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## List of Topics Covered in Shares and Dividends

### Share and Value Shares – Definition

The division of money required into some equal parts is called a share. And the person who purchases the shares is known as the shareholder of the company. The original value of a share printed on the certificate of the share is known as the value of the share.

### Dividends – Definition

The sum of money paid for equal parts in any profits is known as the dividends.

### Formula to Calculate Dividends Per Share

D = DPS multiplied by S,
where D = your dividends and
S = the number of shares you own.

### Shares and Dividends Examples

Example 1.
Find the dividends received on 80 shares of Rs 30 each if a 7% dividend is declared. Then find the dividend.
Solution:
Given that
The value of shares = Rs. 30
The value of 60 shares each = Rs. 30
= 30 × 80 = 2400
The rate of dividend = 8%
The total dividend = Rs. 2400 × 7%
= 2400 × (7/100)
= Rs 168
Therefore the total dividend = 168

Example 2.
Virat and Dhoni invest 36000 each in buying shares of two companies. Virat buys 15%. 40 shares at a discount of 20%, while Dhoni buys.75 shares at a premium of 20%. If both receive equal dividends at the end of the year, find the rate percent of the dividend declared by Dhoni’s company.
Solution:
In the first case,
we have
Investment made by Virat = ₹ 34000
And market value at a discount of 10% = ₹ 40 x (80/100) = ₹ 32
Thus, total face value = ₹ (36000 x 40)/32 = ₹ 45000
Rate of dividend = 15%
Thus, total dividend = ₹ (45000 x 15)/100 = ₹ 6750
Now, in second case, we have
Investment = ₹ 36000
Dividend of Dhoni = ₹ 6750
Face value of each share = ₹ 75
And market value at premium of 20% = ₹ 75 x (120/100) = ₹ 90
Face value = 36000 x (75/90) = 30000
Thus, rate of dividend = (6750 x 100)/30000 %
= 45/2 % = 22.5%

Example 3.
A person invested 20%, 30% and 25% of his savings in buying shares at par values of three different companies A, B and C which declare dividends of 10%, 12% and 15% respectively. If his total income on account of dividends is Rs. 4675, find his savings and the amount which he invested in buying shares of each company.
Solution:
Given that,
Investment in 3 companies A, B and C are 20%, 30% and 25%
Let the total investment be Rs. 100
So, the investment in company A = Rs. 20
Rate of dividend = 10%
Thus, dividend = Rs. (20 x 10)/100 = Rs. 2
Investment in company B = Rs. 30
Rate of dividend = 12%
Thus, dividend = Rs. (30 x 12)/100 = Rs. 36/10 = Rs. 3.6
And, investment in company C = Rs. 25
Rate of dividend = 25%
Thus, dividend = Rs. (25 x 15)/100 = Rs. 375/100 = Rs. 3.75
Total dividend = Rs. 2 + Rs. 3.60 + Rs 3.75 = Rs. 9.35
If dividend is Rs 9.35, then total savings = Rs. 100
Then, if dividend is Rs. 4675 the total savings
= (4675 x 100)/9.35
= (4675 x 100 x 100)/935
= Rs. 50000
Hence,
The amount of investment in shares of company A = Rs. 50000 x (20/100) = Rs. 10000
The amount of investment in shares of company B = Rs. 50000 x (30/100) = Rs. 15000
The amount of investment in shares of company A = Rs. 50000 x (25/100) = Rs. 12500

Example 4.
Divide Rs. 101410 into two parts such that if one part is invested in 8% Rs. 100 shares at 8% discount and the other in 9% Rs. 50 shares at 8% premium, the annual incomes are equal.
Solution:
Given that,
Total investment = Rs. 101410
Let investment in first part be x and in second part will be (101410 – x)
Market value of first kind of shares = Rs. 100 – Rs. 6
= Rs. 92
And rate of dividend = 8%
So, dividend = (x × 8)/92 = Rs. 2x/23
Now, market value of second kind = (101410 – x)
Rate of dividend = 9%
And market value = Rs. (100 + 8)/100 × 50
= Rs. (108/100) × 50
= Rs. 54
So, dividend = Rs. (101410 – x) × 9/(2 × 54)
= Rs. (101410 – x)/12
According to the given in the problem, we have
2x/23 = (101410 – x)/12
24x = 23 (101410 – x)
24x = 101410 × 23 – 23x
47x = 101410 × 23
x = Rs. (101410 × 23)/ 47
= Rs. 49626
Hence, investment of first part = Rs. 49626
And in second part = Rs. (101410 – 49626) = Rs. 51784

Example 5.
A man has some shares of Rs. 200 per value paying 7% dividend. He sells half of these at a discount of 11% and invests the proceeds in 8% Rs. 60 shares at a premium of Rs. 20. This transaction decreases his income from dividends by Rs. 130. Calculate:
(i) the number of shares before the transaction.
(ii) the number of shares he sold.
(iii) his initial annual income from shares.
Solution:
Let’s consider the no. of shares to be x
Value of x shares = x × 200 = 200x
And dividend = (200x × 7)/100 = Rs. 14x
Dividend on half-shares = Rs. 7x/2 = Rs. 3.5x
Now, the no. shares he sold out = x/2
Amount received at 11% discount = x/2 × 180 = Rs. 90x
In investing Rs. 90x, no. of shares he purchased = 90x/80
Thus, the amount of shares = 90x/80 × 60 = Rs. 67.5x
Income at rate of 4% = 67.5x × 4/100 = 2.7x
Difference in income = 3.5 x – 2.7x = 9.45x
According to the given conditions, we have
9.45x = 130
x = 130/9.45
x = 13.75
Hence,
(i) The number of shares he hold initially = 13.75
(ii) No. of shares he held later = 13.75/2 = 6.87
(iii) Amount of income initially = 13.75 × 7 = Rs. 19.25

### FAQs on Shares and Dividends

1. What are shares and dividends?

Shares are units of equity ownership in a corporation. For some companies, shares exist as a financial asset providing for an equal distribution of any residual profits, if any are declared, in the form of dividends. Shareholders of a stock that pays no dividends do not participate in a distribution of profits.

2. How do you calculate dividends per share?

Simply use the formula D = DPS multiplied by S, where D = your dividends and S = the number of shares you own.

3. What are shares in maths?

The sum of money required is called capital. The required capital is divided into small equal parts, and each part is called a share.