Question

Determine the value of a stock with the following variables using the constant growth model: Current annual dividend: $1.20 per share Required return rate: 8% Constant growth rate: 5% a.) $26 b.) $43.20 c.) $42

Answer 1

According to the constant growth model, the value of the stock is $40.00

The calculation for the value of the stock using the constant growth model (also known as the Gordon Growth Model) step by step:

Step 1: Understand the Formula

The formula for the constant growth model is:

`\[ \text{Price} = (D_1)/(r - g) \]`

where:

-
`\( D_1 \)` is the expected dividend per share for the next period (here, we assume the dividend is constant or grows at a steady rate),

-
`\( r \)` is the required rate of return (or discount rate),

-
`\( g \)` is the constant growth rate of the dividend.

Step 2: Identify the Variables

From the information given:

- Current annual dividend
`(\( D_1 \))` = $1.20 per share

- Required return rate
`(\( r \))` = 8% or 0.08 (as a decimal)

- Constant growth rate
`(\( g \))` = 5% or 0.05 (as a decimal)

Step 3: Plug the Values into the Formula

Now, we substitute these values into the formula:

`\[ \text{Price} = (\$1.20)/(0.08 - 0.05) \]`

Step 4: Calculate the Denominator

First, calculate the difference between the required return rate and the growth rate:

`\[ 0.08 - 0.05 = 0.03 \]`

Step 5: Final Calculation

Now, divide the dividend by this difference:

`\[ \text{Price} = (\$1.20)/(0.03) \]`

`\[ \text{Price} = \$40.00 \]`

Conclusion

Therefore, according to the constant growth model, the value of the stock is $40.00. This calculation assumes that the dividend will continue to grow at a constant rate of 5% indefinitely and that the required rate of return is 8%.