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.
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