Discounted Cash Flow Formula
From the constant-growth dividend discount model, we can infer the market capitalization rate, k, or the rate of return demanded by investors. Note that:
Expected Return = Dividend Yield + Capital Gains Yield
If a stock is held for 1 year, and is bought and sold for its intrinsic value, then the following discounted cash flow formula calculates the market capitalization rate:
| Discounted Cash Flow Formula |
|---|
|
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| Capitalization Rate (k) = | Dividend
Yield | + | Capital Gains
Yield | k = Capitalization Rate
D1 = Next Year's Dividend
P0 = This Year's Stock Price
P1 = Next Year's Stock Price
g = Dividend Growth Rate |
| = | D1
───
P0 | + | P1 - P0
──────
P0 |
| = | D1
───
P0 | + | P0(1+g) - P0
──────────
P0 |
| = | D1
────
P0 | + | g |
Often, this is how rates are determined for public utilities by the agencies responsible for setting public rates. Public utilities are generally allowed to charge rates that cover their costs plus a fair market return, with the fair market return being the market capitalization rate.
Implied Growth Rate and Return on Equity
The constant-growth rate DDM formula can also be algebraically transformed, by setting the intrinsic value equal to the current stock price, to calculate the implied growth rate, then using the result to calculate the implied return on equity.
| Implied Growth Rate Formula |
|---|
|
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| Implied Growth Rate (g) = | k - | D1
──────
P | D1 = Next Year's Dividend
k = Capitalization Rate
P = Current Stock Price |
| Implied Return on Equity Formula |
|---|
|
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| Implied Return on Equity = | Implied Growth Rate
─────────────────
Earnings Retention Rate |
Example—Calculating the Implied Growth Rate and Return on Equity
If:
- Current Stock Price = $65
- Next Year's Dividend = $4
- Capitalization Rate = 12%
- Earnings Retention Rate = 50%
Then
- Implied Growth Rate = 12 - 4/65 ≈ 6.15%
- Implied Return on Equity = 6.15/50 = 12.3%
Variable-Growth Rate DDM
Variable-growth rate models (aka multi-stage growth models) can take many forms, even assuming the growth rate is different for every year. However, the most common form is one that assumes 3 different rates of growth: an initial high rate of growth, a transition to slower growth, and lastly, a sustainable, steady rate of growth. Basically, the constant-growth rate model is extended, with each phase of growth calculated using the constant-growth method, but using 3 different growth rates of the 3 phrases. The present values of each stage are added together to derive the intrinsic value of the stock.
Sometimes, even the capitalization rate, or the required rate of return, may be varied if changes in the rate are projected.
Conclusion
The dividend discount model is a useful heuristic model that relates the present stock price to the present value of its future cash flows in the same way that a bond is priced in terms of its future cash flows. However, bond pricing is a more exact science, especially if the bond is held to maturity, since its cash flows and the interest rate of those cash flows are known with certainty, unless the bond issuer defaults. The dividend discount model, however, depends on projections about company growth rate and future capitalization rates of the remaining cash flows. For instance, in a bear market, the capitalization rate will be higher than in a bull market—investors will demand a higher required rate of return to compensate them for a perceived greater amount of risk. Getting either the capitalization rate or the growth rate wrong will yield an incorrect intrinsic value for the stock, especially since even small changes in either of these factors will greatly affect the calculated intrinsic value. Furthermore, the greater the length of time considered, the more likely both factors will be wrong. Hence, the true intrinsic value of a stock is unknowable, and, thus, it cannot be determined whether a stock is undervalued or overvalued based on a calculated intrinsic value, since different investors will have a different opinion about the company’s future.
So while it is obvious that stocks are priced according to the market’s expectations of future cash flows from owning the stock, both as to dividends and future stock price, there is no way to ascertain exactly what that true intrinsic value is.
