Question

"Synovec Co. is growing quickly. Dividends are expected to grow at a rate of 20 percent for the next three years, with the growth rate falling off to a constant 5 percent thereafter. If the required return is 11 percent, and the company just paid a dividend of $3.10, what is the current share price

Answer 1

Solution:

$D_{0}$ = $3.10, $D_{1} - D_{3}$= 20%, $D_{4}$ += 5%, R = 11%

$D_{1}$ = $3.10 • (1 + .20) = $3.10 • 1.20 = $3.720

$D_{2}$ = $3.10 • $(1 + .20)^{2}$ = $3.10 • 1.44 = $4.464

$D_{3}$ = $3.10 • $(1 + .20)^{3}$= $3.10 • 1.728 = $5.357

$D_{4}$ = $5.357 • (1 + 05) = $5.624

$P_{3}$ = $D_{4}$ / (R – g)= $5.624 / 0.06= $93.744

$P_{0}$ = $D_{1} + D_{2} + D_{3} + P_{3}$ =(1 + R) $(1 + R) ^{2} (1 + R)^{3}$

= $3.720 + $4.464 + $5.357 + $93.744

=  (1 + .11) (1 + .11)2(1 + .11)3= $3.720 + $4.464 + $99.101

=(1.11) (1.11)2(1.11)3= $3.720 + $4.464 + $99.101

=1.11 1.232 1.368= $3.351 + $3.623 + $72.462 = $79.44