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Mobray Corp. is experiencing rapid growth. Dividends are expected to grow at 24 percent per year during the next three years, 14 percent over the following year, and then 8 percent per year indefinitely. The required return on this stock is 10 percent, and the stock currently sells for $86 per share. What is the projected dividend for the coming year

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jepessoa

Answer:

$1.25

Explanation:

dividend growth:

year               growth rate        dividends

1                          24%                  Div₁ = 1.24Div₀

2                         24%                  Div₂ = 1.24²Div₀ = 1.5376Div₀

3                         24%                  Div₃ = 1.24³Div₀ = 1.906624Div₀

4                          14%                  Div₄ = 1.906624Div₀ x 1.14 = 2.17355136Div₀

indefinite              8%                  Div₅ = 2.17355136Div₀ x 1.08 = 2.347435Div₀

required rate of return = 10%

current stock price = $86

stock price for terminal growth rate = Div₅ / (10% - 8%) = Div₅ / 2% = 117.3717734Div₀

current stock price = $86 = 1.24Div₀/1.1 + 1.5376Div₀/1.1² + 1.906624Div₀/1.1³ + 2.17355136Div₀/1.1⁴ + 117.3717734Div₀/1.1⁴ = 1.12727Div₀ + 1.27074Div₀ + 1.43247Div₀ + 1.48456Div₀ + 80.1665Div₀ = 85.48154Div₀

$86 = 85.48154Div₀

Div₀ = $86 / 85.48154 = $1.006065

Div₁ = 1.24 x $1.006065 = $1.2475 ≈ $1.25

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