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 D_{0}

=> D1 = 1.25*D_{0}

D2 = 1.25^{2}*D_{0}

D3 = 1.25^{3}*D_{0}

D4 = 1.25^{3}*1.17*D_{0}

D5 = 1.25^{3}*1.17*1.05*D_{0}

Rate of interest = r = 11%

Growth rate indefenitely = g = 5%

According to Gordon Growth model,

P4 = D5/(r-g)

=> P4 = 1.25^{3}*1.17*1.05*D_{0}/(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*D_{0}/1.11 +
1.25^{2}*D_{0}/(1.11)^{2} +
1.25^{3}*D_{0}/(1.11)^{3} +
1.25^{3}*1.17*D_{0}/(1.11)^{4} +
(1.25^{3}*1.17*1.05*D_{0}/(0.11 -
0.05))/(1.11)^{4} = 65

=> 31.67D_{0} = 65 => D0 = $2.05

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

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