Question

synovec corp is experiencing rapid growth. dividends are expected to grow at 25 percent per year during the next three years, 17 percent over the following year and then 5 percent per year, indefinitely. the required return on this stock is 11 percent and the stock currently sells for 65$ per share. what is the projected dividend for the coming year?

Answer 1

Let the Dividends paid this year be D₀

=> D1 = 1.25*D₀
D2 = 1.25²*D₀
D3 = 1.25³*D₀
D4 = 1.25³*1.17*D₀
D5 = 1.25³*1.17*1.05*D₀

Rate of interest = r = 11%

Growth rate indefenitely = g = 5%

According to Gordon Growth model,

P4 = D5/(r-g)

=> P4 = 1.25³*1.17*1.05*D₀/(0.11 - 0.05)

PV of the stock = D1/(1+r) + D2/(1+r)² + D3/(1+r)³ + D4/(1+r)⁴ + P4/(1+r)⁴ = 65

=> 1.25*D₀/1.11 + 1.25²*D₀/(1.11)² + 1.25³*D₀/(1.11)³ + 1.25³*1.17*D₀/(1.11)⁴ + (1.25³*1.17*1.05*D₀/(0.11 - 0.05))/(1.11)⁴ = 65

=> 31.67D₀ = 65 => D0 = $2.05

Hence, dividend in next period = D1 = 2.05*1.25 = $2.56