Calculating the Cost of Equity for a Firm

This question asks us to determine the cost of equity for a firm based on its current earnings, share market value, number of shares outstanding, stable earnings expectation, and 100% payout ratio.

Understanding the Given Information

Here's what we know about the firm:

• Total Earnings: Rs. 50,000
• Shares Outstanding: 5,000
• Current Market Value per Share (\( P_0 \)): Rs. 175
• Earnings are expected to remain stable.
• Payout Ratio: 100%

The payout ratio is the proportion of earnings paid out as dividends. A 100% payout ratio means the firm pays out all its earnings as dividends.

Step 1: Calculate Total Dividends Paid

Since the payout ratio is 100%, the total dividends paid are equal to the total earnings.

\(\text{Total Dividends} = \text{Total Earnings} \times \text{Payout Ratio}\)

\(\text{Total Dividends} = \text{Rs. } 50,000 \times 100\%\)

\(\text{Total Dividends} = \text{Rs. } 50,000\)

Step 2: Calculate Dividend per Share

To find the dividend per share (D), we divide the total dividends by the number of shares outstanding.

\(D = \frac{\text{Total Dividends}}{\text{Shares Outstanding}}\)

\(D = \frac{\text{Rs. } 50,000}{5,000}\)

\(D = \text{Rs. } 10 \text{ per share}\)

Step 3: Determine the Cost of Equity (Ke)

The cost of equity (\( K_e \)) can be calculated using the dividend valuation model. Since the earnings are stable and the payout ratio is 100%, the dividend per share is expected to remain constant. This scenario is a special case of the Gordon Growth Model where the growth rate (g) is zero.

The formula for the cost of equity with a zero growth rate is:

\( K_e = \frac{D}{P_0} \)

Where:

• \( K_e \) is the Cost of Equity
• \( D \) is the expected Dividend per Share
• \( P_0 \) is the Current Market Value per Share

Step 4: Substitute Values and Calculate Ke

We have \( D = \text{Rs. } 10 \) and \( P_0 = \text{Rs. } 175 \). Now, we plug these values into the formula:

\( K_e = \frac{10}{175} \)

To express this as a percentage, we multiply by 100%:

\( K_e = \left(\frac{10}{175}\right) \times 100\% \)

\( K_e \approx 0.05714 \times 100\% \)

\( K_e \approx 5.714\%\)

Rounding to two decimal places, the cost of equity is 5.71%.

Summary of Calculation Steps

Based on the calculations, the cost of equity for the firm is approximately 5.71%.

Revision Table: Key Finance Concepts

Additional Information: Cost of Equity Methods

Besides the dividend discount model (like the Gordon Growth Model used here), other common methods to estimate the cost of equity include:

• Capital Asset Pricing Model (CAPM): This model relates the required return on equity to the risk of the stock, the risk-free rate, and the market risk premium. The formula is \( K_e = R_f + \beta \times (R_m - R_f) \), where \( R_f \) is the risk-free rate, \( \beta \) (beta) is the stock's sensitivity to market risk, and \( (R_m - R_f) \) is the market risk premium.
• Bond Yield Plus Risk Premium Method: This method estimates the cost of equity by adding a risk premium to the company's yield on its long-term debt. It assumes that equity is riskier than debt.

The choice of method depends on the available data and the assumptions that can be reasonably made about the firm and the market. In this specific question, the stable earnings and 100% payout ratio strongly suggest the applicability of the zero-growth dividend discount model.