Question

goode inc.'s stock has a required rate of return of 11.50%, and it sells for $26.00 per share. goode's dividend is expected to grow at a constant rate of 7.00%. what was the last dividend, d0? group of answer choices $0.83 $1.37 $1.27 $1.09 $0.90

Answer 1

Using the Gordon Growth Model and given values for current stock price ($26.00), dividend growth rate (7%), and required rate of return (11.5%), the last dividend paid by Goode Inc. is approximately $1.09.

Step-by-step explanation:

The student's question pertains to finding the last dividend paid (d0) by Goode Inc. given the current share price, expected dividend growth rate, and the required rate of return. To solve this, we can use the Gordon Growth Model (also known as the dividend discount model) which can be expressed as P0 = D0(1 + g) / (r - g), where P0 is the current stock price, D0 is the last dividend paid, g is the growth rate of dividends, and r is the required rate of return. Substituting the values provided (P0 = $26.00, g = 7%, and r = 11.5%) and solving for D0 gives us the last dividend paid by Goode Inc.

First, let's rearrange the formula to solve for D0: D0 = P0(r - g) / (1 + g). Plugging in the numbers: D0 = $26.00(0.115 - 0.07) / (1 + 0.07). Simplifying this expression, we find that D0 is approximately $1.09.

Answer 2

The last dividend
`, \(d₀\)`, for Goode Inc. is $1.09. This value is calculated using the Gordon Growth Model, considering the company's stock price, required rate of return, and expected constant growth rate of dividends.

Step-by-step explanation:

To calculate the last dividend, we can use the Gordon Growth Model, which is given by the formula:

`\[ P_0 = (D_0 * (1 + g))/(r - g) \]`

where:

`\( P_0 \) = Current stock price = $26.00,`

`\( D_0 \) = Last dividend,`

`\( r \) = Required rate of return = 11.50% or 0.115, and`

`\( g \) = Dividend growth rate = 7.00% or 0.07.`

Rearranging the formula to solve for
`\( D_0 \)`:

`\[ D_0 = (P_0 * (r - g))/(1 + g) \]`

Substituting the given values:

`\[ D_0 = (\$26.00 * (0.115 - 0.07))/(1 + 0.07) \]`

`\[ D_0 = (\$26.00 * 0.045)/(1.07) \]`

`\[ D_0 = (\$1.17)/(1.07) \]`

`\[ D_0 \approx \$1.09 \]`

Therefore, the last dividend,
`\( d_0 \),` for Goode Inc. is approximately $1.09. This is the amount per share that was paid as the last dividend, and it aligns with the company's expected constant growth rate and the required rate of return for investors.