Question

Razia buys 200 shares, each of par value Rs. 10 of a company which pays annual dividend of 15% at such a price that she gets 12% on her investment. Find the market value of a share.

Answer 1

Step 1:

Given information:

Number of shares$=200$

Annual dividend$=15\%$

Par value of a share$=\mathrm{Rs}.10$

Step 2:

Calculate the market value of total shares:

Par value of 200 shares$=200\times 10=\mathrm{Rs}.2,000$

Dividend received by Razia is computed as,

$$\begin{gathered} \mathrm{Dividend}=15\%\mathrm{of}\mathrm{Par}\mathrm{value}\mathrm{of}200\mathrm{shares} \\ \Rightarrow \mathrm{Dividend}=2000\times \frac{15}{100} \\ \therefore \mathrm{Dividend}=\mathrm{Rs}.300 \end{gathered}$$

Razia gets 12% on her investment. Let market value of 200 shares be $\mathrm{Rs}.y$

$$\begin{gathered} \Rightarrow 12\%\mathrm{of}y=300 \\ \Rightarrow y\times \frac{12}{100}=300 \\ \Rightarrow y=\frac{300\times 100}{12} \\ \therefore y=\mathrm{Rs}.2,500 \end{gathered}$$

Step 3:

Calculate market value of a share:

$$\begin{gathered} \mathrm{Market}\mathrm{value}\mathrm{of}\mathrm{one}\mathrm{share}=\frac{2,500}{200} \\ \therefore \mathrm{Market}\mathrm{value}\mathrm{of}\mathrm{one}\mathrm{share}=\mathrm{Rs}.12.50 \end{gathered}$$

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