## Dividend valuation model DVM

a model that values a share of stock on the basis of the future dividend stream it is expected to produce; its three versions are zero-growth, constant-growth, and variable-growth.

In the valuation process, the intrinsic value of any investment equals the present value of the expected cash benefits. For common stock, this amounts to the cash dividends received each year plus the future sale price of the stock. One way to view the cash flow benefits from common stock is to assume that the dividends will be received over an infinite time horizon—an assumption that is appropriate so long as the firm is considered a "going concern." Seen from this perspective, the value of a share of stock is equal to the present value of all the future dividends it is expected to provide over an infinite time horizon.

Although a stockholder can earn capital gains in addition to dividends by selling a stock for more than he or she paid for it, from a strictly theoretical point of view, what is really being sold is the right to all remaining future dividends. Thus, just as the current value of a share of stock is a function of future dividends, the future price of the stock is also a function of future dividends. In this framework, the future price of the stock will rise or fall as the outlook for dividends (and the required rate of return) changes. This approach, which holds that the value of a share of stock is a function of its future dividends, is known as the dividend valuation model (DVM).

There are three versions of the dividend valuation model, each based on different assumptions about the future rate of growth in dividends: (1) The zero-growth model, which assumes that dividends will not grow over time. (2) The constant-growth model, which is the basic version of the dividend valuation model, and assumes that dividends will grow by a fixed/constant rate over time. (3) The variable-growth model, which assumes that the rate of growth in dividends varies over time.

See the dividend valuation model at

www.stocksense.com/valuation.html

Zero Growth The simplest way to picture the dividend valuation model is to assume the stock has a fixed stream of dividends. In other words, dividends stay the same year in and year out, and they're expected to do so in the future. Under such conditions, the value of a zero-growth stock is simply the capitalized value of its annual dividends. To find the capitalized value, just divide annual dividends by the required rate of return, which in effect acts as the capitalization rate. That is,

 Value of a Annualdividends share of stock required rate of return

For example, if a stock paid a (constant) dividend of \$3 a share and you wanted to earn 10% on your investment, the value of the stock would be \$30 a share (\$3/0.10 = \$30).

As you can see, the only cash flow variable that's used in this model is the fixed annual dividend. Given that the annual dividend on this stock never changes, does that mean the price of the stock never changes? Absolutely not! For as the capitalization rate—that is, the required rate of return—changes, so will the price of the stock. Thus, if the capitalization rate goes up to, say, 15%, the price of the stock will fall to \$20 (\$3/0.15). Although this may be a very simplified view of the valuation model, it's actually not as far-fetched as it may appear. As we'll see in Chapter 11, this is basically the procedure used to price preferred stocks in the marketplace.

Constant Growth The zero-growth model is a good beginning, but it does not take into account a growing stream of dividends, which is more likely to be the case in the real world. The standard and more widely recognized version of the dividend valuation model assumes that dividends will grow over time at a specified rate. In this version, the value of a share of stock is still considered to be a function of its future dividends, but such dividends are expected to grow forever (to infinity) at a constant rate of growth, g. Accordingly, the value of a share of stock can be found as follows:

Equation 8.8

Equation 8.8a

Equation 8.8

Equation 8.8a

Value of a

Next year's dividends

share of stock

Required rate Constant rate of

of return growth in dividends

V =

A

D1 = annual dividends expected to be paid next year (the first year in the forecast period) k = the capitalization rate, or discount rate (which defines the required rate of return on the investment)

g = the annual rate of growth in dividends, which is expected to hold constant to infinity

This model succinctly captures the essence of stock valuation: Increase the cash flow (through D or g) and/or decrease the required rate of return (k), and the value of the stock will increase. Also note that in the DVM, k defines the total return to the stockholder and g represents the expected capital gains on the investments. We know that, in practice, there are potentially two components that make up the total return to a stockholder: dividends and capital gains. As it turns out, the returns from both dividends and capital gains are captured in the DVM. That is, because k represents total returns and g defines the amount of capital gains embedded in k, it follows that if you subtract g from k (k — g), you'll have the expected dividend yield on the stock. Thus the expected total return on a stock (k) equals the returns from capital gains (g) plus the returns from dividends (k — g).

The constant-growth DVM should not be used with just any stock. Rather, it is best suited to the valuation of mature companies that hold established market positions. These are companies with strong track records that have reached the "mature" stage of growth. This means that you're probably dealing with large-cap (or perhaps even some mature mid-cap) companies that have demonstrated an ability to generate steady—though perhaps not spectacular— rates of growth year in and year out. The growth rates may not be identical from year to year, but they tend to move within such a small range that they are seldom far off the average rate. These are companies that have established dividend policies, particularly with regard to the payout ratio, and fairly predictable growth rates in earnings and dividends. Thus, to use the constant-growth DVM on such companies, all that's required is some basic information about the stock's current level of dividends and the expected rate of growth in dividends, g.

One popular and fairly simple way to find the dividend growth rate is to look at the historical behavior of dividends. If they are growing at a relatively constant rate, you could assume that they'll continue to grow at (or near) that average rate in the future. You can get historical dividend data in a company's annual report, from various online Internet sources, or from publications like Value Line. Given this stream of dividends, you can use basic present-value arithmetic to find the average rate of growth. Here's how: Take the level of dividends, say, 10 years ago and the level that's being paid today. Presumably, dividends today will be (much) higher than they were 10 years ago, so, using your calculator, find the present value discount rate that equates the (higher) dividend today to the level paid 10 years earlier. When you find that, you've found the growth rate, because in this case, the discount rate is the average rate of growth in dividends. (See Chapter 5 for a detailed discussion of how to use present value to find growth rates.)

Once you've determined the dividend growth rate, g, you can find next year's dividend, D1, as D0 X (1 + g), where D0 equals the actual (current) level of dividends. Let's say that in the latest year Amalgamated Anything paid \$2.50 a share in dividends. If you expect these dividends to grow at the rate of 6% a year, you can find next year's dividends as follows: D1 = D0 (1 + g) = \$2.50 (1 + .06) = \$2.50 (1.06) = \$2.65. The only other information you need is the capitalization rate, or required rate of return, k. (Note that k must be greater than g for the constant-growth model to be mathematically operative.)

To see this dividend valuation model at work, consider a stock that currently pays an annual dividend of \$1.75 a share. Let's say that by using the present-value approach described above, you find that dividends are growing at a rate of 8% a year, and you expect they will continue to do so into the future. In addition, you feel that because of the risks involved, the investment should carry a required rate of return of 12%. Given this information, you can use Equation 8.8 to price the stock. That is, given D0 = \$1.75, g = 0.08, and k = 0.12, it follows that

Value of a = Dp (1 + g) = \$1.75 (1.08) = \$1.89 = share of stock k -g 0.12 - 0.08 0.04 '

Thus, if you want to earn a 12% return on this investment—made up of 8% in capital gains (g), plus 4% in dividend yield (i.e., \$1.89/\$47.25 = 0.04)—

then according to the constant-growth dividend valuation model, you should pay no more than \$47.25 a share for this stock.

With this version of the DVM, the price of the stock will increase over time so long as k and g don't change. This occurs because the cash flow from the investment will increase as dividends grow. To see how this happens, let's carry our example further. Recall that D0 = \$1.75, g = 8%, and k = 12%. On the basis of this information, we found the current value of the stock to be \$47.25. Now look what happens to the price of this stock if k and g don't change:

Stock

Year Dividend Price*

Stock

Year Dividend Price*

 (Current year) 0 \$1.75 \$47.25 1 1.89 51.00 2 2.04 55.00 3 2.20 59.50 4 2.38 64.25 5 2.57 69.50

*As determined by the dividend valuation model, given g = 0.08, k = 0.12, and D0 = dividend level for any given year.

*As determined by the dividend valuation model, given g = 0.08, k = 0.12, and D0 = dividend level for any given year.

As the table shows, we can also find the expected price of the stock in the future by using the standard dividend valuation model. To do this, we simply redefine the appropriate level of dividends. For example, to find the price of the stock in year 3, we use the expected dividend in the third year, \$2.20, and increase it by the factor (1 + g). Thus the stock price in year 3 = D3 X (1 + g)/(k - g) = \$2.20 X (1 + 0.08)/(0.12 - 0.08) = \$2.38/0.04 = \$59.50. Of course, if future expectations about k or g do change, the future price of the stock will change accordingly. Should that occur, an investor could use the new information to decide whether to continue to hold the stock.

Variable Growth Although the constant-growth dividend valuation model is an improvement over the zero-growth model, it still has some shortcomings. The most obvious of these is the fact that it does not allow for changes in expected growth rates. To overcome this problem, we can use a form of the DVM that allows for variable rates of growth over time. Essentially, the variable-growth dividend valuation model derives, in two stages, a value based on future dividends and the future price of the stock (which price is a function of all future dividends to infinity). The variable-growth version of the model finds the value of a share of stock as follows:

Equation 8.9

Equation 8.9a

Present value of _

. Present value of the price

### Value of a share future dividends

„ , = , , , + of the stock at the end of of stock during the initial the variable-growth period variable-growth period the variable-growth period variable-growth period where

D1, D2, etc. = future annual dividends

PVIFt = present value interest factor, as specified by the required rate of return for a given year t (Table A.3 in the Appendix) v = number of years in the initial variable-growth period

Note that the last element in this equation is the standard constant-growth dividend valuation model, which is used to find the price of the stock at the end of the initial variable-growth period.

This form of the DVM is appropriate for companies that are expected to experience rapid or variable rates of growth for a period of time—perhaps for the first 3 to 5 years—and then settle down to a constant (average) growth rate thereafter. This, in fact, is the growth pattern of many companies, so the model has considerable application in practice. (It also overcomes one of the operational shortcomings of the constant-growth DVM in that k does not always have to be greater than g. That is, during the variable-growth period, the rate of growth, g, can be greater than the required rate of return, k, and the model will still be fully operational.)

Finding the value of a stock using Equation 8.9 is actually a lot easier than it looks. All you need do is follow these steps:

1. Estimate annual dividends during the initial variable-growth period and then specify the constant rate, g, at which dividends will grow after the initial period.

2. Find the present value of the dividends expected during the initial variable-growth period.

3. Using the constant-growth DVM, find the price of the stock at the end of the initial growth period.

4. Find the present value of the price of the stock (as determined in step 3). Note that the price of the stock is discounted at the same PVIF as the last dividend payment in the initial growth period, because the stock is being priced (per step 3) at the end of this initial period.

5. Add the two present-value components (from steps 2 and 4) to find the value of a stock.

To see how this works, let's apply the variable-growth model to one of our favorite companies: Sweatmore Industries. Let's assume that dividends will grow at a variable rate for the first 3 years (2001, 2002, and 2003). After that, the annual rate of growth in dividends is expected to settle down to 8% and stay there for the foreseeable future. Starting with the latest (2000) annual dividend of \$2.21 a share, we estimate that Sweatmore's dividends should grow by 20% next year (in 2001), by 16% in 2002, and then by 13% in 2003 before dropping to an 8% rate. Using these (initial) growth rates, we therefore project that dividends in 2001 will amount to \$2.65 a share (\$2.21 X 1.20), and will rise to \$3.08 (\$2.65 X 1.16) in 2002 and to \$3.48 (\$3.08 X 1.13) in 2003. In addition, given Sweatmore's risk profile, we feel that the investment should produce a minimum (required) rate of return (k) of at least 14%. We now have all the input we need and are ready to put a value on Sweatmore Industries. Table 8.4 shows the variable-growth DVM in action. The value of Sweatmore stock, according to the variable-growth DVM, is just under \$49.25 a share. In essence, that's the maximum price you should be willing to pay for the stock if you want to earn a 14% rate of return.

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### Responses

• katharina
What is devidend valuation model (dvm)?
3 years ago
• Kauko
What is dividend valuation model?
3 years ago
• Tiziano
What is included in the dividend valuation model when doing stock valuation?
9 months ago
Which growth valuation method assumes no change in dividend rate?
7 months ago
• edwin
What is dividend approach valuation?
4 months ago
• GIORDANO COCCI
Does the dividend valuation model take market conditions intoa account?
3 months ago
• Anna
Why is DVM not a reliable valuation technique?
3 months ago
• amanuel
How does the Dividen valuation model consider risk?
3 months ago