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Question:Ecology Labs Inc. will pay a dividend of \(6.40 per share in the next 12 months (D1). The required rate of return (Ke) is 14 percent and the constant growth rate is 5 percent.

a. Compute P0. (For parts b, c, and d in this problem, all variables remain the same except the one specifically changed. Each question is independent of the others.)

b. Assume Ke, the required rate of return, goes up to 18 percent. What will be the new value of P0?

c. Assume the growth rate (g) goes up to 9 percent. What will be the new value of P0? Ke goes back to its original value of 14 percent.

d. Assume D1 is \)7.00. What will be the new value of P0? Assume Ke is at its original value of 14 percent and g goes back to its original value of 5 percent.

Step by step solution

01

Computation of Price of stock for part a

$$\begin{gathered} \mathbf{Price}\mathbf{}\mathbf{of}\mathbf{}\mathbf{stock}\mathbf{\left(}\mathbf{P}\mathbf{0}\mathbf{\right)}\mathbf{=}\frac{\mathbf{D}\mathbf{1}}{\left(\mathbf{Requiredrate}\mathbf{}\mathbf{of}\mathbf{}\mathbf{return}\mathbf{-}\mathbf{Growth}\mathbf{}\mathbf{Rate}\right)} \\ \mathbf{=}\frac{\mathbf{\$}\mathbf{6}\mathbf{.}\mathbf{40}}{\left(\mathbf{0}\mathbf{.}\mathbf{14}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{05}\right)} \\ \mathbf{=}\mathbf{\$}\mathbf{71}\mathbf{.}\mathbf{11} \end{gathered}$$

02

 Step 2: Computation of Price of stock for part b

$$\begin{gathered} \mathbf{Price}\mathbf{}\mathbf{of}\mathbf{}\mathbf{stock}\mathbf{\left(}\mathbf{P}\mathbf{0}\mathbf{\right)}\mathbf{=}\frac{\mathbf{D}\mathbf{1}}{\left(\mathbf{NewRequired}\mathbf{}\mathbf{rate}\mathbf{}\mathbf{of}\mathbf{}\mathbf{return}\mathbf{-}\mathbf{Growth}\mathbf{}\mathbf{Rate}\right)} \\ \mathbf{=}\frac{\mathbf{\$}\mathbf{6}\mathbf{.}\mathbf{40}}{\left(\mathbf{0}\mathbf{.}\mathbf{18}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{05}\right)} \\ \mathbf{=}\mathbf{\$}\mathbf{49}\mathbf{.}\mathbf{23} \end{gathered}$$

03

 Step 3 Computation of Price of stock for part c

$$\begin{gathered} \mathbf{Price}\mathbf{}\mathbf{of}\mathbf{}\mathbf{stock}\mathbf{\left(}\mathbf{P}\mathbf{0}\mathbf{\right)}\mathbf{=}\frac{\mathbf{D}\mathbf{1}}{\left(\mathbf{Requiredrate}\mathbf{}\mathbf{of}\mathbf{}\mathbf{return}\mathbf{-}\mathbf{New}\mathbf{}\mathbf{Growth}\mathbf{}\mathbf{Rate}\right)} \\ \mathbf{=}\frac{\mathbf{\$}\mathbf{6}\mathbf{.}\mathbf{40}}{\left(\mathbf{0}\mathbf{.}\mathbf{14}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{09}\right)} \\ \mathbf{=}\mathbf{\$}\mathbf{128} \end{gathered}$$

04

Computation of Price of stock for part d

$$\begin{gathered} \mathbf{Price}\mathbf{}\mathbf{of}\mathbf{}\mathbf{}\mathbf{stock}\mathbf{\left(}\mathbf{P}\mathbf{0}\mathbf{\right)}\mathbf{=}\frac{\mathbf{NewD}\mathbf{1}}{\left(\mathbf{Required}\mathbf{}\mathbf{rate}\mathbf{}\mathbf{of}\mathbf{}\mathbf{return}\mathbf{-}\mathbf{Growth}\mathbf{}\mathbf{Rate}\right)} \\ \mathbf{=}\frac{\mathbf{\$}\mathbf{8}}{\left(\mathbf{0}\mathbf{.}\mathbf{14}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{05}\right)} \\ \mathbf{=}\mathbf{\$}\mathbf{88}\mathbf{.}\mathbf{89} \end{gathered}$$

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