T Jones Productions has been a growth firm and not been paying dividends in the past. Now they...

Question:

T Jones Productions has been a growth firm and not been paying dividends in the past. Now they are maturing and growth is moderating which allows them to begin paying dividends. The analysts forecast that the expected dividends will be:

Year 1: 0.95,

Year 2: 1.66,

Year 3: 2.17,

then are expected to grow at g = 3%.

The required rate of return of 8.10% results in an intrinsic 'value' ( {eq}V_o {/eq}) of $38.71.

If the current, market price ({eq}P_o {/eq}) is $36.70, what is the expected rate of return ({eq}E_r {/eq})?

Valuing a Stock Using the Dividend Growth Model

Stocks can be valued as a series of dividend cash flows. The dividend growth model, also known as the Gordon Growth Model, can be used to determine the price of a stock based on its forecast dividends, dividend growth, and returns required by investors.

Answer and Explanation:

The expected return is 8.37% if the share price is $36.70.

Note that a lower expected return of 8.10% produces the higher valuation of $38.71. As the required rate of return decreases, the share price rises.

A simple way to solve this problem is to construct a discounted cash flow model that values the dividends at different required rates of return. The discounted cash flow model for the valuation that yields a share price of $38.71 is pictured below. Note that we value the first 3 years of dividends individually, and then calculate a perpetuity cash flow for the constant growth rate dividends that occur after year 3. The "growth value" figure is calculated using the dividend growth model, which calculates the share price as:

  • Price = Dividend / (Required Return - Growth Rate)
  • Price = (year 3 dividend of $2.17 grown at 3%) / (8.1% - 3%)
  • Price = $2.24 / 0.051 = $43.83

We calculate the present value of this figure to obtain the dividend perpetuity value portion of the share price.

0 1 2 3 Perpetuity
Dividend Per Share $0.95 $1.66 $2.17 $2.24
Growth Value $43.83
Discount Factor@ 8.1% 1.0000 0.9251 0.8558 0.7916 0.7916
Present Value $0.8788 $1.4206 $1.7178 $34.6936
NPV $38.71

Next below is the DCF model that produces the solution for a required rate of return of 8.37%.

1 2 3 Perpetuity
Dividend Per Share $0.95 $1.66 $2.17 $2.24
Growth value $41.62
Discount Factor @8.37% 1.0000 0.9228 0.8515 0.7857 0.7857
Present Value $0.8766 $1.4135 $1.7050 $32.7036
NPV $36.70

An algebraic solution for this problem is very challenging, and will not be illustrated here.


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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