Following are the details regarding two companies A Ltd & B Ltd:- A Ltd:- EPS = 8/- ; Ke=10% ; r=15% B Ltd:- EPS = 8/- ; Ke=10%; r=5% Calculate the value of an equity share applying Walters’s formula when dividend payout ratio is 25%, 50% and 75%.

To calculate the value of an equity share using Walter's formula, we'll use the following formula:

\[
P = \frac{D + \left(\frac{r \times (E - D)}{Ke}\right)}{Ke}
\]

Where:
- \( P \) = Price of the share
- \( D \) = Dividend per share (\(D = \text{Dividend Payout Ratio} \times \text{EPS}\))
- \( r \) = Rate of return on retained earnings
- \( Ke \) = Cost of equity
- \( E \) = Earnings per share (EPS)

### For A Ltd:

Given:
- EPS (\( E \)) = 8
- \( Ke \) = 10% = 0.10
- \( r \) = 15% = 0.15

#### 1. When Dividend Payout Ratio is 25%:

\[
D = 0.25 \times 8 = 2
\]

\[
P = \frac{2 + \left(\frac{0.15 \times (8 - 2)}{0.10}\right)}{0.10}
\]

\[
P = \frac{2 + \left(\frac{0.15 \times 6}{0.10}\right)}{0.10} = \frac{2 + 9}{0.10} = \frac{11}{0.10} = 110
\]

#### 2. When Dividend Payout Ratio is 50%:

\[
D = 0.50 \times 8 = 4
\]

\[
P = \frac{4 + \left(\frac{0.15 \times (8 - 4)}{0.10}\right)}{0.10}
\]

\[
P = \frac{4 + \left(\frac{0.15 \times 4}{0.10}\right)}{0.10} = \frac{4 + 6}{0.10} = \frac{10}{0.10} = 100
\]

#### 3. When Dividend Payout Ratio is 75%:

\[
D = 0.75 \times 8 = 6
\]

\[
P = \frac{6 + \left(\frac{0.15 \times (8 - 6)}{0.10}\right)}{0.10}
\]

\[
P = \frac{6 + \left(\frac{0.15 \times 2}{0.10}\right)}{0.10} = \frac{6 + 3}{0.10} = \frac{9}{0.10} = 90
\]

### For B Ltd:

Given:
- EPS (\( E \)) = 8
- \( Ke \) = 10% = 0.10
- \( r \) = 5% = 0.05

#### 1. When Dividend Payout Ratio is 25%:

\[
D = 0.25 \times 8 = 2
\]

\[
P = \frac{2 + \left(\frac{0.05 \times (8 - 2)}{0.10}\right)}{0.10}
\]

\[
P = \frac{2 + \left(\frac{0.05 \times 6}{0.10}\right)}{0.10} = \frac{2 + 3}{0.10} = \frac{5}{0.10} = 50
\]

#### 2. When Dividend Payout Ratio is 50%:

\[
D = 0.50 \times 8 = 4
\]

\[
P = \frac{4 + \left(\frac{0.05 \times (8 - 4)}{0.10}\right)}{0.10}
\]

\[
P = \frac{4 + \left(\frac{0.05 \times 4}{0.10}\right)}{0.10} = \frac{4 + 2}{0.10} = \frac{6}{0.10} = 60
\]

#### 3. When Dividend Payout Ratio is 75%:

\[
D = 0.75 \times 8 = 6
\]

\[
P = \frac{6 + \left(\frac{0.05 \times (8 - 6)}{0.10}\right)}{0.10}
\]

\[
P = \frac{6 + \left(\frac{0.05 \times 2}{0.10}\right)}{0.10} = \frac{6 + 1}{0.10} = \frac{7}{0.10} = 70
\]

### Summary of Results:

- **A Ltd:**
  - 25% Dividend Payout Ratio: Share Price = 110
  - 50% Dividend Payout Ratio: Share Price = 100
  - 75% Dividend Payout Ratio: Share Price = 90

- **B Ltd:**
  - 25% Dividend Payout Ratio: Share Price = 50
  - 50% Dividend Payout Ratio: Share Price = 60
  - 75% Dividend Payout Ratio: Share Price = 70

Would you like more details or have any questions?

### Related Questions:
1. How does Walter's model differ from the Gordon Growth Model?
2. What are the assumptions of Walter's model?
3. How would changes in the cost of equity (Ke) affect the share price?
4. Why does Company A's share price decrease as the dividend payout ratio increases?
5. How would a change in the rate of return on retained earnings (r) impact the share price?

### Tip:
Walter's model assumes that the firm either reinvests retained earnings at a constant rate of return or pays them out as dividends, making it useful for analyzing the relationship between dividend policy and market value under these assumptions.

Learn how to calculate the value of an equity share using Walter's formula based on different dividend payout ratios. This problem involves financial concepts like equity valuation, dividend payout ratio, and cost of equity. Detailed solutions for Companies A Ltd and B Ltd provided.

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