Question

Market value of shares and dividend declared by two companies is given below. Face Value is the same and it is Rs. 100 for both the shares. Investment in which company is more profitable?
A. Company A – Rs. 132, 12%
B. Company A – Rs. 144, 16%

Answer 1

We will first find the dividend income for both of the companies and then using the formula for Rate of Return for each of the companies, we will find out which has more return and is thus more profitable.

Step-By-Step answer:
Since, we are given that the Face Value of the share for both the companies is Rs. 100.
Now, the dividend is given to be 12% for Company A and 16% for Company B.
Now, we will use the following formula to calculate the dividend income from the dividend% and the face value:-
$\Rightarrow$ Dividend Income = $\dfrac{{Dividend\% }}{{100}} \times$ Face Value
Now, we will put in the face value as 100 for both the companies and the dividend % as per given to us:-
Company A: Dividend Income = $\dfrac{{12}}{{100}} \times 100$
So, dividend income for company A is Rs. 12. …………………(1)
Company B: Dividend Income = $\dfrac{{16}}{{100}} \times 100$
So, dividend income for company B is Rs. 16. ……………………(2)
Now, we will use the formula given by the following expression to calculate the rate of return for both of the companies:-
$\Rightarrow$ Rate of Return is given by multiplying the result obtained by dividing the dividend income by Sum invested by 100.
$\Rightarrow$ Rate of Return = $\left( {\dfrac{{{D_i}}}{S} \times 100} \right)\%$, where ${D_i}$ represents the dividend income and S represents the sum invested.
Now, find the same for both the companies:-
Company A:
$\Rightarrow$ Rate of Return = $\left( {\dfrac{{{D_i}}}{S} \times 100} \right)\%$
Using the equation (1) and the fact that S = Rs. 132
$\Rightarrow$ Rate of Return = $\left( {\dfrac{{12}}{{132}} \times 100} \right)\%$
Simplifying the calculations on RHS to obtain:-
$\Rightarrow$ Rate of Return = $\dfrac{{100}}{{11}}\%$
Company B:
$\Rightarrow$ Rate of Return = $\left( {\dfrac{{{D_i}}}{S} \times 100} \right)\%$
Using the equation (2) and the fact that S = Rs. 144
$\Rightarrow$ Rate of Return = $\left( {\dfrac{{16}}{{144}} \times 100} \right)\%$
Simplifying the calculations on RHS to obtain:-
$\Rightarrow$ Rate of Return = $\dfrac{{100}}{9}\%$
Therefore, Rate of return from Company B > Rate of return from Company A.

Thus, Investment in Company B is more profitable.

Note: The students must note that while comparing both the values in the end, we can clearly see that the numerators of both the rates were equal. So, the greater the denominator is, the less the rate will be. And, 9 < 11. So,
Rate of return of A < Rate of return of B.
The students must also note that this kind of concept is extremely useful in our real life as well. Because, we can easily calculate the more beneficial plan like this and invest in that only.