Many investment texts focus on the dividend discount model in their valuation chapter. At first sight, the model is very appealing. Dividends are the cash flows that shareholders get from the firm, so value should be based on expected dividends. In valuing bonds we forecast the cash flows from the bond, so, in valuing stocks, why not forecast the cash flows from stocks? The dividend discount model is stated as follows:

Value of equity = Present value of expected dividends (4.1)

(The ellipsis in the formula indicates that dividends must be forecast indefinitely into the future, for years 5, 6, and so on.) The model instructs us to forecast dividends and to convert the forecasts to a value by discounting them at one plus the equity cost of capital, ρE. One might forecast varying discount rates for future periods but for the moment we will treat the discount rate as a constant. The dividend discount model is a straight application of the bond valuation model to valuing equity. That model works for a terminal investment. Will it work for a going-concern investment under the practical criteria?

Well, going concerns are expected to pay out dividends for many (infinite?) periods in the future. Clearly, forecasting for infinite periods is a problem. How would we proceed by forecasting (realistically) for a finite period, say 10 years? For a finite horizon forecast of T years, we might be able to predict the dividends to Year T but we are left with a problem: The payoff for T years includes the terminal price, P_{T}, as well as the dividends, so we also need to forecast P_{T}, the price at which we might sell at the forecast horizon. Forecasting just the dividends would be like forecasting the coupon payments on a bond and forgetting the bond repayment. This last component, the terminal payoff, is also called the **terminal value**. So we have the problem of calculating a terminal value such that

Value of equity= Present value of expected dividends to time T + Present value of expected terminal value at T (4.2)

You can see that this model is technically correct, for it is simply the present value of all the payoffs from the investment that are laid out in Figure 3.3. The problem is that one of those payoffs is the price that the share will be worth T years ahead, PT. This is awkward, to say the least: The value of the share at time zero is determined by its expected value in the future, but it is the value we are trying to assess. To break the circularity, we must investigate fundamentals that determine value.

A method often suggested is to assume that the dividend at the forecast horizon will be the same forever afterward. Thus

(4.3)

The terminal value here (in the bracketed term) is the value of a perpetuity, calculated by capitalizing the forecasted dividend at T + 1 at the cost of capital. This terminal value is then discounted to present value.

This perpetuity assumption is a bold one. We are guessing. How do we know the firm will maintain a constant payout? If there is less than full payout of earnings, one would expect dividends to grow as the retained funds earn more in the firm. This idea can be accommodated in a terminal value calculation that incorporates growth:

(4.4)

where g is 1 plus a forecasted growth rate.1 The terminal value here is the value of a perpetuity with growth. If the constant growth starts in the first period, the entire series collapses to V_{0}^{E} = d_{1}/(ρE – g), which is sometimes referred to as the constant growth model. See Box 4.1.

What would we do, however, for a firm that might be expected to have zero payout for a very long time in the future? For a firm that has exceptionally high payout that can’t be maintained? What if payout comes in stock repurchases (that typically don’t affect shareholder value) rather than dividends?

The truth of the matter is that dividend payout over the foreseeable future doesn’t mean much. Some firms pay a lot of dividends, others none.A firm that is very profitable and worth a lot can have zero payout and a firmthat is marginally profitable can have high payout, at least in the short run. Dividends usually are not necessarily tied to value creation. Indeed, firms can borrow to pay dividends, and this has nothing to do with their investing and operating activities where value is created. Dividends are distributions of value, not the creation of value.

Dividends are not relevant to value. To be practical we have to forecast over finite horizons. To do so, the dividend discount model (equation 4.2) requires us to forecast dividends up to a forecast horizon plus the terminal price. But payoffs (dividends plus the terminal price) are insensitive to the dividend component: If you expect a stock to pay you more dividends, it will pay off a lower terminal price; if the firm pays out cash, the price will drop by this amount to reflect that value has left the firm. Any change in dividends will be exactly offset by a price change such that, in present value terms, the net effect is zero. In other words, paying dividends is a zero-NPV activity. That’s dividend irrelevance! Dividends do not create value. If dividends are irrelevant, we are left with the task of forecasting the terminal price, but it is price that we are after. Box 4.2 summarizes the advantages and disadvantages of the dividend discount model.

This leaves us with the so-called **dividend conundrum**: Equity value is based on future dividends, but forecasting dividends over a finite horizon does not give an indication of value. The dividend discount model fails the first criterion for a practical analysis. We have to forecast something else that is tied to the value creation. The model fails the second criterion—validation—also. Dividends can be observed after the fact, so a dividend forecast can be validated for its accuracy. But a change in a dividend from a forecast may not be related to value at all, just a change in payout policy, so ex-post dividends cannot validate a valuation.

The failure of the dividend discount model is remedied by looking inside the firm to the features that do create value—the investing and operating activities. Discounted cash flow analysis does just that.

### Dividend Discount Analysis 4.2

**ADVANTAGES**

Easy concept: Dividends are what shareholders get, so forecast them.

Predictability: Dividends are usually fairly stable in the short run so dividends are easy to forecast (in the short run).

**DISADVANTAGES**

Relevance: Dividend payout is not related to value, at least in the short run; dividend forecasts ignore the capital gain component of payoffs.

Forecast horizons: Typically requires forecasts for long periods.

**WHEN IT WORKS BEST**

When payout is permanently tied to the value generation in the firm. For example, when a firm has a fixed payout ratio (dividends/earnings).