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# Discounted Cash Flow Method

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A company’s earnings play a role in the valuation of its stock. However, in the discounted cash flow method it is dividends that play a key role and not earnings directly. Future estimated dividends are discounted to the present value at the investor’s required rate of return to determine the intrinsic value of the stock. Suppose, for example, that a stock pays a dividend of \$0.50 per year, indefinitely, and that your required rate of return is 10 percent; the stock’s value is \$5 (the perpetual dividend divided by the required rate of return). For a greater than 10 percent required rate of return, the purchase price of the stock must be less than \$5 per share. Astock price of greater than \$5 per share will result in a lower than 10 percent required rate of return.

In reality, the amount of a common stock dividend is not fixed indefinitely. Dividends fluctuate over time depending on the company’s earnings and the board of directors’ decision to pay dividends or retain the profits for internal reinvestment by the company. Dividends can remain constant, grow at fixed rates, or grow or decline at variable rates. To get around these difficulties in the valuation of a stock, this model assumes that dividends grow at a constant rate.

The following formula illustrates the valuation model by discounting the constantly growing dividend by using an investor’s required rate of return.

Consider the following example using this formula to value a company’s stock. Company X paid a dividend last year of \$1 per share and is expected to continue paying dividends every year. The company is expected to grow at 8 percent. An investor interested in buying this stock has a required rate of return of 10 percent.

The dividend of \$1 was paid last year, which means that you must compute the next or future dividend to be paid.
Future dividend = current dividend * (1 + growth rate)
= \$1(1 + 0.08)
= \$1.08
You can now substitute the figures into the equation.
Value of the stock = \$1.08/(0.10 – 0.08)
= \$50
Aprice greater than \$50 results in a lower required rate of return of 10 percent, and a price below \$50 results in a rate of return greater than 10 percent.

This valuation model depends on dividends paid by the company, and the investor’s expected rate of return is the dividend yield plus the company’s growth rate. Suppose that the dividend is \$1.08 and that the stock price is \$55:
Expected rate of return = (\$1.08/55) + 8% = 9.96%

The dividend growth valuation model makes a number of assumptions:
* The required rate of return of the investor is greater than the rate of growth of the company. The purpose of the valuation process is to find stocks with intrinsic values that are less than their market values (which occurs only when the growth rate is less than the required rate of return).
* Dividends are expected to grow at a constant growth rate. This valuation model can be adapted to include variable dividend growth rates.

The implications of this model are
* The larger the dividend, the greater the stock price. Table 9–1 discusses whether a company should pay dividends or retain its earnings.
* The greater the growth rate of a company, the greater the stock price.
* The lower an investor’s required rate of return, the greater the stock price.

Table 9-1
Should Companies Pay Dividends or Retain Their Earnings?

One implication of the dividend growth valuation model is that the larger the dividend payments to shareholders, the greater is the stock price. However, if a company can generate a rate of return on its investment higher than an investor’s required rate of return, the stock price should see greater increases than if the earnings were paid to shareholders in dividends. For example, suppose that a company generates earnings per share of \$2 and pays out the entire amount in dividends. If an investor’s required rate of return is 8 percent, the stock is valued at \$25 per share (\$2 / 0.08). No earnings growth takes place because the company has not retained any earnings.

If the company’s dividend payout ratio (the percentage of net income paid to shareholders) is 40 percent, the dividend is \$0.80 (0.40 * \$2). The earnings retention ratio (percentage of net income that is not paid out in dividends) is 60 percent. If the company has a return on its investment (equity) of 12 percent, the growth rate for the company is 7.2 percent (0.12 * 0.60).

Value of the stock = dividend/(required rate of return – growth rate)
= \$ 0.80/(0.08 – 072)
= \$100
When the company retains and reinvests part of its earnings in new investments, its share price increases from \$25 to \$100 per share.

The degree of risk of a company is not measured directly in the dividend growth model but is instead adjusted through the investor’s required rate of return. Acompany’s risk is measured by its beta coefficient, which in itself is a problem. The beta coefficient has not been a consistent measure of risk. Beta coefficients for the same stock differ because different market measures are used. Use of the Standard & Poor’s (S&P) 500 Index as a measure of the market versus the Value Line Stock Index results in two different beta coefficients for the same company. Similarly, the use of different time periods results in different beta coefficients for the same stock.

Another problem for the dividend growth valuation model is the growth rate. Should you use past earnings growth or estimate future growth rates for a company? If historical growth rates are chosen, what length of time should you choose? Table 9–2 illustrates how to determine the growth rate of a company.

Although the dividend growth valuation model is sound theoretically, these problems do have a bearing on the valuation of a company’s stock. Consequently, other approaches to valuing common stock are less theoretical and more intuitive.

Table 9-2
Determining the Growth Rate of a Stock Using a Computer Spreadsheet

A company’s sustained earnings are a major determinant of whether the company can afford to pay out dividends, maintain its dividend payments, or increase dividend payouts. If a company decides to retain earnings and reinvests the profits in its business rather than paying them out, it can accelerate its earnings growth. You can determine a company’s growth rate by measuring the increase in a company’s earnings over a certain period. This is just one way to measure a company’s growth rate. Others are the growth of a company’s assets or sales.
List the earnings per share (EPS) and dividends per share (DPS) for a company for the past five years. You can find this information on a company’s website by clicking on financial statements or looking at its annual report. For example, the following EPS and DPS for Johnson & Johnson are on its website at www.johnsonandjohnson.com:
 2005 2004 2003 2002 2001 2000 Diluted EPS \$3.46 \$2.84 \$2.40 \$2.16 \$1.84 \$1.61 DPS \$1.275 \$1.095 \$0.925 \$0.795 \$0.70 \$0.62

Price per share: \$60.10 (year-end close)
Determine the growth rate. In 2000, earnings per share were \$1.61 and grew to \$3.46 in five years. Follow these steps using Excel:
Step 1: Click on f* in the tool bar.
Step 2: Highlight financial, and click on rate.
Step 3: Enter the data as shown below:
Nper 5
Pmt 0
PV –1.61
FV 3.46
Type 0
Formula result – 0.165332999
Johnson & Johnson’s growth rate for the five-year period was 16.533 percent. Using this historical rate of growth, you can compute the expected return for this company:
Expected return = (future dividend/price of stock) + growth rate
Future dividend = present dividend * (1 + growth rate)
= \$1.275(1 + 0.16533)
= \$1.423
Expected rate of return = (\$1.423/\$60.10) + 0.16533
= 18.901%
The expected rate of return is 18.901 percent if the investor bought the stock at \$60.10 per share.

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