⟹ Income % = (15% × 100) / 120 = 12.5%

Teacher's Note

The difference between nominal and market value affects actual returns - this is like buying products on sale where the discount changes what you actually pay.

4 - 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

and M.V. of each share = ₹ 120

∴ No. of shares bought = 67,200 / 120 = 560

Given - dividend (income) on 1 share = 12% of N.V.

= 12% of ₹ 100 = ₹ 12

∴ Total income from the shares = 560 × ₹ 12 = ₹ 6,720 Ans.

Dividend (income) = No. of shares × Div. % × N.V. of each share

= 560 × (12 / 100) × 100 = ₹ 6720

Teacher's Note

Calculating total income helps investors verify if their investment meets their financial goals - like checking if your part-time job earnings will cover your expenses.

5 - Find the dividend due at the end of a year on 250 shares of ₹ 50 each, if the half-yearly dividend is 4% of the value of the share.

Solution:

∴ Half-yearly dividend on 1 share = 4% of ₹ 50

⟹ The yearly dividend on 1 share = 8% of ₹ 50 = (8 / 100) × ₹ 50 = ₹ 4

⟹ Total dividend due at the end of the year = 250 × ₹ 4 = ₹ 1,000. Ans.

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