Sorenson Corp.'s expected year-end dividend is D₁ = $4.00,its required return is r_s = 11.00%,its dividend yield is 6.00%,and its growth rate is expected to be constant in the future.What is Sorenson's expected stock price in 7 years,i.e. ,what is $\tilde { P } _ { 7 }$
? Do not round intermediate calculations.

Question

Sorenson Corp.'s expected year-end dividend is D₁ = $4.00,its required return is r_s = 11.00%,its dividend yield is 6.00%,and its growth rate is expected to be constant in the future.What is Sorenson's expected stock price in 7 years,i.e. ,what is

\tilde { P } _ { 7 }

? Do not round intermediate calculations.

Quizplus · Accepted Answer

The expected stock price in 7 years, $\tilde { P } _ { 7 }$, can be calculated using the dividend discount model for a constantly growing dividend, which is given by the formula: $$P_0 = \frac{D_0 \times (1 + g)}{r - g}$$ where $P_0$ is the current stock price, $D_0$ is the most recent dividend paid, $r$ is the required return, and $g$ is the growth rate. Given that the dividend yield is 6.00% and the expected year-end dividend is $4.00, we can calculate the current stock price ($P_0$) and then project it 7 years into the future.First, we find the growth rate ($g$) using the relationship between dividend yield, required return ($r$), and growth rate ($g$): $$r = \text{Dividend Yield} + g$$ $$11.00\% = 6.00\% + g$$ $$g = 5.00\%$$Now, we calculate the current stock price ($P_0$) using the given dividend ($D_1 = $4.00$), required return ($r = 11.00\%$), and growth rate ($g = 5.00\%$): $$P_0 = \frac{$4.00}{0.11 - 0.05} = \frac{$4.00}{0.06} = $66.67$$To find the expected stock price in 7 years ($\tilde { P } _ { 7 }$), we grow $P_0$ at the growth rate ($g$) for 7 years: $$\tilde { P } _ { 7 } = P_0 \times (1 + g)^7 = $66.67 \times (1 + 0.05)^7 = $66.67 \times 1.4071 = $93.81$$Therefore, the expected stock price in 7 years is $93.81.

Sorenson Corp P~7\tilde { P } _ { 7 }P~7​ ? Do Not Round Intermediate Calculations

Sorenson Corp $\tilde { P } _ { 7 }$ ? Do Not Round Intermediate Calculations