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**.

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.

**(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).

(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).

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

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

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

Percentage of return= *Income / Investment* x 100

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

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

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 = *₹*100*x*

*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.

Tags : Financial Mathematics , 11th Business Mathematics and Statistics(EMS) : Chapter 7 : Financial Mathematics

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

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