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"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

Respuesta :

letmeanswer

Solution:

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

[tex]D_{1}[/tex] = $3.10 • (1 + .20) = $3.10 • 1.20 = $3.720

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

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

[tex]D_{4}[/tex] = $5.357 • (1 + 05) = $5.624

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

[tex]P_{0}[/tex] = [tex]D_{1} + D_{2} + D_{3} + P_{3}[/tex] =(1 + R) [tex](1 + R) ^{2} (1 + R)^{3}[/tex]

= $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

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