A stock pays dividends of $1.00 at t=1. (D1 is provided here, not D0) It is growing at 35%...

Question:

A stock pays dividends of $1.00 at t=1. (D1 is provided here, not D0) It is growing at 35% between t=1 and t=2, after which the growth rate drops to 10%, and will continue at that rate into the future. If the discount rate for this stock is 12%, what should be the value of the stock at t=0? Hint: Make a diagram indicating ranges of the growth rates and the resulting dividends.

a. $53.04

b. $21.74

c. $55.70

d. $58.41

e. $61.16

A stock pays dividends of $1.00 at t=1 (t=1 NOT t=0). Dividends are expected to grow at a constant rate of 14% into the future. With a discount rate of 24%, what should the price of the stock be at t=1? (price needed for t=1 NOT t=0) (hint: there is more than one way to do this problem).

a. $11.20

b. $11.40

c. $11.60

d. $11.80

e. $12.00

Dividend Gordon Growth Model:

Dividend Gordon growth model is a stock valuation model that calculates the fair market value of the stock based on the present value of the future dividends of the company.

Answer and Explanation:

Question (a)

Calculate the value of the stock at t=0 using the two stage dividend growth model:

{eq}Stock~value=\displaystyle\sum_{t=0}^{n} \frac{D}{(1+r)^{t}} + \frac{\frac{D_{n}*(1+g)}{k-g}}{(1+r)^{n}}\\ where:\\ D=dividend\\ r=discount~rate\\ t=respective~period\\ D_{n}=value~of~issued~dividend~prior~to~constant~growth\\ g=constant~growth~rate\\ n=number~of~periods\\ {/eq}

{eq}\begin{align*} Stock~value&=\frac{1.00}{(1+.12)^{1}}+\frac{1.00*(1+.35)}{(1+.12)^{2}}+\frac{\frac{1.00*(1+.35)*(1+.10)}{.12-.10}}{(1+.12)^{2}}\\ &=\frac{1.00}{1.1200}+\frac{1.35}{1.2544}+\frac{\frac{1.4850}{.02}}{1.2544}\\ &=.829+1.0762+\frac{74.25}{1.2544}\\ &=1.9691+59.1916\\ &=61.1607 \end{align*} {/eq}

The market value of the stock in t=0 is E. $61.16

Question (b)

The market value of the stock can be calculated using the dividend growth model:

{eq}Stock~value=\dfrac{D*(1+g)}{k-g}\\ where:\\ D=dividend\\ g=growht~rate\\ k=required~return\\ {/eq}

{eq}\begin{align*} Stock~value&=\dfrac{1.00*(1+.14)}{.24-.14}\\ &=\dfrac{1.14}{.10}\\ &=11.40 \end{align*} {/eq}

The market value of the stock is B. $11.40


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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