Great Pumpkin Garms just paid a dividend of $3.50 on its stock. The growth rate in dividends is...

Question:

Great Pumpkin Farms just paid a dividend of $3.50 on its stock. The growth rate in dividends is expected to be a constant 5% per year indefinitely. Investors require a 16% return on the stock for the first 3 years, a 14% return on the stock for the next 3 years and an 11% return thereafter.

What should be the current share price?

Dividend growth model

The Dividend growth model is a stock valuation model that is used to determine the fair market value of a stock based on its future dividend payments.

Answer and Explanation:

The current market price of the stock can be calculated using the two stage dividend discount model with the following formula.

{eq}Stock~value=\displaystyle \sum \frac{D*(1+g)^{n}}{(1+k)^{n}}+\frac{\frac{D_{1}*(1+g)}{k-g}}{(1+k)^{n}}\\ whereas:\\ D=dividend\\ g=constant~growth~rate\\ n=number~of~periods\\ k=required~return\\ {/eq}


{eq}\begin{align*} Stock~value&=\frac{3.50*(1+.05)^{1}}{(1+.16)^{1}}+\frac{3.50*(1+.05)^{2}}{(1+.16)^{2}}+\frac{3.50*(1+.05)^{3}}{(1+.16)^{3}}+\frac{3.50*(1+.05)^{4}}{(1+.14)^{4}}+\frac{3.50*(1+.05)^{5}}{(1+.14)^{5}}+\frac{3.50*(1+.05)^{6}}{(1+.14)^{6}}+\frac{\frac{3.50*(1+.05)^{6}*(1+.05)}{.11-.05}}{(1+.11)^{6}}\\ &=\frac{3.50*1.05000}{1.16000}+\frac{3.50*1.10250}{1.34560}+\frac{3.50*1.15763}{1.56090}+\frac{3.50*1.21551}{1.68896}+\frac{3.50*1.27628}{1.92541}+\frac{3.50*1.34010}{2.19497}+\frac{\frac{3.50*1.34010*1.05}{.06}}{1.870415}\\ &=\frac{3.67500}{1.16000}+\frac{3.85875}{1.34560}+\frac{4.05169}{1.56090}+\frac{4.25427}{1.68896}+\frac{4.46699}{1.92541}+\frac{4.69033}{2.19497}+\frac{\frac{4.92485}{.06}}{1.870415}\\ &=3.16810+2.86768+2.59574+2.51887+2.32001+2.13685+\frac{82.08086}{1.870415}\\ &=15.60726+43.88378\\ &=59.43 \end{align*} {/eq}

The current market value of the stock is $59.43


Learn more about this topic:

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The Dividend Growth Model

from Finance 101: Principles of Finance

Chapter 14 / Lesson 3
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