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# Stocks, shares, debentures and Brokerage

To start any big business, a large sum of money is needed.

Stocks, shares, debentures and Brokerage

To start any big business, a large sum of money is needed. It is generally not possible for an individual to manage such a large sum. Therefore the total sum of money can be divided into equal parts called shares. The holder of shares are called shareholders.

## 1. Types of shares:

There are two type shares namely common (or equity) and preferred.

The profit gained by the company is distributed among the share holders The preferred share holders have a first claim on dividend. When they have been paid, the remaining profit is distributed among the common share holders.

## 2. Definitions

(i) Capital stock is the total amount invested to start a company.

(ii) The share purchased by the individual is also called stock.

(iii) The persons who buy the shares are also called stock holders

(iv) Face value : The original value of a share at which the company sells/ buys it to investors is called a face value or nominal value or par value. It is to be noted that the original value of share is printed on the share certificate.

(v) Market value : The price at which the stock is bought or sold in the market is called the market value (or cash value).

### Remarks:

(i) If the market value of a share is greater than the face value then, the share is said to be above par (or at premium).

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

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

### Dividend :

The profit gained by a company, distributed among the share holders is called dividend. It is calculated on the face value of the share.

## Some useful results:

### (i) Investment:

Money invested = number of shares × market value of a share

### (ii) Income:

Annual income = number of shares × face value of a share × rate of dividend

### (iii) Return percentage (or yield percentage):

Percentage of return= Income / Investment x 100

### (iv) Number of shares:

Number of shares purchased = Investment / market value of a share

### Stock exchange:

The place where the shares are traded is called the stock exchange (or) stock market.

### Brokerage:

A broker who executes orders to buy and sell shares through a stock market is called Stock Broker. A fee or commission for their service is called the brokerage.

Brokerage is generally based on the face value and expressed as a percentage.

NOTE

(i) When the stock is purchased, brokerage is added to cost price.

(ii) When the stock is sold, brokerage is subtracted from the selling price..

Example 7.11

Find the market value of 325 shares of amount 100 at a premium of 18.

Solution :

Face value of a share =  100

Premium per share =  18

M.V. of 1 share =  118

Market value of 325 shares =  number of shares × M.V of 1 share

= 325 × 118

= 38,350

Therefore market value of 325 shares = 38,350.

Example 7.12

A man buys 500 shares of amount 100 at 14 below par. How much money does he pay?

Number of shares =       500

Face value of a share     =       ₹100

Discount     =       ₹14

Market value of a share =       100 – 14 (face value – discount)

=       ₹86.

Market value of 500 shares =  Number of shares × market value of 1share

=       500 × 86

=       43,000

Market value of 500 shares =  ₹43,000

Example 7.13

A person buy 20 shares (par value of 10) of a company which pays 9% dividend at such a price that he gets 12% on his money. Find the market value of a share.

Solution :-

Face value of one share  =       ₹10

Face value of 20 shares  =       ₹200 Example 7.14

If the dividend received from 10% of 25 shares is 2000. Find the number of shares.

Solution :

Let x be the number of shares.

Market value of ‘x’ shares = 25 x Hence the number of shares = 800

Example 7.15

Find the number of shares which will give an annual income of 3,600 from 12% stock of face value 100.

Solution :

Let ‘x’ be the number of shares.

Face Value = = 100

Market value of ‘x’ shares = 100x

12/100 × 100x = ₹ 3600

12 x  = 3600 & x = 300

Hence the number of shares = 300

Example 7.16

A man invest 96,000 on 100 shares at 80. If the company pays him 18% dividend, find

(i) the number of shares he buys

(ii) his total dividend

(iii) his percentage return on the shares.

Solution :-

(i)      Investment  = ₹96,000

Face Value  = ₹100

Market Value       =       ₹80

The number of shares bought  =

Investments / M.V of one share

=       96, 000 / 80

= 1200 shares

(ii)     Total dividend      = No. of shares × Rate of dividend × Face value of one share

= 1200× 18/100 x 100

= ₹21,600

(iii) Dividend on ₹ 96000 = ₹21600

Percentage return on the shares = 21600/96000  ×100

= 45/2 = 22.5

Thus return on the shares  = 22.5%

Example 7.17

A person brought at 12% stock for 54,000 at a discount of 17%. If he paid 1% brokerage, find the percentage of his income.

Solution :

Face value = 100

Market value = (100 – 17 + 1)

= 84

percentage of his income Example 7.18

Equal amounts are invested in 10% stock at 89 and 7% stock at 90 (1% brokerage paid in both transactions). If 10% stock bought 100 more by way of dividend income than the other, find the amount invested in each stock.

Solution :

Let x be the amount invested in each stock

F.V. = 100, M.V. = 90 x = 2925

The amount invested in each stock = Rs.2925

Example 7.19

A capital company is made up of 1,00,000 preference shares with a dividend of 16% and 50,000 shares.The par value of each of preference and ordinary shares is 10.The total profit of a company is 3,20,000.If 40,000 were kept in reserve and 20,000 were kept in depreciation fund, what percent of dividend is paid to the ordinary share holders

Solution:

F.V. = ₹10

Preference shares investments = ₹1,00,000 × 10 = ₹10,00,000

Ordinary shares investments = ₹50,000 × 10 = ₹5,00,000

Total dividend = ₹(3,20,000 – 40,000 – 20,000) = ₹2,60,000

Dividend for preference shares = 10016 × 10,00,000 = ₹1,60,000

Dividend to ordinary shares  = 2,60,000 – 1,60,000 = ₹1,00,000

Dividend rate for ordinary share  = Example 7.20

A person sells a 20% stock of face value ₹10,000 at a premium of 42%. With the a money obtained he buys a 15% stock at discount of 22%. What is the change in his income if the brokerage paid is 2%.

Solution:- Change of income = 2625 – 2000 = 625

Example 7.21

Which is better investment 12% 20 shares at 16 (or) 15% 20 shares at 24 .

Solution:

Let the investment in each case be (16× 24) Exercise 7.2

1. Find the market value of 62 shares available at 132 having the par value of 100.

2. How much will be required to buy 125 of 25 shares at a discount of 7

3. If the dividend received from 9% of 20 shares is 1,620, find the number of shares.

4. Mohan invested 29,040 in 15% of 100 shares of a company quoted at a premium of 20%. Calculate

(i) the number of shares bought by Mohan

(ii) his annual income from shares

(iii) the percentage return on his investment

5. A man buys 400 of 10 shares at a premium of 2.50 on each share. If the rate of dividend is 12% find

(i) his investment

(ii) annual dividend received by him

(iii) rate of interest received by him on his money

6. Sundar bought 4,500 of 10 shares, paying 2% per annum. He sold them when the price rose to 23 and invested the proceeds in 25 shares paying 10% per annum at 18. Find the change in his income.

7. A man invests 13,500 partly in 6% of 100 shares at 140 and partly in 5% of 100 shares at 125. If his total income is 560, how much has he invested in each?

8. Babu sold some 100 shares at 10% discount and invested his sales proceeds in 15% of 50 shares at 33. Had he sold his shares at 10% premium instead of 10% discount, he would have earned 450 more. Find the number of shares sold by him.

9. Which is better investment? 7% of 100 shares at 120 (or) 8% of 100 shares at 135.

10. Which is better investment? 20% stock at 140 (or) 10% stock at 70.

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11th Business Mathematics and Statistics(EMS) : Chapter 7 : Financial Mathematics : Stocks, shares, debentures and Brokerage | Financial Mathematics