Question

A man has a choice to invest in hundred-rupee shares of two firms at $Rs120$ or at $Rs132$. The first firm pays a dividend of $5\% $ per annum and the second firm pays a dividend of $6\% $ per annum.
i) Find which company is giving the better return?
ii) If a man invests $Rs26,400$ with each firm, how much will be the difference between the annual returns from the two firms?

Answer 1

Hint:In this problem firstly we should find the number of shares later on we should find the dividend per one share and calculate the dividend for the entire number of shares the investor has bought. Compare this value between two companies to get the solution for this problem.

Complete step-by-step answer:
Let us discuss the solution in two different parts.
In the first part we will discuss the first company and in the second part we will discuss the second company. Later on, we can compare them to get the solution.
Before that we should know one thing that, the one with a share started is known as the face value of that share. The present value of the share is known as the market value of the share.
In the first company,
Market value of one share is $Rs120$.
Money invested is $Rs26,400$.
When we divide the total invested money with the single share market value, we will get the total number of shares.
So, the number of shares $ = \dfrac{{26400}}{{120}}= 220$
According to the given data,
Dividend on one-hundred-rupee share is $5\% $.
So, in terms of amount it will be $Rs5$.
The above value of dividend is only for the one share. To get for the shares that the investor has bought, we need to multiply this value with the number of shares.
Total dividend for $220$ share is $220 \times 5 = Rs1100$
So, from here we can conclude that the annual return from the first company is $Rs1100$
In the second company,
Market value of one share is $Rs132$.
Money invested is $Rs26,400$.
When we divide the total invested money with the single share market value, we will get the total number of shares.
So, the number of shares $ = \dfrac{{26400}}{{132}}= 200$
According to the given data,
Dividend on one-hundred-rupee share is $6\% $.
So, in terms of amount it will be $Rs6$.
The above value of dividend is only for the one share. To get for the shares that the investor has bought, we need to multiply this value with the number of shares.
Total dividend for $200$ share is $200 \times 6 = Rs1200$
So, from here we can conclude that the annual return from the first company is $Rs1200$

From the above two results, we can conclude that,
Second company is paying the highest return.
Difference in annual return is $1200 - 1100 = Rs100$

Note:In order to solve this kind of stock market related problem, we need to have some basic knowledge regarding its terms like shares, dividend, etc. Remember one thing that the percentage of dividend should be always calculated on the share initial value. There will be changes in the share values as time passes on. The one with a share started is known as the face value of that share. The present value of the share is known as the market value of the share.