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A Stock pays dividends of $1.00 at t = 1 (D1 is provided, not D0). It is growing at 20% between t...

Question:

A Stock pays dividends of $1.00 at t = 1 (D1 is provided, not D0). It is growing at 20% 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 15%, what should be the value of the stock at t = 0?

Valuation Using Dividend Growth Model

Dividend growth model is a model that is used to determine the value of a stock. If a stock pays dividends,the total amount of the present value of all the future cash flows/dividends is the value of the stock.

Answer and Explanation:

To compute the the price of the common stock using the dividend growth model we use the formula below;-

{eq}P_o = D1/(1+r)^1 + D2/(1+r)^2 +D3/(1+r)^3...........+Dn/(1+r)^n + Dn(1+g)/(r-g)/(1+r)^n {/eq}

Where;-

  • D1,D2,D3,D4.....Dn are dividends issued at different periods
  • Po -The price of the common stock
  • r- Required rate of return
  • g -growth rate

Given;-

  • D1 = 1
  • g = 20% for year 2
  • D2 = 1(1+0.2) = 1.2

Terminal value given a constant growth of 10%

{eq}*Terminal\ value = D3 / (Ke - g) {/eq}

{eq}*Terminal\ value = 12(1+0.1) / (0.15-0.1) = 26.4 {/eq}

Computing the value at time t= 0 we get....

{eq}*P_o = 1/(1+0.15)^1 + (1.2+26.4)/(1+0.15)^2 = 21.74 {/eq}

The value of the stock at time t=0 is $21.74


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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