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Basic Stock Valuation: Dividend GrowthModel

The value of a share of common stock depends on the cash flowsit is expected to provide, and those flows consist of the dividendsthe investor receives each year while holding the stock and theprice the investor receives when the stock is sold. The final priceincludes the original price paid plus an expected capital gain. Theactions of themarginal investor determine the equilibrium stockprice. Market equilibrium occurs when the stock's price is-Select-less thanequal togreater thanCorrect 1 of Item 1itsintrinsic value. If the stock market is reasonably efficient,differences between the stock price and intrinsic value should notbe very large and they should not persist for very long. Wheninvesting in common stocks, an investor's goal is to purchasestocks that are undervalued (the priceis-Select-abovebelowequivalent toCorrect 2 of Item 1the stock'sintrinsic value) and avoid stocks that are overvalued.

The value of a stock today can be calculated as the presentvalue of-Select-a finitean infiniteCorrect 3 of Item 1stream ofdividends:

This is the generalized stock valuation model. We will now lookat 3 different situations where we can adapt this generalized modelto each of these situations to determine a stock's intrinsicvalue:
1. Constant Growth Stocks;
2. Zero Growth Stocks;
3. Nonconstant Growth Stocks.

Constant Growth Stocks:

For many companies it is reasonable to predict that dividendswill grow at a constant rate, so we can rewrite the generalizedmodel as follows:

This is known as the constant growth model or Gordon model,named after Myron J. Gordon who developed and popularized it. Thereare several conditions that must exist before this equation can beused. First, the required rate of return, r_s, must begreater than the long-run growth rate, g. Second, the constantgrowth model is not appropriate unless a company's growth rate isexpected to remain constant in the future. This condition almostnever holds for -Select-maturestart-upCorrect 4 of Item 1firms, butit does exist for many-Select-maturestart-upCorrect 5 of Item1companies.

Which of the following assumptions would cause the constantgrowth stock valuation model to be invalid?

1. The growth rate is zero.
2. The growth rate is negative.
3. The required rate of return is greater than the growthrate.
4. The required rate of return is more than 50%.
5. None of the above assumptions would invalidate the model.

-Select-Statement aStatement bStatement cStatement dStatementeCorrect 6 of Item 1

Quantitative Problem 1: Hubbard Industries justpaid a common dividend, D₀, of $1.30. It expects to growat a constant rate of 4% per year. If investors require a 9% returnon equity, what is the current price of Hubbard's common stock? Donot round intermediate calculations. Round your answer to thenearest cent.

$   per share

Zero Growth Stocks:

The constant growth model is sufficiently general to handle thecase of a zero growth stock, where the dividend is expected toremain constant over time. In this situation, the equation is:

Note that this is the same equation developed in Chapter 5 tovalue a perpetuity, and it is the same equation used to value aperpetual preferred stock that entitles its owners to regular,fixed dividend payments in perpetuity. The valuation equation issimply the current dividend divided by the required rate ofreturn.

Quantitative Problem 2: Carlysle Corporationhas perpetual preferred stock outstanding that pays a constantannual dividend of $1.70 at the end of each year. If investorsrequire an 10% return on the preferred stock, what is the price ofthe firm's perpetual preferred stock? Do not round intermediatecalculations. Round your answer to the nearest cent.

$   per share

Nonconstant Growth Stocks:

For many companies, it is not appropriate to assume thatdividends will grow at a constant rate. Most firms go through lifecycles where they experience different growth rates duringdifferent parts of the cycle. For valuing these firms, thegeneralized valuation and the constant growth equations arecombined to arrive at the nonconstant growth valuationequation:

Basically, this equation calculates the present value ofdividends received during the nonconstant growth period and thepresent value of the stock's horizon value, which is the value atthe horizon date of all dividends expected thereafter.

Quantitative Problem 3: Assume today isDecember 31, 2018. Imagine Works Inc. just paid a dividend of $1.35per share at the end of 2018. The dividend is expected to grow at18% per year for 3 years, after which time it is expected to growat a constant rate of 5.5% annually. The company's cost of equity(r_s) is 9%. Using the dividend growth model (allowingfor nonconstant growth), what should be the price of the company'sstock today (December 31, 2018)? Do not round intermediatecalculations. Round your answer to the nearest cent.

$   per share