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

a$.$ The growth rate is zero.

b$.$ The growth rate is negative.

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

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

e$.$ None of the above assumptions would invalidate the model.

Quantitative Problem $1$: Hubbard Industries just paid a common dividend, $D0,$ of $$2\mathrm{.}00.$ It expects to grow at a constant rate of $4\%$ per year. If investors require a $8\%$ return on equity, what is the current price of Hubbard's common stock? Do not round intermediate calculations. Round your answer to the neare cent.

$ per share

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:

widehat$(P{)}_0=\frac{D}{I^{\text{'}}}$

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{.}20$ at the end of each year. If investors require an $10\%$ 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

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: