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Chapter 7

Department

ManagementCourse Code

MGT338H5Professor

Gabor ViragChapter

7This

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Chapter 7 – Valuing Stocks

Chapter 7 – Valuing Stocks

Dividend-Discount Model; Total Payout & Free Cash Flow Valuation Models; Valuation

Based on Comparable Firms; Information, Competition, and Stock Prices

→ NOTATION

→ 7-1: THE DIVIDEND-DISCOUNT MODEL

The Law of One Price implies that the price of a security should equal the present value of the expected

cash flows an investor will receive from owning it. Using this, we derive the first method of valuing a

stock: the dividend-discount model.

A One-Year Investor

There are 2 potential sources of cash flows from owning a stock; dividends and selling the share at

some future date. The total amount received in dividends and from selling the stock will depend on the

investor’s investment horizon. Let’s consider a 1-year investor.

They buy a stock for the current market price P0. Let Div1 be the total dividends paid at the end of the

year. At the end of the year, the investor sells the share at the new market price P1.

Given these expectations, the investor will be willing to pay a price today up to the point that this

transaction has a zero NPV. Since there’s some risk involved, we must discount these cash flows based

on the equity cost of capital rE. This is the expected return of other investments available in the market

with equivalent risk to the firm’s shares.

Dividend Yields, Capital Gains, and Total Returns

We can reinterpret the equation of P0 by multiplying by (1 + rE), divide by P0, and subtract 1 from both

sides. By doing this, we get the total return.

The dividend yield is the expected annual dividend of the stock divided by its current price. It’s the

percentage return the investor expects to earn from the dividend paid by the stock.

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Prof. Gabor Virag MGT338 Page 2 of 11

Chapter 7 – Valuing Stocks

The capital gain is what the investor will earn on the stock, P1 – P0. We divide it by the current stock

price to express the capital gain as a percentage return, called the capital gain rate.

The sum of the dividend yield and capital gain rate is called the total return, which is what an investor

will earn for a 1-year investment. The equation states that the expected total return of the stock should

equal the expected return of other investments available in the market with equivalent risk.

If a stock offers a higher return than other securities with the same risk, investors would buy the stock

and put upward pressure on the price. This increase in the price would lower the dividend yield and

capital gain rate. The opposite is also true; lower return causes price to decrease, which increases total

return until the equation is satisfied.

A Multiyear Investor

Suppose we hold the stock for 2 years.

Setting the stock price equal to the present value of the future cash flows in this case implies:

Note: There is no underlying difference between the 1-year equation and the 2-year equation. In the 1-

year equation, there is no second term and the selling price of the stock is in the numerator of the first

term as P1. However, P1 is determined by the expected future cash flows. In other words, we can get

the second equation from the first one:

The Dividend-Discount Model Equation

We can continue this process for any number of years by replacing the final stock price with the value

that the next holder of the stock would be willing to pay. Doing so leads to the general dividend-

discount model for the stock price, where the horizon n is arbitrary:

This applies to a single n-year investor, who collects dividends for n years and then sells the stock, OR

applies to a series of investors who hold the stock for shorter periods and then resell it.

For the special case in which the firm eventually pays dividends and is never acquired, it is possible to

hold the shares forever. Consequently, we can let n go to infinity:

That is, the price of the stock is equal to the present value of the expected future dividends it will pay.

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Chapter 7 – Valuing Stocks

→ 7-2: APPLYING THE DIVIDEND-DISCOUNT MODEL

Constant Dividend Growth

A common approximation to help estimate dividends in the future is to assume that, in the long run,

dividends will grow at a constant rate g. The timeline for an investor who buys and holds a stock is:

Constant Dividend Growth Model

For another interpretation, we can rearrange is as follows:

We see that g equals the expected capital gain rate. In other words, with constant expected dividend

growth, the expected growth rate of the share price matches the growth rate of dividends.

Dividends vs. Investment & Growth

With the equation above, we now know that a firm’s share price increases with the current dividend

level Div1 and the expected growth rate g. To maximize share price, a firm wants to increase both.

However, there’s a tradeoff; increasing growth may require investment but money spent on investment

cannot be used to pay dividends.

A Simple Model of Growth

If we define a firm’s dividend payout rate as the fraction of its earnings that the firm pays as dividends

each year, we can write the firm’s dividend per share at date t as follows:

The firm can increase its dividends in 3 ways:

1) Increase its earnings (net income).

2) Increase its dividend payout ratio.

3) Decrease shares outstanding.

To simplify things, let’s make the following assumptions:

o Firms do not issue new or buy back shares. The number of shares outstanding is fixed.

o If a firm does not invest, the firm does not grow, so earnings generated remains constant.

It can now do 2 things with earnings; pay dividends, or it retain/reinvest them. Therefore:

New investment equals earnings multiplied by the firm’s retention rate, the fraction of current

earnings that the firm retains.

Using substitution, we can get an expression for the growth rate of earnings:

If the firm chooses to keep its dividend payout rate constant, then the growth in dividends will equal

growth of earnings:

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