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Phillips is growing and dividends are growing at a rate of 25% for the next three years, then...

Question:

Phillips is growing and dividends are growing at a rate of 25% for the next three years, then failing off to a constant 5% thereafter. If the required return is 12% and the company just paid a dividend of $3.10, what is the current share price?

Dividend Growth Model:

Companies that pay regular dividends can be valued using the growth model. The idea is to calculate the present value of all future dividend inflow to shareholders to determine the fair value. The key determinants of fair value include the steady rate of dividend growth and the required rate of return by investors.

Answer and Explanation:

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As a first step, we need to calculate the dividend and the present value of dividends for the next three years.

  • Dividend for Year 1 = {eq}3.10 * ( 125 / 100 ) = $3.88 {/eq}
  • Dividend for Year 2 = {eq}3.88 * ( 125 / 100 ) = $4.85 {/eq}
  • Dividend for Year 3 = {eq}4.85 * ( 125 / 100 ) = $6.06 {/eq}

Further, at a discount rate of 12%, the present value of dividend is as follows -

  • Present Value of Year 1 to 3 Dividends = {eq}[ 3.88 / ( 1 + 0.12 ) ^ 1 ] + [ 4.85 / ( 1 + 0.12 ) ^ 2 ] + [ 6.06 / ( 1 + 0.12 ) ^ 3 ] {/eq}
  • Present Value of Year 1 to 3 Dividends = {eq}3.46 + 3.87 + 4.31 = $11.64 {/eq}

Since dividends grow at a constant rate after year 3, we can use the growth model to calculate the stock price for year 3.

  • Stock Price (P3) = {eq}D3 * ( 1 + G ) / ( K - G ) {/eq}
  • Stock Price (P3) = {eq}6.06 * ( 1 + 0.05 ) / ( 0.12 - 0.05 ) {/eq}
  • Stock Price (P3) = {eq}$90.90 {/eq}

Once we have the year 3 stock price, the current stock price is the sum of present value of year 1 to 3 dividend and present value of year 3 stock price.

  • Stock Price (Po) = {eq}11.64 + [ 90.90 / ( 1 + 0.12 ) ^ 3 ] {/eq}
  • Stock Price (Po) = {eq}11.64 + 64.70 {/eq}
  • Stock Price (Po) = {eq}$76.34 {/eq}

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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