Calculating the market risk premium – with the dividend discount model (DDM)

Key Assumptions and Data Selection

The discounted dividend model is based on the assumption that a stock's value equals the present value of all future dividends the company distributes. Additionally, a residual value is determined from the book value remaining when the company is dissolved.

To determine the risk premium for a single stock, the calculation typically uses a broad market index like the S&P 500 to derive the expected market return.

The central formula of the DDM:

where:

P₀: current share price.

D_T: expected dividend in year t.

R_i: expected return.

g: terminal growth rate of dividends.

BV_T: book value of the share.

The expected dividend in year t is calculated using the average expected earnings for year t, multiplied by the historical payout ratio. The perpetual growth rate must be estimated. Typically, it is between 0% and 2%.

Steps for calculating the market risk premium using the DDM

1. Calculate the expected dividend: The expected dividend is calculated as the product of the future profit expectation and the historical payout ratio. The detailed forecast period is usually three to five years.
2. Estimate the terminal growth rate: The long-term growth rate of dividends is assumed to be in the range of 0% to 2% based on macroeconomic estimates (e.g. GDP growth).
3. Discounting dividends: All future dividends are discounted to determine the present value of the dividends. In addition, the residual value of future dividends is calculated to estimate the value of the dividends after the detailed forecast period.
4. Calculation of the book value: The book value for t_1 can be taken from the balance sheet. Retained earnings for the detailed forecast period can be added to this initial book value. To calculate the residual value, part of the book value (〖BV〗_T*g) remains in the company to generate constant earnings. The remaining part of the book value (〖BV〗_T*(1-g)) is available as residual value and is to be discounted.
5. Calculation of the total valuation: The total value of the company is the sum of the discounted dividends for the detailed forecast period, the discounted residual value of the dividends and the discounted residual value of the book value.
6. Calculating the expected return: Then, select the discount rate so that the calculated total value of the company equals the current market capitalization at the cut-off date.
7. Calculating the MRP: Finally, calculate the risk premium by subtracting the risk-free rate from the expected return (MRP=〖E(r〗_i)-r_f).

The risk-free interest rate (r_f)

To determine the risk-free interest rate (r_f), the Svensson method is often used. This method models the yield curve and provides a precise estimate for different maturities of risk-free interest rates, which are incorporated into the MRP calculation.

Market risk premium

In order to deduce the market risk premium from the individual risk premium of a stock, the (weighted) average of the risk premiums of a market is calculated. Typically, the stocks, countries or regions of specific indices are used (e.g. Dax, S&P 500, Stock Europe 600).

Conclusion

The Dividend Discount Model (DDM) offers a robust approach to estimating the market risk premium. By projecting future dividends and discounting them back to their present value, we can uncover the implied market return. When combined with the risk-free rate, this implied return yields the market risk premium.

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