Question

If the face value for both the shares are the same, then which investment out of the following is more profitable?
Company A: dividend = 16%, MV = Rs. 80.
Company B: dividend = 20%, MV = Rs. 120.
(a) Investment in company A
(b) Investment in company B
(c) Investment in both the company
(d) No profit in any company

Answer 1

Hint: Assume the face value for both the shares as ‘x’. Find the ‘dividend per share’ by using the formula: - Dividend per share = Face value \[\times \] dividend rate, for both the companies. Now, use the formula: - Rate of return = (Dividend per share) / MV, where ‘MV’ is the given market value, to calculate ‘Rate of return’ for both the companies. The company having a higher rate of return will be more profitable.

Complete step by step answer:
Here, we have been provided with the dividend rate and market value (MV) for company A and B. It is given that they have the same face value. We have to find a more profitable company. To do so, we have to find and compare their ‘rate of return’. Let us assume face value for both as ‘x’.
(i) For company A: -
Dividend rate = 16%
Market value (MV) = Rs. 80
Face value = x
Therefore, applying the formula: - Dividend per share = Face value \[\times \] dividend rate, we get,
Dividend per share = \[x\times 16\%=x\times \dfrac{16}{100}=\dfrac{4x}{25}\]
Now, applying the formula: - Rate of return = (Dividend per share) / MV, we get,
Rate of return = \[\dfrac{4x}{25\times 80}=\dfrac{x}{500}\]
(ii) For company B: -
Dividend rate = 20%
Market value (MV) = Rs.120
Face value = x
Therefore, applying the formula: - Dividend per share = Face value \[\times \] dividend rate, we get,
Dividend per share = \[x\times 20\%=x\times \dfrac{20}{100}=\dfrac{x}{5}\]
Now, applying the formula: - Rate of return = (Dividend per share) / MV, we get,
Rate of return = \[\dfrac{x}{5\times 120}=\dfrac{x}{600}\]
Now, let us compare the rate of return for both the companies: -
\[\because 600>500\]
Taking reciprocal, we get,
\[\Rightarrow \dfrac{1}{600}<\dfrac{1}{500}\]
Multiplying both sides with ‘x’, we get,
\[\Rightarrow \dfrac{x}{600}<\dfrac{x}{500}\]
Therefore, the conclusion is “rate of return for company A is greater than rate of return for company B”. So, company A is more profitable.

So, the correct answer is “Option A”.

Note: One may note that, when we are comparing two numbers and we take reciprocal both sides, the sign of inequality changes its direction. To solve the above question we must remember the formulas of “Dividend per share” and “rate of return”.