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Chapter 7

This

**preview**shows pages 1-2. to view the full**6 pages of the document.**Chapter 7: Common Stock Valuation

7.1 Security Analysis:

Fundamental Analysis: examination of a firm’s accounting statements and other financial and

economic information to assess the economic value of a company’s stock

Numbers such as a company’s earnings per share, cash flow, book equity value, and sales are often

called fundamentals because they describe, on a basic level, a specific firm’s operations and profits (or

lack of profits)

7.2 The Dividend Discount Model:

A fundamental principle of finance holds that the economic value of a security is properly measured by

the sum of its future cash flows, where the cash flows are adjusted for risk and the time value of money

Dividend Discount Model (DDM): method of estimating the value of a share of stock as the present

value of all expected future dividend payments (where dividends are adjusted for risk and the time value

of money)

For example, suppose a company pays a dividend at the end of the year.

- Let D(t) denote a dividend to be paid t years from now

- Let V(0) represent the present value of the future dividend steam

- Let k denote the appropriate risk-adjusted discount rate

- Using the dividend discount mode, the present value of a share of this company’s stock is

measured as this sum of discounted future dividends:

- Assumes that the last dividend is paid T years from now, where the value of T depends on the

specific valuation problem considered

Constant Dividend Growth Rate Model: a version of the dividend discount model that assumes a

constant dividend growth rate

- Letting a constant growth rate be denoted by g, then successive annual dividends are stated as:

- If the number of dividends to be paid is large, calculating the present value of each dividend

separately is tedious and possibly prone to error

- Fortunately, if the growth rate is constant, some simplified expressions are available to handle

certain special cases

- The present value of the next T dividends, that is, D(1) through D(T), can be calculated using this:

- Requires that the growth rate and the discount rate does not equal to each other (), since this

requires division to be zero

- When the growth rate is equal to the discount rate, that is, k=g, the effects of growth and discounting

cancel exactly, and the present value V(0) is simply the number of payments T times the current

dividend D(0):

Constant Perpetual Growth:

- Where a firm will pay dividends that grow at the constant rate g forever

- Constant perpetual growth model: a version of the dividend discount model in which dividends

grow forever at a constant rate, and the growth rate is strictly less than the discount rate

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

- Constant perpetual growth model:

- Since D(0)(1+g)= D(1), we could also write the constant perpetual growth model as:

Applications of the Constant Perpetual Growth Model:

- The constant perpetual growth model can be usefully applied only to companies with a history of

relatively stable earnings and dividend growth expected to continue into the distant future

Historical Growth Rates:

- In the constant growth model, a company’s historical average dividend growth rate is frequently

taken as an estimate of future’s dividend growth

- There are two ways to calculate a historical growth rate yourself:

1. Geometric Average Dividend Growth Rate: a dividend growth rate based on a geometric

average of historical dividends

D(0) is the earliest dividend and D(N) is the latest dividend to be used.

2. Arithmetic Average Dividend Growth Rate: a dividend growth rate based on an arithmetic

average of historical dividends

o We first calculate each year’s dividend growth rate separately and then calculate an

arithmetic average of these annual growth rates

o Example on page 195

The Sustainable Growth Rate:

- It is necessary to come up with an estimate of g, the growth rate in dividends

- In our previous discussions, we described two ways to do this: (1) using the company’s historic

average growth rate or (2) using an industry median or average growth rate

- We now describe a third way, know as the sustainable growth rate: a dividend growth rate that can

be sustained by a company’s earnings

- Retained Earnings: earnings retained within the firm to finance growth

- Payout Ratio: proportion of earnings paid out as dividends

- Retention Ratio: proportion of earnings retained for reinvestment

- If we let D stand for dividends and EPS stand for earnings per share, then the payout ratio is:

- The Retention Ratio:

- Return on equity is commonly computed using an accounting-based performance measure and is

calculated as a firm’s net income dividend by stockholders’ equity:

- Common problems with sustainable growth rates is that they are sensitive to year-to-year

fluctuations in earnings

- Security analysts routinely adjust sustainable growth rate estimates to smooth out the effects of

earning variations

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