BMM10233_Chapter 7_Stocks & Shares

Chapter 7 | Stocks and Shares | BMM10233 | 124 of 204

A company, in order to meet its requirement of funds may

(i) Borrow money from the public or

(ii) Invites the public to invest money and become co – owners of the company.

Debentures

When a company borrows money from the public, it promises to pay a fixed rate of interest to the lenders and also issues

certificate acknowledging the loan. This certificate, known as a ‘debenture certificate’ is tradable. The amount which the

company promises to pay on redemption is the face value of the debenture.

Indian companies Act allows a company to issue one aggregate loan fund or composite stock known as debenture stock

instead of issuing debentures, each in respect of a separate and distinct debt. Hence debenture stock is a borrowed capital

consolidated into one mass for convenience.

Shares

When a company invests money and becomes co- owner of the company, it issues certificates acknowledging the

investment. These certificates are called share certificates and the investors are called the share – holders. They are partners

of the company to the extent of their investment in the total capital of the company i.e., an investment of Rs. 10, 0000 in a

company whose capital is 10,00,0000 makes the investor a 10% partner of the company.

The company invites these investment in smaller denomination. For instance, if a company needs to raise Rs. 10,00,000, it

could issue 100000 shares of face value Rs. 10 or 10000 shares of face value Rs 100.

Fully paid and partly paid shares

A company may provide installment options to the investors. If a company that issues Rs. 10 face value shares with an

installment scheme of down payment of Rs 4, 1st installment of Rs 4 and a second installment of Rs. 2, an investor who has

paid only the down payment is said to have bought Rs 10 stock with Rs 4 paid up. After the payment of the 2nd installment,

the share is Rs 8 paid up and finally after the last installment is paid, the share stands fully paid.

A company can convert its fully paid shares into stock. If an investor has originally held 100 shares of Rs 10 each after

conversion to stock his investment in the company remains the same as Rs 1000. He now holds a Rs 1000 worth of stock

instead of Rs. 100 shares of Rs 10 each.

Dividend

The net annual profits of a company are divided among the shareholders, and the proportion of profits which the shareholders

receive according to the shares they possess in the capital is called dividend. Generally dividend is either paid at the rate of

so many rupees per share or on the basis of a percentage on the paid up value of the shares.

Note: When the share is partly paid up, any interest or dividend paid by the company is on the part paid and not on the face

value of the share.

Stocks and Shares


Nominal and market value of shares and stock

Nominal value is the original face value of the share. Share in the capital of a company or Government stock can be bought

and sold like commodities. The value at which they are bought and sold is not necessarily equal to the face value. They may

be sold at a price lower than the face value in which case the share is said to be sold at a discount or below par. If they are

sold at a price higher than the face value, they are sold at a premium or above par and if they are sold at a price equal to the

face value they are said to be at par. The value at which they are bought and sold in the market is called the market price.

Brokerage

Share can be bought and sold in the market through intermediaries or middlemen called stock brokers. Stock brokers have to

be paid a certain commission called “ Brokerage”, whenever stocks and shares are bought or sold. When shares are sold the

brokerage is deducted from the selling price and when shares are purchased, it is added to the cost price.

Yields / Returns

The total profit as a percentage of the total investment from any transaction is known as yields or return from the investment.

The following formulas come in very handy.

1. Investment

Number of shareMarket value of one share.

=

2. Annual Income (nominal or dividend)

Number of share nominal value dividend percent=

100

(unless otherwise mentioned, the nominal value is Rs.100).

× ×

3. Annual Income

Yield or Rate of returns 100Investment

= ×

SOLVED EXAMPLES

Example: 1.

What is the annual income derived by investing Rs.1000 at 12.5% at 80?

Sol:

1000Number of share 12.5

80= =

12.5Annual Income 12.5 100 156.25

100= × × =

156.25 100Rate of returns 15.625%

1000

×= =


Example: 2.

Ravi invests Rs 12000 in Rs 100 share selling at a premium of Rs 20. The company pays a dividend of 8%. Calculate,

(a) The number of share held by Ravi,

(b) His annual income,

(c) Yield.

Sol:

12000Number of share = 100

120=

8Annual Income 100 100 Rs.800.

100= × × =

800Rate of returns 100 6.67%

12000= × =

Example: 3.

What is the nominal interest earned by investing Rs.12,000 in 16% stock at at 96?

Sol:

12000Number of share = 125.

96=

16Nominal interest income 100 125 Rs.2000

100= × × =

Example: 4.

What is the yield in Rs.1000 investment in 14% at 85?

Sol:

1000Number of share = 11.76

85=

14Annual Income 100 11.76 Rs.164.7

100= × × =

164.7 100Yield 16.47%.

1000

×= =

Example: 5.

What is the amount paid as brokerage at 2% on the purchase of Rs. 15, 000 (Nominal Value) in 15% stock at 81?

15000Number of shares 150

100= =

Investment 150 81 12,150

2Brokerage 12150 Rs.243.

100

= × =

= × =

[some books say, that brokerage is a % on the nominal value. Here it is used on the market value].


Example: 6.

What is the total value of 16% stock at 93.5 that can be purchased for Rs. 1122?

Sol:

1122 11220Number of shares 12

93.5 935

Total value of the stock 12 100 Rs.1200.

= = =

= × =

Example: 7.

Ram sold his car for 40,000 and invested 75% of the proceeds in Rs. 10 shares at 15 paying a dividend of 20%. After a year,

he sold the shares for Rs. 18 and invested the proceeds in Rs. 100 shares trading at Rs. 120 offering a dividend of 24%. Find

the change in his annual income.

Sol:

Case I

75Investment 40,000 Rs.30,000

100= × =

30,000Number of shares in the first company, 2000

15= =

20Annual Income 2000 10 Rs.4000

100= × × =

Case II

36000Number of shares 300

120= =

24Annual Income 300 100 Rs.7200

100= × × =

Change in the annual income = 7200 - 4000 = Rs. 3200

Example: 8.

What is the cash price of 14.5% stock if it yields a return of 3.75%

14.5Annual Income 1 100 14.5

100= × × =

Annual IncomeRate of return 100

Investment= ×

14.5Therefore 3.75 100

x= ×

145000Solving, x 386.67

375

cash price R s.386.67.

= =

∴ =


Example: 9.

Which of the following investment is better ? 8% Rs. 100 share at Rs. 120 or 9% Rs. 10 share at Rs 15.

Sol:

8Annual Income from Rs.100 share at 120 at 8% 1 100 Rs.8

100= × × =

8Rate of return 100 6.67%

120= × =

9 9Annual Income from Rs.10 share 1 10 0.9

100 10= × × = =

0.9Rate of return 100 6%

15= × =

Hence the former investment is better.

Example: 10.

How much should be invested in 14.2% stock at 98 to produce the same income as would be obtained by investing Rs. 9975

in 15% stock at 105?

Sol:

9975Number of share = 95.

105=

15Annual Income 95 100 Rs.1425.

100= × × =

Annual Income from 14.2% stock at 98

14.2100 (when x is the number of shares).

100= × ×

= 14.2 x

∴1425 = 14.2x ⇒ x = 100

Investment = number of share × Market value = 100 × 98 = Rs 9800.

Example: 11.

A person sells out Rs. 4000 shares at 6.25% of Government of Indian stock at 112.5 and reinvests the proceeds in 8% railway

debentures thereby increasing his annual income by Rs. 50. At what price did he buy the debenture?

Sol:

4000Number of share = 40

100=

62.5Annual Income 40 100 Rs.250

100= × × =

Annual income from the railway debenture = 250 + 50 = Rs 300

Let the number of debentures purchased be x.

∴ Annual Income = 8

100 × 100 x

∴ 300 = 8x or x = 300

8 = 37 . 5


Investment = 40 × 112.5 = Rs 4500.

Market value = 4500

37.5 = 120

∴ He bought the debenture at Rs 120.

Example: 12.

A person purchased share of two companies A and B for a total investment of Rs. 4500 paying Rs. 30 for the first share and

Rs 7.5 for the second share. His annual income from both the shares is Rs 200. If the first company pays a dividend of 8%

and the second company at 20%, calculate his investment in each kind of share, assuming the nominal value of each share

is Rs 10.

Sol:

Let x and y be the number of shares of companies A and B

Investment = 30x + 7.5y = 4500 ..... (1)

Annual returns = x × 10 × 8

100 + y × 10 ×

20

100

∴ 8x

10 + 2y = 200 ..... (2)

Solving (1) and (2), x = 138.88, y = 44.44

Example: 13.

Raja buys 200 shares, each of par value Rs. 10 of a company which pays annual dividend of 15% at such a price he gets 12%

on his investment. Find the market value of a share.

Sol:

Par value of 200 shares = Rs. (200 × 10) = Rs. 2000.

Dividend received by Raja = Rs. 2000 15

100

×

= Rs. 300.

Let the market value of 200 shares be Rs. x. We have to find x such that 12% of x = 300,

i.e. 12

x 300100

× = 100 300x 2500

12

×∴ = =

i.e. Market value of 200 shares = Rs. 2500

Hence, the market value of one share = Rs. 12.50

Example: 14.

Find the income from Rs. 2875 of 4% stock.

Sol:

By 4 % stock, we mean a stock of Rs. 100 will fetch a dividend of Rs. 4 p.a.

Hence, the income from Rs. 2875 of 4% stock = 2875 4

100

×= Rs. 115.


Example: 15.

Find the income on 10% stock of Rs. 25000 purchased at Rs. 120.

Sol:

Face value of stock = Rs. 25000

Income on Rs. 100 stock = Rs. 10

Income on Re. 1 stock = Rs. 10

100

Income on Rs. 25000 stock = Rs. 25000 10

100

×

= Rs. 2500.

Example: 16.

Find the investment required to get an income of Rs. 4200 from 10 1

2% stock at 80 (Brokerage: 2%).

Sol:

Brokerage = 2% of Rs. 80 = Rs.2

80 Rs.1.60100

× =

∴ Investment needed to buy Rs. 100 stock

= Rs. 81.60 on which the income is Rs. 101

2

For income of Rs. 101

2, the investment = Rs. 81.60

For income of Rs. 4200, the investment = 2

Rs. 81.60 4200 Rs.3264021

= × × =

Example: 17.

Ram bought Rs. 12000, 8% stock at 92 and sold it when the price rose to 98. Find his total gain and gain percent

Sol:

Investment made by Ram in buying Rs. 12000 of 8% stock at 92

= Rs. 92

12000 Rs.11040100

× =

When the price rose to Rs. 98, Ram sold the stock, thus money realized from selling the stock

= Rs. 98

12000 Rs.11760100

× =

∴ Gain realized in the transaction = Rs. (11760 – 11040) = Rs. 720

∴ Gain percent ( )720 100 12

6 %11040 23

×=

ff

fdgdfgdg


Example: 18.

Ram invests Rs. 46500 in 6% stock at 93 and sells the stock when its price rose to Rs. 95. He invests the sale proceeds in 9%

stock at 95. Find the change in Ram’s income.

Sol:

Income from first stock = Rs. 6

4650093

×

= Rs. 3000

We have to find the amount realized on selling this stock.

Amount realized on selling Rs. 93 stock = Rs. 95

∴ Amount realized on selling Rs. 46500 stock = Rs. 95

46500 Rs.4750093

× =

This amount is invested in 9% stock at 95

∴ Income from 2nd stock = Rs. 9

47500 Rs.450095

× =

Hence, increase in income = Rs. (4500 – 3000) = Rs. 1500.

Example: 19.

Find the income percent of a buyer on 8% debentures of face value Rs. 120 and available in the market at Rs. 180.

Sol:

The market value of a debenture is Rs. 180

∴ Income on Rs. 180 is Rs. 8

∴ Income on Rs. 120 is Rs. 8 1

120 Rs.5180 3

× =

∴ Percent income on the debenture is 1

53

.

Example: 20.

Ram has 500 shares of par value Rs. 10 each of a company and 500 debentures of par value Rs. 100 each. The company pays

a dividend of 8% on the shares and pays an interest of 10% on its debentures. Find the total annual income of Ram and the

rate of return on his investments.

Sol:

(500 10 8)Annual dividend on 500 shares Rs. Rs.400.

100

× ×= =

(500 100 10)Annual interest on 500 debentures Rs. Rs.5000.

100

× ×= =

Total annual income of Ram Rs.(5000 400) Rs.5400.∴ = + = d

Total investment of Ram Rs.(500 10 500 100) Rs.55000.= × + × =

5400 108 9Rate of return on Ram's investment 100 % %or 9 .

55000 11 11

= × =


1. Jatin invested Rs. 17260 in buying Rs. 100 shares of a company at Rs. 116 each. If the company paid 16 % dividend at the

end of the year, find his income from the dividend. (Access Code - 01307001)

(1) Rs. 2716.6 (2) Rs. 2760 (3) Rs. 3570 (4) Rs. 3660 (5) Rs. 2380.7

2. A company issued 50000 shares of per value Rs. 10 each. If the total dividend declared by the company is Rs. 62500, find

the rate of dividend paid by the company. (Access Code - 01307002)

(1) 1

8 %2

(2) 1

12 %2

(3) 12 % (4) 3

13 %4

(5) 13 %

3. A company declared a semi-annual dividend of 1

17 %2

.Find the annual dividend of Chetan, owning 1250 shares of the

company having a par value of Rs. 10 each (Access Code - 01307003)

(1) Rs. 2078.5 (2) Rs. 1757 (3) Rs. 1680 (4) Rs. 1093.75 (5) Rs. 2187.5

4. Mac buys 200 shares of par value Rs. 10 each, of a company, which pay an annual dividend of 8% at such a price that he

gets 10% on his investment. Find market value of one share? (Access Code - 01307004)

(1) Rs. 9 (2) Rs. 10 (3) Rs. 6 (4) Rs. 12 (5) Rs. 8

5. Find the income on 12% stock of Rs. 60000 purchased at Rs. 110. (Access Code - 01307005)

(1) Rs. 7000 (2) Rs. 7500 (3) Rs. 6545.45 (4) Rs. 8200 (5) Rs. 7200

6. A person buys 1

9 %2

stock of Rs. 72000 at 144. Find his annual income. (Access Code - 01307006)

(1) Rs. 4750 (2) Rs. 6840 (3) Rs. 6900 (4) Rs. 7240 (5) Rs. 6500

7. Raja invested Rs. 99000 in 1

7 %2

stocks at 112 (Brokerage: Rs. 2) Find annual income of Ram from this investment. (Access

Code - 01307007)

(1) Rs. 6750 (2) Rs. 6629 (3) Rs. 6513 (4) Rs. 7425 (5) Rs. 7525

8. Find the investment required to get an income of Rs. 1938 from 1

9 %2

stock at 90 (Brokerage 1%). (Access Code - 01307008)

(1) Rs. 19642.60 (2) Rs. 17543.00 (3) Rs. 18543.60 (4) Rs. 18600.60 (5) Rs. 18532.71

9. A man invests Rs. 27600 in 4% stock at 92. He sold Rs. 20000 stock when the price rose to Rs. 96, and sold the remaining

stock when the market value fell to Rs. 90. How much does he gain or loss in the transaction? (Access Code - 01307009)

(1) Gain= Rs. 600 (2) Loss = Rs. 600 (3) Loss = Rs. 650 (4) Gain = Rs. 650 (5) None of these

10. A person invests Rs. 28500 in 5% stock at 95. He sold Rs. 15000 stock when the price rose to Rs. 98 and sold the remaining

stock when the market value of the stock fell to Rs. 90. How much does he gain or loss in the transaction? (Access Code -

01307010)

(1) Gain = Rs. 300 (2) Loss = Rs. 300 (3) Gain = Rs. 400 (4) Loss = Rs. 400 (5) Gain = Rs. 500

Practice Exercise - 1


11. A man who owned 25% of the equity capital of a certain company sold 1/3 of his holding last year and 5/12 of the remaining

this year. What part of the business does he now own? (Access Code - 01307011)

(1) 1/5 (2) 5/144 (3) 8/13 (4) 65/72 (5) 7/72

12. Find what a purchaser would have to pay for 300 shares of Rs. 10 each quoted at Rs. 25. What would be the gain to the

shareholder, if he had purchased the share at par? (Access Code - 01307012)

(1) Rs. 5000, Rs. 4500 (2) Rs. 5500, Rs. 450 (3) Rs. 7500, Rs. 4500 (4) Rs. 4000, Rs. 7500 (5) None of these

13. Which one of the following is the best investment? (Access Code - 01307013)

(1) 13% stock at 104 (2) 17% stock at 140 (3) 15% stock at 125 (4) 9 % stock at 70 (5) 9 % stock at 17

14. Divide Rs. 5300 into two parts such that if one part is invested in 1

10 %2

at 98 and the other in 12% at par, the resulting

income are equal (neglect brokerage). (Access Code - 01307014)

(1) Rs. 2800, Rs. 2500 (2) Rs. 3200, Rs. 2100 (3) Rs. 2500, Rs. 2800 (4) Rs. 2100, Rs. 3200 (5) Data insufficient

15. Find the cash realized by selling Rs. 2400, 1

5 %2

stock at 5 premium (brokerage 1

%4

). (Access Code - 01307015)

(1) Rs. 2614 (2) Rs. 2400 (3) Rs. 2514 (4) Rs. 2714 (5) Rs. 3500

SCORE SHEET

Use HB pencil only. Abide by the time-limit

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1 2 3 4 5

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1. Find the annual dividend received by Sunil for his 200 preferred shares and 1000 common shares, both of par value Rs. 100

each if the dividend declared on a preferred share is 10% per annum and an annual dividend of 1

12 %2

on the common

shares (Access Code - 01307016)

(1) Rs. 12500 (2) Rs. 14500 (3) Rs. 12000 (4) Rs. 15000 () Rs. 13500

2. Company issued 50000 shares of par value Rs. 100 each. If the total dividend declared by the company is Rs. 125000, out

of which Rs. 50000 have been kept in reserve fund and the remaining is distributed as dividend, find the rate of dividend

paid by the company. (Access Code - 01307017)

(1) 1

2 %2

(2) 1

1 %2

(3) 1

1 %4

(4) 2 % (5) 3 %

3. Determine the increase in income obtained by transferring Rs. 4000 of 1

3 %4

stock at 87 to 1

6 %4

stock at 145. (Access

Code - 01307018)

(1) Rs. 10 increase (2) Rs. 20 increase (3) Rs. 15 increase (4) Rs. 25 increase (5) None of these

4. A company has issued 10000 preferred shares and 50000 common shares both of par value Rs. 100 each. The dividend on

a preferred share and a common share is 12% and 17.6 %, respectively. The company had a total profit of 15 lakh rupees out

of which some amount was kept in reserve fund and the remaining distributed as dividend. Find the amount kept in reserve

fund. (Access Code - 01307019)

(1) Rs. 5 lakh (2) Rs. 6 lakh (3) Rs. 6.5 lakh (4) Rs. 5.5 lakh (5) Rs. 7 lakh

5. A man sells 5000 common shares of a company X (each of par value Rs. 10), which pays a dividend of 20%, at Rs. 30 per

share. He invests the sale proceeds in ordinary shares of Company Y each of par value Rs. 25) that pays a dividend of 15%.

If the market value of a share of Company Y is Rs. 40, find the number of shares of Company Y purchased by the man.

(Access Code - 01307020)

(1) 3850 (2) 3600 (3) 3700 (4) 3800 (5) 3750

6. A man invested Rs. 260000 in 5% stock at 104. He sold the stock when the price rose to Rs. 125 and invested the sale

proceeds in 6% stock. By doing this, his income increased by Rs. 2500. At what price did he purchase the second stock?


(1) Rs. 225 (2) Rs. 175 (3) Rs. 200 (4) Rs.150 (5) Rs. 125

7. By investing in a company paying a dividend of 30% one obtains a return of 12%. Company’s Rs. 10 shares is quoted at


(1) Rs. 35 (2) Rs. 20 (3) Rs. 25 (4) Rs. 45 (5) Rs. 40

8. A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value

of each share must be (Access Code - 01307023)

(1) Rs. 12 (2) Rs. 15 (3) Rs. 18 (4) Rs. 21 (5) Rs. 19

Practice Exercise - 2


9. Having Rs. 8370 to invest, a man puts part of it in 9% stock at 96 and the remainder in 12% stock at 120. If his dividend from

each investment is same, amount invested in second stock was (Access Code - 01307024)

(1) Rs. 4140 (2) Rs. 4320 (3) Rs. 4050 (4) Rs. 4230 (5) Rs. 4530

10. The sale proceeds of Rs. 4500, 1

6 %2

stock at 95 is transferred to 16% stock and there by income increases by Rs 11.50. The

price of 16% stock is (Access Code - 01307025)

(1) Rs. 110 (2) Rs. 150 (3) Rs. 175 (4) Rs. 200 (5) Rs. 225

SCORE SHEET

Use HB pencil only. Abide by the time-limit

1

2

1 2 3 4 5

1 2 3 4 5

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5

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3. (2)

4. (1)

5. (5)

6. (5)

7. (3)

8. (2)

9. (3)

10. (4)

1. (2)

2. (2)

4. (5)

5. (5)

6. (2)

7. (3)

8. (3)

9. (1)

10. (2)

11. (5)

12. (3)

13. (4)

14. (1)

15. (3)

1. (5)

2. (3)

3. (5)

Practice Exercise -2

Answer Key

Practice Exercise -1

Documents

BMM10233_Chapter 7_Stocks & Shares