Problems on Shares and Dividends

We will discuss here some of the problems on shares and dividends.

1. Michael buys shares of face value $ 50 of a company which pays 10 % dividend. At what price did he buy each share from the market if his profit is 16 % on his investment?

Solution:

Let the market value (M.V.) of each share be x.

The dividend is calculated on nominal value.

The dividend on one share = 10% of $ 50 = $ 5.

Therefore, he earned $ 5 on an investment of x.

A profit of 16 % on x = \(\frac{16}{100}\) × x = \(\frac{4x}{25}\)

Therefore, \(\frac{4x}{25}\) = $ 5

⟹ x = $\(\frac{25 × 5}{4}\)

⟹ x = $\(\frac{125}{4}\)

⟹ x = $ 31.25

Therefore, Michael bought each share at $ 31.25 from the market.


2. Jackson buys a $ 40 shares in a company, which pays 10% dividend. Jackson buys the share at such a price that his profit is 16% on his investment. At what price did Jackson buy the share?

Solution:

Dividend (profit) given by the company on 1 share = 10% of $ 40 = $ 4.

Suppose the man buys one share for x.

Therefore, Jackson’s profit = 16% of $ x = $ \(\frac{16x}{100}\)

According to the problem, \(\frac{16x}{100}\) = 4

⟹ x = $ 25

Jackson bought the share at $ 25.

 

3. Robert bought shares of 6% $ 100 shares at $ 120. Adrian bought shares of 8% $ 20 shares at $ 30. Whose investment was better?

Solution:

6% $ 100 shares at $ 120

i.e., the annual income from 1 share of nominal value $ 100 is $ 6, investment for 1 share being $ 120.

Therefore, profit percentage = \(\frac{6}{120}\) × 100 % = 5%

Therefore, Robert’s shares give him a profit of 5%

8 % $ 20 shares at $ 30

i.e., the annual income from 1 share of nominal value $ 20 is $ \(\frac{8 × 20}{100}\) = $ \(\frac{8}{5}\), investment for 1 share being $ 30.

Profit percentage = \(\frac{$\frac{8}{5}}{$ 30}\) × 100 %

                        = \(\frac{16}{3}\) %

                        = 5\(\frac{1}{3}\)%

Therefore, Adrian’s shares give him a profit of 5\(\frac{1}{3}\)%

Therefore, Adrian’s investment was better.






10th Grade Math

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