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Shares and Dividends

Certain business organizations need to raise money from public. In India, such an organization needs to be registered under the Indian Companies Act. Such an organization is called a public limited company.

A company may need money to start business or to start a new project. The sum of money required is called capital. The required capital is divided into small equal parts, and each part is called share. The company prepares a detailed plan of the proposed project and frames rules and regulations regarding its functioning. They, then, draft a proposal, issue a prospectus, explaining the plan of the project and invite the public to invest money in their project. They, thus, pool up the required funds from the public, by assigning them shares of the company. The value of a share may be Re 1, Rs 10, Rs 100, Rs 1000, etc. The capital is raised by selling these shares. A person who purchases shares of the company becomes a shareholder of the company.

Value of shares

The original value of a share printed in the certificate of the share is called its face value or nominal value (in short, NV). The NV of a share is also known as register value, printed value and par value. The price at which the share is sold or purchased in the capital market through stock exchanges is called its market value (in short, MV).

A share is said to be:

  • At premium or Above par, if its market value is more than its face value.
  • At par, if its market value equals its face value.
  • At discount or Below par, if its market value is less than its face value.

The share of a company that is doing well or expected to do well is sold in the market at a price higher than its NV. In such a situation, we say the share is at premium or above par. For example, if a share of NV of Rs 10 is selling at Rs 16 then the share is at a premium of Rs 6. The share of a company that is neither doing well nor poorly is sold in the market at a price equal to its NV. For example, if a share of NV of Rs 100 is selling at Rs 100 then the share is at par. The share of a company that is doing poorly or may do poorly in the future is sold in the market at a price lower than its NV. In such a case, we say the share is at a discount or below par. For example, if a share of NV of Rs 100 is selling at Rs 80 then the share is at a discount of Rs 20.

Dividend, Rate of Dividend

The part of the annual profit of a company distributed among its shareholders is called dividend. The dividend is always reckoned on the face value of a share irrespective of its MV.

The rate of dividend is expressed as a percentage of the NV of a share per annum.

Meaning of the statement “r% Rs 100 at Rs M”

The statement r% Rs 100 shares at Rs M means the following:

  • The NV of a share is Rs 100.
  • The MV of a share is Rs M.
  • The dividend on a share is r% of NV, i.e., Rs r per annum.
  • An investment of Rs M gives an annual income of Rs r.
  • Rate of return per annum = Annual income from an investment of Rs 100 =(\dfrac{Income}{Investment} \times 100) \%=(\dfrac{r}{M} \times 100)\%

Look at the statement given below:

  • 9% Rs 100 shares at Rs 120 means
  • Face value (NV) of 1 share = Rs 100.
  • Market value (MV) of 1 share = Rs 120.
  • The dividend on a share is 9% of its face value = 9% of Rs 100 = Rs 9
  • An investment of Rs 120 gives an annual income of Rs 9.
  • Rate of return per annum = Annual income from an investment of Rs 100 =(\dfrac{Income}{Investment} \times 100) \%=(\dfrac{9}{120} \times 100) \%=7\dfrac{1}{2} \%

Formula

1. Sum invested = No. of shares bought \times MV of 1 share

2. No. of shares bought =\dfrac{Sum \: invested}{MV \: of \: 1 \: share}

Also, no. of shares bought =\dfrac{Total \: dividend}{Dividend \: on \: 1 \: share}=\dfrac{Total \: income \: (profit)}{Income \: (profit)}  from 1 share

3. Income (return or profit) = (No. of shares) \times (rate of dividend) \times (NV) =(No. of shares) \times (Dividend on 1 share)

4. Return % = Income (profit) % =\dfrac{Income}{Investment} \times 100 \%

NOTE: The face value of a share remains the same. The market value of a share changes from time to time.

Examples

Example 1: Calculate the money required to buy: (i) 350, Rs 20 shares at a premium of Rs 7. (ii) 275, Rs 60 shares at a discount of Rs 10. (iii) 50, Rs 75 shares quoted at Rs 71.50.

Solution: (i) No. of shares = 350

NV = Rs 20

MV = Rs (20+7) = Rs 27

Therefore, money required to buy 350 shares = Rs (350 \times 27)= Rs 9450

(ii) No. of shares = 275

NV= Rs 60

MV= Rs (60-10) = Rs 50

Therefore, money required to buy 275 shares = Rs (275 \times 50) =Rs 13750

(iii) No. of shares = 50

NV= Rs 75

MV= Rs 71.50

Therefore, money required to buy 50 shares= Rs (50 \times 71.50) = Rs 3575

Example 2: A man invests in shares for which we have the condition “7% Rs 100 shares at Rs 120”. What is the annual income of a person holding 150 such shares? Also, find his annual profit percentage.

Solution: Given,

Rate of dividend=7%

Nominal value (NV) = Rs 100

Market value (MV) = Rs 120

No. of shares= 150

Therefore, Income =No. of shares \times rate of dividend \times NV= Rs \: (150 \times \dfrac{7}{100} \times 100)=Rs \: 1050

First we need to find the sum invested to find the profit percentage.

Investment=No. of shares \times MV= Rs \: (150 \times 120)=Rs \: 18000

Therefore, Required profit percentage =\dfrac{Income}{Investment} \times 100 \% =\dfrac{Rs \: 1050}{Rs \: 18000} \times 100=5\dfrac{5}{6} \%

Example 3: Which is a better investment: 16% at 80 or 20% at 120?

Solution: 16% at 80 means MV of 1 share is Rs 80, NV of 1 share is Rs100 and dividend paid is 16%.

Similarly, 20% at 120 means MV of 1 share is Rs 120, NV of 1 share is Rs 100 and dividend paid is 20%.

Case 1:

Income on Rs 80=16% of Rs 100=Rs 16

Therefore, income on Re \: 1=Rs \: \dfrac{16}{80}= Rs \: 0.20

Case 2:

Income on Rs 120=20% of Rs 100= Rs 20

Therefore, income on Re \: 1=Rs \: \dfrac{20}{120}= Rs \: 0.16

Therefore, the first investment is better.

Example 4: A company declares semiannual dividend of 6%. A man has 500 shares of NV Rs 25 each. Find his annual income.

Solution: Total NV of shares= Rs(25 \times 500)= Rs 12500

Semiannual dividend = 6% of Rs 12500= \dfrac{6}{100} \times 12500=Rs \: 750

Therefore, his annual income= Rs (750 \times 2)=Rs 1500

Example 5: Divide Rs 29184 into two parts such that if one part is invested in 12%, Rs 100 shares at 4% discount and the other in 15%, Rs 100 shares at 8% premium, the annual incomes are equal.

Solution: Let the investment in 12%, Rs 100 shares at 4% discount be Rs \: x .

Then, investment in 15%, Rs 100 shares at 8% premium be Rs \: (29184-x) .

MV of Rs 100 shares at 4% discount= Rs (100-4% of 100) = Rs 96

Annual income on 1 share of Rs 96=Rs (12% of 100) = Rs 12

Annual income on Rs \: x=Rs \: {12x}{96}=Rs \: {x}{8}

MV of Rs 100 shares at 8% premium= Rs (100+8% of 100) = Rs 108

Annual income on 1 share of Rs 108=Rs (15% of 100) = Rs 15

Annual income on Rs \: (29184-x) = Rs \: \dfrac{15(29184-x)}{108} =Rs \: \dfrac{5(29184-x)}{36}

\therefore \dfrac{x}{8}=\dfrac{5(29184-x)}{36}

\Rightarrow \dfrac{x}{8}+ \dfrac{5x}{36}= \dfrac{12160}{3}

So,x=15360

So, the first part is Rs 15360.

Second part= Rs (29184-15360) = Rs 13824

Example 6: Mukul invests Rs 9000 in a company paying a dividend of 6% per annum when a share of NV Rs 100 stands at Rs 150. What is his annual income? If he sells 505 of his shares when the price rises to Rs 200, what is his gain in this transaction?

Solution: No. of shares bought by Mukul=\dfrac{Investment}{MV}=\dfrac{9000}{150}=60

His annual income on 1 share=6% of NV=6% of Rs 100= Rs 6

His total annual income=60 \times  Rs 6= Rs 360

Since, 50% of shares= 50% of 60 =30

Money received on selling these shares =30 \times  Rs 200=Rs 6000

Also, cost of these shares=30 \times  Rs 150=Rs 4500

Therefore, Mukul’s gain= Rs (6000-4500) = Rs 1500

Example 7: A man wants to buy 62 shares available at Rs 132(NV being Rs 100).

  1. How much will he have to invest?
  2. If the dividend is 7.5%, what will be his annual income?
  3. If he wants to increase his annual income by Rs 150, how many extra shares should he buy?

Solution: 1. He will have to invest= 62 \times  Rs 132= Rs 8184

2. Dividend on 1 share= 7.5% of Rs 100=Rs 7.50

Therefore, his annual income = 62 \times  Rs 7.50= Rs 465

3. The man wants to increase his income by Rs 150 and income on 1 share= Rs 7.50

Therefore, no. of extra shares he must buy= $latex\dfrac{150}{7.50} = 20 $

Exercise

  1. Rahul buys Rs 100 shares at Rs 20 premium in a company paying 15% dividend. Find:
    • The market value of 200 shares
    • His annual income and
    • His percentage income
  2. Which is a better investment: 12% Rs 100 shares at 120 or 8% Rs 100 shares at 90?
  3. Divide Rs 1,21,824 into two parts such that if one part is invested in 8% Rs100 shares at 8% discount and the other in 9% Rs100 shares at 8% premium, the annual incomesfrom both the investments are equal.
  4. Ms Tirkey buys shares of a company for Rs 8000 at a discount of Rs 20(par value Rs 100). The company pays a 6% dividend annually. Find:
    1. The number of shares bought by Ms Tirkey
    2. Her annual income from the shares.
    3. Her annual profit percentage from the shares
  5. A man invests Rs 15,840 in buying shares of face value Rs 24 selling at a premium of 10%. The company pays a 15% dividend annually. Find:
    1. The dividend he receives annually
    2. The rate of return from his investment
  6. Mr. Chaudhury invests Rs 20,800 in 6% Rs100 shares at a premium of 4% and Rs 14,300 in 10.5% Rs100 shares at a premium of 43%. What will be his total annual income from these shares?
  7. A company declares semi-annual dividend of 6%. A man has some shares of the company, nominal value of each share being Rs100. If his annual income from the shares is Rs 1800, find the number of shares held by him.
  8. Mr. Dixit invests Rs 43,680 in buying Rs100 shares at a discount of 9%. He sells shares worth Rs 24000 at a premium of 5% and the rest at a discount of 10%. Find the total gain or loss from the transaction.
  9. A man sold 400 Rs 20 shares of a company paying 5% at Rs 18 and invested the proceeds in Rs10 shares of another company paying 7% at Rs12. How many Rs10 shares did he buy and what was the change in his income?
  10. Mrs. Sharma buys 85 shares (par value Rs 100) at Rs150 each. i) If the dividend is 6.5% what will be her annual income? ii) If she wants to increase her income by Rs260 how much more should she invest?
  11. Two brothers A and B invest Rs16000 each in buying shares of two companies. A buys 3% Rs100 shares at 80 and B buys Rs10 shares at par. If they both receive equal dividend at the end of the year, find the rate percent of the dividend received by B.


Comments

  3. kavya mehra says

    i think that you should improve you variety of question … like this page doesn’t contains the questions involving proceeds and neither are they explained…..but the tips are quite satisfying…

    Reply

  4. kavya mehra says

    i think that you should improve your variety of question … like this page doesn’t contains the questions involving proceeds and neither are they explained…..but the tips are quite satisfying…

    Reply

  9. sumit says

    Please slove this.

    A company pays a dividend of 15% on its ?100 shares from which income tax at the rate of 20% is deducted. Find: (1) the net annual income of gopal who owns 7200 shares of this company. (2) the sum invested by ramesh when the shares of this company are bought by him at 20% premium and the gain required by him (after deduction of income tax) is ?9000.

    Reply

  11. Fareha Naseem says

    Plz give the answer
    mrs. kulkarni invests rupees 131040 in buying rupees 100 shares at a discount of 9%. she sells shares worth rupees 72000 at a premium of 10% and the rest at a discount of 5%. find her total gain or loss on the whole.

    Reply

  13. Rajesh das says

    Plz solve it – by selling at Rs 92 , some 2 1/2 percent shares of Rs 100 FV and investing the proceeds in 5 percent shares of FV Rs 100 , selling at Rs 115 , a person increased in the income by Rs 90 a year , find – 1 – no. Of shares sold. 2 – no. Of shares bought . 3- original income

    Reply

  14. SULATA says

    Solve this a man holds 56shares of the company and receives a dividend of rupees 31.5 per quarter. If the dividend he received be 9%p.a. find face value of share

    Reply

  15. karma tenzing says

    plz can anyone solve this sum for me.
    Rs7225 paying 12% when a Rs100 share is available at 15% discount.

    Reply

  17. Ashish Gupta says

    Hi good website
    I have done my all the project in this website it is very good for everyone who want to write shares and dividend project and this best for ICSE student so I recommend for all ICSE student and also the teachers of ICSE schools

    Reply

  19. Alina says

    Mr. Salman with surplus funds wants to make an investment in the shares of listed companies. A stock broker has offered him following two options:

    Shares of company X at a price of Rs.22 per share with an expected price gain of 10% at the year end.
    Shares of company Y at a price of Rs.42 per share bearing a fixed rate of dividend with an expectation that next year company will offer 1 free share against holding of 5 shares.
    Required:

    You are required to identify the classes of shares and type of benefits in both of the above options.

    Reply

  20. bharat bhushan swarat says

    an investor has invested in the shares of XYZ ltd.. which expected no growth in dividends. XYZ Ltd.. has paid a dividend of Rs. 3 per share. if the required rate of return is 14%, what would be the value of the share.

    Reply

  21. bharat bhushan swarat says

    an investor has invested in the shares of XYZ ltd.. which expected no growth in dividends. XYZ Ltd.. has paid a dividend of Rs. 3 per share. if the required rate of return is 14%, what would be the value of the share.

    Reply

  22. Jeena says

    Plzz solve this for me….
    A company declares a semi-annual dividend of 6%. A man has 250 shares of the company. If his annual income is $960, find the face value of each share.

    Reply

  27. raj says

    A company sold 25,000 shares. The company made a profit of Rs.75,00,000 and distributed a certain percent of profit as dividend. A shareholder having 500 shares received Rs.30,000 dividend, find the rate of dividend.

    Reply

  28. Rashi says

    Plzzzzzzz solve this
    Rakesh invest rupees X in company A offering shares of rupees hundred rupees 80 each paying 12% he also invests rupees X in company B offering rupees 100 shares at rupees 120 paying 16% dividend he finds that if he had bought equal number of shares of each company with his total investment of rupees X his income would have been Rs 20 less find x

    Reply

  29. Parthajyoti Roy says

    Can anyone solve this
    .
    A man transfers his rupees 100 shares from 10% at 75 to 16% at 80 and there by increases his annual income by rupees 2000.Find the number of original shares held by him .

    Reply

  30. Parthajyoti Roy says

    Can anyone solve this ..
    .
    A man transfers his rupees 100 shares from 10% at 75 to 16% at 80 and there by increases his annual income by rupees 2000.Find the number of original shares held by him .

    Reply

  32. tejaswini bhavar says

    Plz solve this
    Murali holds 300 shares of rs 20 each the company issues shares in the ratio 3:5 the concept declared a dividend of 15% on the enlarged capital. What is the average rate of return on his investment?

    Reply

  33. Rrk says

    Pls solve this :
    A man invests 1680 in buying shares of nominal value24% n selling at 12% premium…the dividend on shares is 15% per annum…calculate the no of shares he buys

    Reply

  35. abc says

    Ashok bought an equity share whose face value is Rs. 10 for Rs. 250 and earned 50% dividend in year 1, 60% dividend in year 2, and sold it off after three years for Rs. 300. What is the return on his investment ?

    Reply

  37. Laxina says

    A hydro power company makes a profit of RS.2,50,00,000 annually. It distributes the dividends to it’s 1000 shareholders with equal number of shares so that each shareholder receives RS.20,000 as a dividend. Find the rate dividend.

    Reply

  38. Latisha says

    please solve this
    A company declares an annual dividend of 6%.The value of each share is R25.00 and Mr Smith has 500 shares.Find his annual dividend.

    Reply

    • Maths Tutor says

      The dividend of 6% is on the face value of the share and so we need to know the face value. Is Rs.25 the face value or the price?

      Reply

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