Discounted Dividend Valuation

Evaluate whether a stock is overvalued, fairly valued, or undervalued by the market based on a DDM estimate of value:

If a stock is trading at a price (market price) higher than the price implied by a dividend discount model (model price), the stock is considered to be overvalued. Similarly, if the market price is lower than the model price, the stock is considered to be undervalued, and if the model price is equal to the market price, the stock is considered to be fairly valued.

Valuation Using the H-Model:

The H-model approximates the value of a firm assuming that an initially high rate of growth declines linearly over a specified period. The formula for this approximation is:

Free cash flow to equity (FCFE) is:

The cash available to stockholders after funding capital requirements and expenses associated with debt financing.

Free cash flow to the fir m (FCFF) is defined as:

The cash flow generated by the firm's operations that is in excess of the capital investment required to sustain the firm's current productive capacity.

In stock valuation models, there are three predominant definitions of future cash flows:

1. Dividends, 2. Free cash flow, and 3. Residual income

Valuation Models Using Spreadsheets:

A spreadsheet allows the analyst to easily calculate values based on models with many stages, growth rates, and required rates of return.

A firm that has additional opportunities to earn returns in excess of the required rate of return would benefit from retaining earnings and investing in those growth opportunities rather than paying out dividends. The fundamental value then represents not only the present value of the future dividends (on a non-growth basis) but also the present value of the growth opportunities (PVGO):

A substantial portion of the value of growth companies is in their PVGO. In contrast, companies in slow-growth industries (e.g., utilities) have low PVGO, and most of their value comes from their assets in place.

Valuation Using the Three-Stage DDM:

A three-stage model can be used to estimate the value of a firm that is projected to have three stages of growth with a fixed rate of growth for each stage. The approach is the same as the two-stage model, with the projected dividends and the terminal value of the shares discounted to their present value at the required rate of return.

The Gordon growth model (GGM):

Assumes that dividends increase at a constant rate indefinitely.

Dividend discount models (DDMs):

Define cash flow as the dividends to be received by the shareholders.

A firm that has no additional opportunities to earn returns in excess of the required rate of return should:

Distribute all of its earnings to shareholders in the form of dividends. Under this assumption the growth rate would be zero, and the current value of the firm would be equal to the current dividend divided by the required rate of return. This is exactly the same approach used to determine the value of fixed-rate perpetual preferred shares.

There are cases in which the application of a free cash flow model may be very difficult:

Firms that have significant capital requirements may have negative free cash flow for many years into the future. This can be caused by a technological revolution in an industry that requires greater investment to remain competitive or by rapid expansion into untapped markets. This negative free cash flow complicates the cash flow forecast and makes the estimates less reliable.

The DDM models are just as useful in determining the required rate of return, given the current value and dividends of a stock. No matter which model you're using (whether it's a two-stage DDM, an H-model, a three-stage DDM, or a spreadsheet model), in theory this is easy:

Given all the other inputs to the model, we can back into the expected return that makes the present value of the forecasted dividend stream equal to the current market price.

Rate of return using the Gordon growth model:

If the dividend growth rate is constant forever, we can use the Gordon growth model to calculate the implied expected return given the expected dividend, the current market price, and the expected growth rate.

The General Dividend Discount Model

If we extend the holding period indefinitely, the value simply becomes the present value of an infinite stream of dividends, represented by John Burr Williams's (1938) original DDM formula.

The Gordon growth model includes four variables, so if we know any three of them, we can solve for the fourth. In practice, we can typically observe the price and current dividend for a publicly traded stock. Consequently, we are usually interested in either backing out the:

Implied required return, using an assumed growth rate, or the implied growth rate, using an assumed required return.

Spreadsheet modeling:

In practice we can use spreadsheets to model any pattern of dividend growth we'd like with different growth rates for each year because the spreadsheet does all the calculations for us. Spreadsheet modeling is applicable to firms about which you have a great deal of information and can project different growth rates for differing periods, such as construction firms and defense contractors with many long-term contracts.

The primary disadvantage of dividends as a cash flow measure is that:

It is difficult to implement for firms that don't currently pay dividends. It is possible to estimate expected future dividends by forecasting the point in the future when the firm is expected to begin paying dividends. The problem with this approach in practice is the uncertainty associated with forecasting the fundamental variables that influence stock price (earnings, dividend payout rate, growth rate, and required return) so far into the future. A second disadvantage of measuring cash flow with dividends is that it takes the perspective of an investor who owns a minority stake in the firm and cannot control the dividend policy. If the dividend policy dictated by the controlling interests bears a meaningful relationship to the firm's underlying profitability, then dividends are appropriate. However, if the dividend policy is not related to the firm's ability to create value, then dividends are not an appropriate measure of expected future cash flow to shareholders.

The primary advantage of using dividends as the definition of cash flow is that:

It is theoretically justified. The shareholder's investment today is worth the present value of the future cash flows he expects to receive, and ultimately he will be repaid for his investment in the form of dividends. An additional advantage of dividends as a measure of cash flow is that dividends are less volatile than other measures (earnings or free cash flow), and therefore the value estimates derived from dividend discount models are less volatile and reflect the longterm earning potential of the company.

Residual income.

Residual income is the amount of earnings during the period that exceeds the investors' required return. The theoretical basis for this approach is that the required return is the opportunity cost to the suppliers of capital, and the residual income is the amount that the firm is able to generate in excess of this return. The residual income approach can be applied to firms with negative free cash flow and to dividend- and non-dividend-paying firms.

Explain the use of spreadsheet modeling to forecast dividends and to value common shares. *The last step is where the use of the spreadsheet really pays off. The analyst is in position to conduct detailed scenario analyses wherein the model inputs can be altered to see how changes in the pattern of future dividends, interest rates, and firm risk affect firm valuation estimates*:

Step 1: Establish the base level of cash flows or dividends. In the case of dividends, this would ordinarily be either the amount paid over the preceding year or some normalized level based upon projected firm earnings. Step 2: Estimate changes in the firm's dividends for the foreseeable future (also known as the supernormal growth period) and project future cash dividends on the basis of these estimates. Because the spreadsheet can be programmed in a virtually infinite series of combinations, any dividend pattern desired can be achieved. Step 3: Because an equity security has an infinite life, the analyst needs to estimate what normalized level of growth will occur at the end of the supernormal growth period. This allows for an estimate of a terminal value, representing the cash flow (i.e., the firm's value if sold at this time) to be received at the end of the supernormal growth period. Step 4: Discount all projected dividends and the terminal value back to today to obtain an estimate of the firm's current value.

Multi-Period DDM:

The DDM can easily be adapted to any number of holding periods by adjusting the discount factor to match the time to receipt of each expected return. With this, the present value becomes the sum of the properly discounted values of all expected cash flows (dividends and terminal value).

H-Model: The problem with the basic two-stage DDM is that it is usually unrealistic to assume that a stock will experience high growth for a short period, then immediately fall back to a long-run level. The H-model utilizes a more realistic assumption:

The growth rate starts out high and then declines linearly over the high-growth stage until it reaches the long-run average growth rate.

The two-stage fixed growth rate model is based on the assumption that the firm will enjoy an initial period of high growth, followed by a mature or stable period in which growth will be lower but sustainable:

The value of a firm that doesn't currently pay a dividend is a simple version of the two-stage DDM, where the firm pays no dividends in the first stage. Therefore, the value of the firm is just the present value of the terminal value computed at the point in time at which dividends are projected to start.

Two-Period DDM:

The value of a share of stock using the two-period DDM is the present value of the dividends in years 1 and 2, plus the present value of the expected price in Year 2.

One advantage of free cash flow models is that:

They can be applied to many firms, regardless of dividend policies or capital structures. The ability to influence the distribution and application of a firm's free cash flow makes these models more pertinent to a firm's controlling shareholders. Free cash flow is also useful to minority shareholders because the firm may be acquired for a market price equal to the value to the controlling party.

Residual income models can be more difficult to apply, however, because:

They require indepth analysis of the firm's accounting accruals. Management discretion in establishing accruals for both income and expense may obscure the true results for a period. If the accounting is not transparent or if the quality of the firm's reporting is poor, the accurate estimation of residual income is likely to be difficult.

If the other factors remain constant, we can see that the growth of a firm's earnings (and dividends) is a function of its ROE and its retention rate:

This has also been called the PRAT model, where SGR is a function of the profit margin (P), the retention rate (R), the asset turnover (A), and financial leverage (T).

Three-stage DDM:

Three-stage models are appropriate for firms that are expected to have three distinct stages of earnings growth. A three-stage model is a slightly more complex refinement of a two-stage model.

PRAT model:

Two of these factors are functions of the firm's financing decisions (leverage and earnings retention), and two are functions of performance (return on assets equals profit margin multiplied by asset turnover). These factors can be used as building blocks in developing an estimate of a firm's growth. If the actual growth rate is forecasted to be greater than SGR, the firm will have to issue equity unless the firm increases its retention ratio, profit margin, total asset turnover, or leverage. Technically, the correct way to calculate sustainable growth rate is with ROE based on beginning shareholders' equity.

The most basic multistage model is a:

Two-stage DDM in which we assume the company grows at a high rate for a relatively short period of time (the first stage) and then reverts to a long-run perpetual growth rate (the second stage). The length of the high-growth phase is a function of the visibility of the company's operations; in other words, it tells how far into the future the analyst can predict growth rates with a certain degree of confidence.

The price-to-earnings (P/E) ratio is the most commonly:

Used relative valuation indicator. An analyst derives a justified P/E based on the firm's fundamentals. The two most common forms are the leading P/E, which is based on the earnings forecast for the next period, and the trailing P/E, which is based on the earnings for the previous period.

No matter which dividend discount model we use, we have to estimate a terminal value at some point in the future. There are two ways to do this:

Using the Gordon growth model and using the market multiple approach. The most common method (on the exam) is to estimate the terminal value with the Gordon growth model. Many analysts also use market price multiples to estimate the terminal value rather than use the GGM method of discounting dividends. For example, we could forecast earnings and a P/E ratio at the forecast horizon and then estimate the terminal value as the P/E multiplied by the earnings estimate.

Rate of return using the two-stage DDM model:

Using the general two-stage model is more difficult because we have to solve for r with an iterative process because there is no closed-form solution.

One-Period DDM:

We can rearrange the holding period formula to solve for the value today of the stock given the expected dividend, the expected price in one year, and the required return.

While the basic GGM assumes constant growth, most firms go through a pattern of growth that includes several phases:

• An initial growth phase,where the firm has rapidly increasing earnings, little or no dividends, and heavy reinvestment. • A transition phase,in which earnings and dividends are still increasing but at a slower rate as competitive forces reduce profit opportunities and the need for reinvestment. • A mature phase,in which earnings grow at a stable but slower rate, and payout ratios are stabilizing as reinvestment matches depreciation and asset maintenance requirements.

The residual income approach is most appropriate for:

• Firms that do not have dividend histories. • Firms that have negative free cash flow for the foreseeable future (usually due to capital demands). • Firms with transparent financial reporting and high quality earnings.

Free cash flow models are most appropriate:

• For firms that do not have a dividend payment history or have a dividend payment history that is not clearly and appropriately related to earnings. • For firms with free cash flow that corresponds with their profitability. • When the valuation perspective is that of a controlling shareholder.

We can use one of several growth models, including the:

• Gordon constant growth model. • Two-stage growth model. • H-model. • Three-stage growth model. With the appropriate model, we can forecast dividends up to the end of the investment horizon where we no longer have confidence in the forecasts and then forecast a terminal value based on some other method, such as a multiple of book value or earnings. Choosing the appropriate growth model is essential to accurate forecasts.

The Gordon growth model (GGM) has a number of characteristics that make it useful and appropriate for many applications. The model:

• Is applicable to stable, mature, dividend-paying firms. • Is appropriate for valuing market indices. • Is easily communicated and explained because of its straightforward approach. • Can be used to determine price-implied growth rates, required rates of return, and value of growth opportunities. • Can be used to supplement other, more complex valuation methods.

Dividends are appropriate as a measure of cash flow in the following cases:

• The company has a history o f dividend payments. • The dividend policy is clear and related to the earnings o f the firm. • The perspective is that of a minority shareholder. Firms in the mature stage of the industry life cycle are most likely to meet the first two criteria.

The Gordon growth model assumes that:

• The firm expects to pay a dividend, D1, in one year. • Dividends grow indefinitely at a constant rate, g (which may be less than zero). • The growth rate, g, is less than the required return, r. A firm's growth rate projections can be compared to the growth rate of the economy to determine if it can continue indefinitely. It is unrealistic to assume that any firm can continue to grow indefinitely at a rate higher than the long-term growth rate in real gross domestic product (GDP) plus the long-term inflation rate. In general, a perpetual dividend growth rate forecast above 5% is suspect.

There are also some characteristics that limit the applications of the GGM:

• Valuations are very sensitive to estimates of growth rates and required rates of return, both of which are difficult to estimate with precision. • The model cannot be easily applied to non-dividend-paying stocks. • Unpredictable growth patterns of some firms would make using the model difficult and the resulting valuations unreliable.

For most companies, the Gordon growth model assumption of constant dividend growth that continues into perpetuity is unrealistic. We need more realistic multistage growth models to estimate value for companies with several stages of future growth. There are two important points to keep in mind:

• We're still just forecasting dividends into the future and discounting them back to today to find intrinsic value. • Over the long term, growth rates tend to revert to a long-run rate approximately equal to the long-term growth rate in real gross domestic product (GDP) plus the long-term inflation rate. Historically, that number has been between 2% and 5%. Anything higher than 5% as a long-run perpetual growth rate is difficult to justify. The required rate o f return applicable to each stage might also be different.