Value of a Preferred Stock
Unlike common equity, preferred stocks pay a fixed dividend. As such, the value of a preferred stock can be calculated using the dividend discount model. The value of the preferred stock is essentially the present value of the dividend in perpetuity, where k is the required return.

Formula 13.1

Value of preferred stock

Example: Calculating the value of a preferred stock
Assume that Newco's preferred stock pays out to an investor an annual dividend of $8 per share. Given a rate of return of 10%, what is the value of Newco's preferred stock?

Answer:
Value of Newco's preferred stock = ($8/0.10) = $80

Value of a Common Stock
Much like a preferred stock, holders of common stock can also receive dividends. However, dividends on common stock are not guaranteed, nor are they a fixed amount from year-to-year. As such, we can value common stock using dividends over various time horizons.

1. One-year Holding period
Consider a one-year holding period, in this time frame, an investor will receive a dividend and the price of the common stock at the end of the one year, both discounted back by the rate of return on the common equity.

Keeping this in mind, we can calculate the value of the common stock as follows:

Formula 13.2

Common Stock = Dividend + Price at the end of the year
(1+k)1 (1+k)1

Example: Calculate the value of a stock with a 1-year holding period
Newco expects to pay its shareholders common equity, $0.25 per share this year. The investor anticipates Newco's stock will close the year at $30 per share. Given a rate of return of 10%, what is the value of Newco's common stock?

Answer:
Value of Newco's common stock = $0.25 + $30 = $27.50 per share
(1.10) (1.10)

2. Multiple-year holding period
Given investors can hold a common stock for over a year, it is useful to value a stock over the investor's expected holding period. In this case, the DDM model can be used.

Formula 13.3

Value of common equity

Example: Calculate the value of a stock with a multiple-year holdingperiod
An investor plans to hold Newco's stock for 2 years. Newco expects to pay its shareholders common equity, $0.25 per share over the next two years. The investor anticipates Newco's stock will close the end of that time period at $40 per share. Given a rate of return of 10%, what is the value of Newco's common stock at the end of the two-year time period?

Answer:
Value of Newco's common stock = $0.25 + $0.25 + $40 = $33.49
(1.10)1 (1.10)2 (1.10)2

3. Infinite Period DDM
To value a common stock using the infinite period DDM, the calculation is simplified much like it is when valuing a preferred stock with infinite dividends.

Formula 13.4


Where k = rate of return, g = growth rate

Example: Calculate the value of common stock with infinite dividends
Newco paid a $0.25 annual dividend in 2004 and expects to pay $0.265 in 2005. Assuming a 6% growth rate and a required rate of return of 10%, calculate the value of Newco's stock.

Answer:
Value of Newco's common stock = $0.265 = $6.63
(0.10 - 0.06)

Valuing the Common Stock of Companies with Supernormal Growth
When valuing a common stock of a company which is experiencing significant growth, we take a similar approach to valuing the common stock with a multi-year holding period. The difference in the approaches is related to the dividend. A multi-year holding period approach assumes a stable dividend, whereas the dividend changes given the supernormal growth in this approach.

Formula 13.5

Example: Calculate the value of common stock with temporary supernormal growth
An investor plans to hold Newco's stock for 3 years. In that time period, Newco plans to grow at a rate of 6% in the first two years and 3% thereafter. Newco's last dividend was $0.25. Given a rate of return of 10%, what is the value of Newco's common stock at the end of the three-year time period?

Answer:
To begin, the dividend in each time period must be calculated [D = D0(1+g)]

D1 = (0.25)(1.06) = 0.265
D2 = (0.265)(1.06) = 0.281
D3 = (0.281)(1.03) = 0.289

Since we expect the dividend to grow indefinitely in year 3 and on, the present value of the stock price in year 3 is calculated as follows:

P3 = 0.289 = 4.133
(0.10-0.03)

The value of Newco's common stock is as follows:

Newco'scs = $0.265 + $0.281 + 0.289 + $4.133 = $3.80
(1.10)1 (1.10)2 (1.10)3 (1.10)3

Using the DDM to Develop an Earnings Multiplier Model
Developing the earnings multiplier using the DDM begins with the basic determinant of price. Recall, to determine the price of a stock using the DDM, the infinite dividend is divided by the required return minus the growth rate as follows:

To determine the price to earnings multiple, the price of the stock is simply divided by the earnings per share of the stock as follows:

Formula 13.6

Example: Determining a company's price-to-earnings ratio using the DDM
With Newco's $0.25 dividend payout, an EPS of $1.00, calculate the stock's P/E ratio assuming 10% required return and 5% growth.

Answer:
P/E ratio = 0.25/1.00 = 5%
(0.10-0.05)

Look Out!

In terms of changes in the dividend, the required return and the growth rate affect the DDM. Changes in these variables will also affect the stock's P/E ratio.



DDM and the Earnings Multiplier

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