Question

Hundred rupee shares of a company are available in the market at a premium of Rs. 20. Find the rate of dividend given by the company, when a man’s return on his investment is 15 percent.
(a) $$18\mathrm{\%}$$
(b) $$20\mathrm{\%}$$
(c) $$25\mathrm{\%}$$
(d) None of these

Answer 1

Hint: Here, we need to find the rate of dividend given by the company. First, we will calculate the nominal and market value of each share. Then, we will calculate the return on each share earned by the man. Finally, we will use the return on each share and the nominal value to find the rate of dividend given by the company.

Complete step-by-step answer:
The shares of the company are Rs. 100 shares.
This means that the face value of the shares is Rs. 100.
Thus, we get
Nominal value of each share of the company $$=$$ Rs. 100
Therefore, we get
Market value of each share of the company $$=$$ Rs. $$100+20$$
Adding the terms, we get
$$\Rightarrow$$ Market value of each share of the company $$=$$ Rs. 120
Now, it is given that the return on investment of the man is $$15\mathrm{\%}$$.
The man pays the market price of each share and gets a return of $$15\mathrm{\%}$$ on the market price of each share.
Therefore, we get
Return on each share $$=15\mathrm{\%}\text{ of }120$$
Simplifying the expression, we get
$$\Rightarrow$$ Return on each share $$={\displaystyle \frac{15}{100}}\times 120$$
Multiplying the terms in each expression, we get
$$\Rightarrow$$ Return on each share $$=18$$
Therefore, the return on each share is Rs. 18.
The return on each share is the same as the dividend earned on each share.
Therefore, we get
Dividend earned on each share $$=$$ Rs. 18
Now, we will calculate the rate of dividend given by the company.
The dividend given on each share is Rs. 18.
The nominal value of each share is Rs. 100.
Therefore, we get
Rate of dividend given by the company $$={\displaystyle \frac{\text{Rs}\text{. }18}{\text{Rs}\text{. }100}}\times 100$$
Multiplying the terms, we get
$$\Rightarrow$$Rate of dividend given by the company $$=18\mathrm{\%}$$
Therefore, we get the rate of dividend given by the company as $$18\mathrm{\%}$$.
Thus, the correct option is option (a).

Note: A common mistake we can make is to use the nominal value in the formula for return on each share, and write the return/dividend on each share as 15 percent. This is incorrect because it does not take into account the premium paid on each share.
We need to keep in mind that the rate of dividend given by the company is the percentage of face value of shares, given out as dividends. The market value of a share is the sum of the nominal value and the premium.