This is the generalized stock valuation model. We will now look at $3$ different situations where we can adapt this generalized model to each of these situations to determine a stock's intrinsic value:

$1.$ Constant Growth Stocks;

$2.$ Zero Growth Stocks;

$3.$ Nonconstant Growth Stocks.

Constant Growth Stocks:

For many companies it is reasonable to predict that dividends will grow at a constant rate, so we can rewrite the generalized model as follows:

This is known as the constant growth model or Gordon model, named after Myron J$.$ Gordon who developed and popularized it$.$ There are several conditions that must exist before this equation can be used. First, the required rate of return, rs$,$ must be greater than the long$-$run growth rate, g$.$ Second, the constant growth model is not appropriate unless a company's growth rate is expected to remain constant in the future. This condition almost never holds for

start$-$up

firms, but it does exist for many

mature

companies.

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

The growth rate is zero.

The growth rate is negative.

The required rate of return is greater than the growth rate.

The required rate of return is more than $50\%.$

None of the above assumptions would invalidate the model.

Statement b

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Quantitative Problem $1$: Hubbard Industries just paid a common dividend, D$0,$ of $$1\mathrm{.}00.$ It expects to grow at a constant rate of $4\%$ per year. If investors require a $11\%$ return on equity, what is the current price of Hubbard's common stock? Do not round intermediate calculations. Round your answer to the nearest cent.

$

per share

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Realize that the correct valuation equation to use is the constant growth model.

Understand that the dividend given in the problem has just been paid so it is only used to calculate the dividend expected to be paid next year. So you must calculate D$1$ in the valuation equation as D$0\backslash$times $(1+$ g$).$

Remember the correct order of mathematical operations. You will calculate the numerator as shown above and then calculate the denominator as the difference between the required return on equity and the constant growth rate. Then you can proceed with dividing the numerator by the denominator.

Zero Growth Stocks:

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

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

Quantitative Problem $2$: Carlysle Corporation has perpetual preferred stock outstanding that pays a constant annual dividend of $$1\mathrm{.}00$ at the end of each year. If investors require an $7\%$ return on the preferred stock, what is the price of the firm's perpetual preferred stock? Round your answer to the nearest cent.

$

per share

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Understand that the dividend payment represents an annuity.

Refer to the valuation equation for a perpetual preferred stock.

Make sure that you use correct decimal for return number in the denominator.

Nonconstant Growth Stocks:

For many companies, it is not appropriate to assume that dividends will grow at a constant rate. Most firms go through life cycles where they experience different growth rates during different parts of the cycle. For valuing these firms, the generalized valuation and the constant growth equations are combined to arrive at the nonconstant growth valuation equation:

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

Quantitative Problem $3$: Assume today is December $31,2019.$ Imagine Works Inc. just paid a dividend of $$1\mathrm{.}25$ per share at the end of $2019.$ The dividend is expected to grow at $12\%$ per year for $3$ years, after which time it is expected to grow at a constant rate of $6\%$ annually. The company's cost of equity $($rs$)$ is $9\mathrm{.}5\%.$ Using the dividend growth model $($allowing for nonconstant growth$),$ what should be the price of the company's stock today $($December $31,2019)?$ Do not round intermediate calculations. Round your answer to the nearest cent.

$

per share