Question

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

Answer 1

$1.25

Step-by-step 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