Jen's Fashions is growing quickly. Dividends are expected to grow at a 19 percent rate for the next 3 years, with the growth rate falling off to a constant 8 percent thereafter. The required return is 12 percent and the company just paid a $3.80 annual dividend. What is the current share price?

Hi, we first have to establish the dividend for the first 3 years and the dividend when the growth rate falls off to a constant rate of 8% with the formula to find the present value of a perpetuity with constant growth rate. From there, we need to bring all the above cash flows to present value and that is the price of the share. The formula is as follows.

[tex]Price=\frac{D1}{(1+r)^{1}}+\frac{D2}{(1+r)^{2} } +\frac{D3}{(1+r)^{3} } +\frac{D3(1+g)}{(r-g)} \frac{1}{(1+r)^{3} }[/tex]

To find D1, D2,and D3, we have to do this.

D1=Do(1+0.19)

D2=D1(1+0.19)

D3=D2(1+0.19)

Since 0.19 is the growth rate for 3 years. Everything should look like this

[tex]Price=\frac{4.04}{(1+0.12)^{1}}+\frac{4.29}{(1+0.12)^{2} } +\frac{25.52}{(1+0.12)^{3} } +\frac{25.52(1-0.08)}{(0.12+0.08)} \frac{1}{(1+0.12)^{3} } =33.85[/tex]

notice that the sign of the last part do not coincide with the formula, that is because the growth rate from the first 3 years is -8%.

Best of luck.