A man has a choice to invest in hundread rupee shares of two firms at `120rs` or at `132rs`. The first firm pays a dividend of `5%` per annum and the second firm pays a dividend of `6%` per annum. Find :
(i) which company is giving a better return.
(ii) if a man invests `26400rs` with each firm how much will be the difference between the annual returns from the two firms ?

Answer

To solve the problem step by step, we will analyze the investments in both firms and calculate the returns.

### Step 1: Determine the number of shares purchased from each firm.

**For Firm 1:**
- Share price = ₹120
- Face value of shares = ₹100
- Dividend = 5% of face value

**For Firm 2:**
- Share price = ₹132
- Face value of shares = ₹100
- Dividend = 6% of face value

### Step 2: Calculate the effective return (dividend yield) for each firm.

**Dividend Yield Formula:**
\[ \text{Dividend Yield} = \left(\frac{\text{Dividend}}{\text{Market Price}}\right) \times 100 \]

**For Firm 1:**
- Dividend = 5% of ₹100 = ₹5
- Market Price = ₹120

\[ \text{Dividend Yield for Firm 1} = \left(\frac{5}{120}\right) \times 100 = \frac{500}{120} \approx 4.17\% \]

**For Firm 2:**
- Dividend = 6% of ₹100 = ₹6
- Market Price = ₹132

\[ \text{Dividend Yield for Firm 2} = \left(\frac{6}{132}\right) \times 100 = \frac{600}{132} \approx 4.55\% \]

### Step 3: Compare the returns from both firms.

From the calculations:
- Firm 1 yields approximately 4.17%
- Firm 2 yields approximately 4.55%

**Conclusion for Part (i):** Firm 2 is giving a better return.

### Step 4: Calculate the annual returns if ₹26,400 is invested in each firm.

**For Firm 1:**
- Total investment = ₹26,400
- Number of shares purchased = \(\frac{26400}{120} = 220\)
- Annual return = Number of shares × Dividend per share = \(220 \times 5 = ₹1100\)

**For Firm 2:**
- Total investment = ₹26,400
- Number of shares purchased = \(\frac{26400}{132} = 200\)
- Annual return = Number of shares × Dividend per share = \(200 \times 6 = ₹1200\)

### Step 5: Calculate the difference between the annual returns.

\[ \text{Difference} = \text{Annual return from Firm 2} - \text{Annual return from Firm 1} = 1200 - 1100 = ₹100 \]

**Conclusion for Part (ii):** The difference between the annual returns from the two firms is ₹100.

### Summary of Solutions:
(i) Firm 2 is giving a better return.
(ii) The difference between the annual returns from the two firms is ₹100.

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