In the strictest sense, the only cash flow you receive from a firm when you buy publicly traded stock is the dividend. The simplest model for valuing equity is the dividend discount model — the value of a stock is the present value of expected dividends on it. While many analysts have turned away from the dividend discount model and viewed it as outmoded, much of the intuition that drives discounted cash flow valuation is embedded in the model. In fact, there are specific companies where the dividend discount model remains a useful tool for estimating value.
The General Model
When an investor buys stock, she generally expects to get two types of cash-flows – dividends during the period she holds the stock and an expected price at the end of the holding period. Since this expected price is itself determined by future dividends, the value of a stock is the present value of dividends through infinity.
The rationale for the model lies in the present value rule – the value of any asset is the present value of expected future cash flows discounted at a rate appropriate to the riskiness of the cash flows. There are two basic inputs to the model – expected dividends and the cost on equity. To obtain the expected dividends, we make assumptions about expected future growth rates in earnings and pay-out ratios. The required rate of return on a stock is determined by its riskiness, measured differently in different models – the market beta in the CAPM and the factor betas in the arbitrage and multi-factor models. The model is flexible enough to allow for time-varying discount rates, where the time variation is caused by expected changes in interest rates or risk across time.
Gordon Growth Model
The Gordon growth model can be used to value a firm that is in ‘steady state’ with dividends growing at a rate that can be sustained forever. The Gordon growth model relates the value of a stock to its expected dividends in the next time period, the cost of equity and the expected growth rate in dividends.
Where,
DPS1 = Expected Dividends one year from now (next period)
Ke= Required rate of return for equity investors
g = Growth rate in dividends forever
What is a stable growth rate?
While the Gordon growth model is a simple and powerful approach to valuing equity, its use is limited to firms that are growing at a stable rate. There are two insights worth keeping in mind when estimating a ‘stable’ growth rate. First, since the growth rate in the firm’s dividends is expected to last forever, the firm’s other measures of performance (including earnings) can also be expected to grow at the same rate. To see why, consider the consequences in the long term of a firm whose earnings grow 6% a year forever, while its dividends grow at 8%. Over time, the dividends will exceed earnings. On the other hand, if a firm’s earnings grow at a faster rate than dividends in the long term, the pay-out ratio, in the long term, will converge towards zero, which is also not a steady state. Thus, though the model’s requirement is for the expected growth rate in dividends, analysts should be able to substitute in the expected growth rate in earnings and get precisely the same result, if the firm is truly in steady state The second issue relates to what growth rate is reasonable as a ‘stable’ growth rate. This growth rate has to be less than or equal to the growth rate of the economy in which the firm operates. This does not, however, imply that analysts will always agree about what this rate should be even if they agree that a firm is a stable growth firm for three reasons.
1. Given the uncertainty associated with estimates of expected inflation and real growth in the economy, there can be differences in the benchmark growth rate used by different analysts, i.e., analysts with higher expectations of inflation in the long term may project a nominal growth rate in the economy that is higher.
2. The growth rate of a company may not be greater than that of the economy but it can be less. Firms can becomes smaller over time relative to the economy.
3. There is another instance in which an analyst may stray from a strict limit imposed on the ‘stable growth rate’. If a firm is likely to maintain a few years of ‘above-stable’ growth rates, an approximate value for the firm can be obtained by adding a premium to the stable growth rate, to reflect the above-average growth in the initial years. Even in this case, the flexibility that the analyst has is limited. The sensitivity of the model to growth implies that the stable growth rate cannot be more than 1% or 2% above the growth rate in the economy. If the deviation becomes larger, the analyst will be better served using a two-stage or a three-stage model to capture the ‘super-normal’ or ‘above-average’ growth and restricting the Gordon growth model to when the firm becomes truly stable.
Limitations of the model
The Gordon growth model is a simple and convenient way of valuing stocks but it is extremely sensitive to the inputs for the growth rate. Used incorrectly, it can yield misleading or even absurd results, since, as the growth rate converges on the discount rate, the value goes to infinity. Consider a stock, with an expected dividend per share next period of Rs. 2.50, a cost of equity of 15%, and an expected growth rate of 5% forever. The value of this stock should be :
As the growth rate approaches the cost of equity, the value per share approaches infinity. If the growth rate exceeds the cost of equity, the value per share becomes negative. This issue is tied to the question of what comprises a stable growth rate. For instance, an analyst who uses a 14% growth rate and obtains a Rs. 250 value would have been violating a basic rule on what comprises stable growth.
In summary, the Gordon growth model is best suited for firms growing at a rate comparable to or lower than the nominal growth in the economy and which have well established dividend pay-out policies that they intend to continue into the future. The dividend pay-out of the firm has to be consistent with the assumption of stability, since stable firms generally pay substantial dividends. In particular, this model will under estimate the value of the stock in firms that consistently pay out less than they can afford and accumulate cash in the process.
Two-stage Dividend Discount Model
The two-stage growth model allows for two stages of growth – an initial phase where the growth rate is not a stable growth rate and a subsequent steady state where the growth rate is stable and is expected to remain so for the long term. While, in most cases, the growth rate during the initial phase is higher than the stable growth rate, the model can be adapted to value companies that are expected to post low or even negative growth rates for a few years and then revert back to stable growth. The model is based upon two stages of growth, an extraordinary growth phase that lasts n years and a stable growth phase that lasts forever afterwards.
The same constraint that applies to the growth rate for the Gordon Growth Rate model, i.e., that the growth rate in the firm is comparable to the nominal growth rate in the economy, applies for the terminal growth rate (gn) in this model as well. In addition, the pay-out ratio has to be consistent with the estimated growth rate. If the growth rate is expected to drop significantly after the initial growth phase, the pay-out ratio should be higher in the stable phase than in the growth phase. A stable firm can pay out more of its earnings in dividends than a growing firm.
Expected Growth = Retention Ratio * Return on Equity
Stable Payout Ratio = Stable Growth Rate / Stable Period ROE
Thus, a firm with a 5% growth rate and a return on equity of 15% will have a stable period pay-out ratio of 33.33%.
Limitations of the model
There are three problems with the two-stage dividend discount model – the first two would apply to any two-stage model and the third is specific to the dividend discount model.
1. The first practical problem is in defining the length of the extraordinary growth period. Since the growth rate is expected to decline to a stable level after this period, the value of an investment will increase as this period is made longer. It is difficult in practice to convert these qualitative considerations into a specific time period.
2. The second problem with this model lies in the assumption that the growth rate is high during the initial period and is transformed overnight to a lower stable rate at the end of the period. While these sudden transformations in growth can happen, it is much more realistic to assume that the shift from high growth to stable growth happens gradually over time.
3. The focus on dividends in this model can lead to skewed estimates of value for firms that are not paying out what they can afford in dividends. In particular, we will under estimate the value of firms that accumulate cash and pay out too little in dividends.
Since the two-stage dividend discount model is based upon two clearly delineated growth stages, high growth and stable growth, it is best suited for firms which are in high growth and expect to maintain that growth rate for a specific time period, after which the sources of the high growth are expected to disappear. One scenario, for instance, where this may apply is when a company has patent rights to a very profitable product for the next few years and is expected to enjoy super-normal growth during this period. Once the patent expires, it is expected to settle back into stable growth. Another scenario where it may be reasonable to make this assumption about growth is when a firm is in an industry which is enjoying supernormal growth because there are significant barriers to entry (either legal or as a consequence of infra-structure requirements), which can be expected to keep new entrants out for several years. The assumption that the growth rate drops precipitously from its level in the initial phase to a stable rate also implies that this model is more appropriate for firms with modest growth rates in the initial phase. For instance, it is more reasonable to assume that a firm growing at 12% in the high growth period will see its growth rate drops to 6% afterwards than it is for a firm growing at 40% in the high growth period.
Finally, the model works best for firms that maintain a policy of paying out most of residual cash flows – i.e, cash flows left over after debt payments and reinvestment needs have been met – as dividends.
The two-stage model can also be extended to a multi-stage model that takes into consideration the gradual transition in the growth rates, etc. However, in reality, forecasting the growth rates in distant future is a task involving so many uncertainties that it’s not worthwhile doing so in realistic valuation exercise.