Question

If the face value of both the shares is the same, then which investment out of the following is more profitable?
Company A: dividend \[16\% \], \[{\rm{MV}} = {\rm{Rs}}80\],
Company B: dividend \[20\% \], \[{\rm{MV}} = {\rm{Rs120}}\]

Answer 1

Hint:
Here, we will assume a value of the face value to find the dividend per share in terms of that assumed value. Then we will find the rate of return of the company by using the formula of rate of return. We will perform this process for both the companies and find out whose rate of return is higher.

Formula used:
We will use the following formulas:
1) Dividend per share \[ = \] Face value \[ \times \] Rate
2) Rate of return \[ = \] Dividend per share \[ \div \] MV

Complete step by step solution:
Let us take \[x\] to be the face value of both the companies.
We will find out the dividend per share in terms of \[x\].
For company A:
Substituting the dividend rate as \[16\% \] and \[{\rm{MV}} = {\rm{Rs}}80\] in the formula Dividend per share \[ = \] Face value \[ \times \] Rate, we get
Dividend per share \[ = x \times \dfrac{{16}}{{100}} = \dfrac{{4x}}{{25}}\]
Now we will find the rate of return for company A.
Substituting the value of dividend per share and MV in the Rate of return \[ = \] Dividend per share \[ \div \] MV, we get
Rate of return \[ = \dfrac{{4x}}{{25}} \times \dfrac{1}{{80}} = \dfrac{1}{{500x}}\]…………… \[\left( 1 \right)\]
For company B:
Substituting the dividend rate as \[20\% \] and \[{\rm{MV}} = {\rm{Rs120}}\] in the formula Dividend per share \[ = \] Face value \[ \times \] Rate, we get
Dividend per share \[ = x \times \dfrac{{20}}{{100}} = \dfrac{x}{5}\]
Now we will find the rate of return for company B.
Substituting the value of dividend per share and MV in the Rate of return \[ = \] Dividend per share \[ \div \] MV, we get
Rate of return \[ = \dfrac{x}{5} \times \dfrac{1}{{120}} = \dfrac{1}{{600x}}\]…………… \[\left( 2 \right)\]
Now we will compare the equation \[\left( 1 \right)\] and equation \[\left( 2 \right)\] .
 \[\therefore \dfrac{1}{500x}>\dfrac{1}{600x}\]
We can clearly see that the equation \[\left( 1 \right)\] is greater than equation \[\left( 2 \right)\]. This means that the rate of return of company A is greater than the rate of return of company B.

We know that higher the rate of return means higher the profit gain. Hence, company A is more profitable than company B.

Note:
We have to note that while calculating the dividend per share, we have to convert the rate of dividend into the normal form i.e. removing the percent from the dividend rate.
Here, to know which company is more profitable we have to take the rate of return into consideration because this is the factor which gives us the knowledge of profits. High value of the rate of return means that the profit gained is higher. We should know the basic formulas of the dividend per share and rate of return. MV in the question is termed as market value of the share which shows us the price of the share in the current market.