Understanding the Walter Model and Market Price

The Walter model is a dividend model that suggests the dividend policy of a firm affects its market price per share. It posits that the market price is the sum of the present value of future dividends and the present value of future earnings retained and reinvested by the firm. The model highlights the relationship between the firm's rate of return on investments (\(r\)) and the cost of equity or required rate of return (\(K_e\)).

According to the Walter model, the market price per share (\(P\)) is calculated using the following formula:

\( P = \frac{D + \frac{r}{K_e}(E-D)}{K_e} \)

Where:

• \(P\) = Market price per share
• \(D\) = Dividend per share
• \(E\) = Earnings per share
• \(r\) = Internal rate of return or profitability rate of the firm
• \(K_e\) = Cost of equity capital or required rate of return

Applying the Walter Model to Find Market Price

Let's identify the values given in the question:

• Face Value per share = Rs. 100
• Profitability Rate (\(r\)) = 16% or 0.16
• Payout Ratio = 80% or 0.80
• Cost of Capital (\(K_e\)) = 10% or 0.10

First, we need to determine the Earnings Per Share (\(E\)) and Dividend Per Share (\(D\)). Assuming the profitability rate is applied to the face value to determine earnings:

Earnings Per Share (\(E\)) = Face Value \(\times\) Profitability Rate

\( E = 100 \times 0.16 = \text{Rs. } 16 \)

Dividend Per Share (\(D\)) = Earnings Per Share \(\times\) Payout Ratio

\( D = 16 \times 0.80 = \text{Rs. } 12.80 \)

Now we have all the necessary components to apply the Walter model formula.

Walter Model Calculation Steps

Substitute the calculated and given values into the Walter model formula:

\( P = \frac{D + \frac{r}{K_e}(E-D)}{K_e} \)

\( P = \frac{12.80 + \frac{0.16}{0.10}(16 - 12.80)}{0.10} \)

Calculate the term \(\frac{r}{K_e}\):

\( \frac{0.16}{0.10} = 1.6 \)

Calculate the retained earnings per share (\(E-D\)):

\( 16 - 12.80 = 3.20 \)

Substitute these values back into the formula:

\( P = \frac{12.80 + 1.6(3.20)}{0.10} \)

Calculate the term \(1.6 \times 3.20\):

\( 1.6 \times 3.20 = 5.12 \)

Substitute this back into the numerator:

\( P = \frac{12.80 + 5.12}{0.10} \)

Sum the terms in the numerator:

\( 12.80 + 5.12 = 17.92 \)

Finally, divide the numerator by the cost of capital (\(K_e\)):

\( P = \frac{17.92}{0.10} = 179.20 \)

Thus, the market price per share as per the Walter model is Rs. 179.20.

Revision Table: Walter Model Components

Additional Information: Walter Model Insights

The Walter model operates under several simplifying assumptions, including that the firm has an infinite life, its business risk remains constant, and all financing is done through retained earnings or internal accruals (no external debt or equity). A key insight from the model is how the relationship between \(r\) and \(K_e\) influences optimal dividend policy:

• If \(r > K_e\), the firm earns more on retained earnings than shareholders require. Retaining earnings (lower payout ratio) increases the firm's value. Growth stocks often fit this category.
• If \(r < K_e\), the firm earns less than shareholders require. Distributing earnings as dividends (higher payout ratio) increases the firm's value. Decline/Mature stocks may fit this category.
• If \(r = K_e\), the firm earns exactly what shareholders require. Dividend policy does not affect the firm's value. The market price will be \(E/K_e\), regardless of the payout ratio. Normal stocks may fit this category.

In this specific problem, \(r\) (0.16) is greater than \(K_e\) (0.10), which suggests that retaining earnings would be beneficial. However, the question asks for the price given a specific payout ratio (80%), not the optimal policy. The calculation shows the market price based on the given conditions.