Questions: Assume Evoo, Ino, has a current stock price of 37 and will pay a 1.75 dividend in one year; its equity cost of capital is 11%. What price must you expect Evoo stock to sell for immediately after the firm pays the dividend in one year to justify its current price? The expected price is . (Round to the nearest cent.)

Assume Evoo, Ino, has a current stock price of 37 and will pay a 1.75 dividend in one year; its equity cost of capital is 11%. What price must you expect Evoo stock to sell for immediately after the firm pays the dividend in one year to justify its current price?

The expected price is . (Round to the nearest cent.)

Transcript text: Assume Evoo, Ino, has a current stock price of $\$ 37$ and will pay a $\$ 1.75$ dividend in one year; its equity cost of capital is $11 \%$. What price must you expect Evoo stock to sell for immediately after the firm pays the dividend in one year to justify its current price? The expected price is $\$$ $\square$ . (Round to the nearest cent.)

Solution

Solution Steps

To find the expected price of Evoo stock in one year, we can use the Dividend Discount Model (DDM). The formula for the price of a stock today is given by:

\[ P_0 = \frac{D_1 + P_1}{1 + r} \]

Where:

$ P_0 $ is the current stock price (\$37)
$ D_1 $ is the dividend in one year (\$1.75)
$ P_1 $ is the expected price of the stock in one year
$ r $ is the equity cost of capital (11% or 0.11)

We need to solve for $ P_1 $.

Step 1: Given Values

We start with the following values:

Current stock price, $ P_0 = 37 $
Dividend in one year, $ D_1 = 1.75 $
Equity cost of capital, $ r = 0.11 $

Step 2: Rearranging the Formula

Using the Dividend Discount Model, we have the equation: \[ P_0 = \frac{D_1 + P_1}{1 + r} \] Rearranging this to solve for $ P_1 $: \[ P_1 = P_0 \cdot (1 + r) - D_1 \]

Step 3: Substituting Values

Substituting the known values into the equation: \[ P_1 = 37 \cdot (1 + 0.11) - 1.75 \] Calculating $ P_1 $: \[ P_1 = 37 \cdot 1.11 - 1.75 = 41.07 - 1.75 = 39.32 \]