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Synovec co. is growing quickly. dividends are expected to grow at a rate of 25 percent for the next three years, with the growth rate falling off to a constant 6 percent thereafter. if the required return is 11 percent, and the company just paid a dividend of $1.15, what is the current share price

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Edufirst

Answer:

  • $25.42

Explanation:

The price of a stock is the present value of the future dividends.

1. Dividends for the next three years:

Considering the dividends are expected to grow at a rate of 25% for the next three years:

  • One year from now: Dividend = $1.15 × 1.25 = $1.44
  • Two years from now: Dividend = $1.15 × (1.25)² = $1.80
  • Three years from now: Divident = $1.15 × (1.25)³ = $2.25

2. Calculate the present value, A,  of those three dividends at the required return rate of 11%.

      [tex]A=\dfrac{\$1.44}{1.11}+\dfrac{\$1.80}{1.11^2}+\dfrac{\$2.25}{1.11^3}[/tex]

      [tex]A=\$4.40[/tex]

3. Calculate the value of the dividends from year 4.

The formula for the price of a stock when the dividends, D, paid since the next year, will grow at a constant rate, g, less than the expected return, r is.

    [tex]Price=\dfrac{D}{r-g}[/tex]

Here, D = $1.15 × 1.25,  g = 6% and r = 11%

    [tex]Price=\dfrac{\$1.15\times 1.25}{0.11-0.06}[/tex]

    [tex]Price=\dfrac{\$1.15\times 1.25}{0.11-0.06}=\$28.75[/tex]

That price must be discounted from the year 3 to the current year:

      [tex]B=\dfrac{\$28.75}{1.11^3}=\$21.02[/tex]

4. Add the values of the two streams of dividends, A + B

  • A + B = $4.40 + $21.02 = $25.42 ← answer

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