Suppose we have used analysts’ estimates to determine that the market believes our dividends will grow at 6% per year and our last dividend was $2.  Our stock is currently selling for $42.4. What is our cost of equity?

a.            5  b. 6  c. 7   d. 8   e.  9   f.    10  g. 11  h. 12   i. 14   j. 16

To calculate the cost of equity using the Dividend Discount Model (DDM), specifically the Gordon Growth Model, we use the following formula:

\[
r_e = \frac{D_1}{P_0} + g
\]

Where:
- $ r_e $ = Cost of equity
- $ D_1 $ = Dividend expected in the next year
- $ P_0 $ = Current price of the stock
- $ g $ = Growth rate of dividends

Given:
- Last dividend ($ D_0 $) = $2
- Growth rate ($ g $) = 6% or 0.06
- Current stock price ($ P_0 $) = $42.4

First, calculate $ D_1 $ (the expected dividend for the next year):

\[
D_1 = D_0 \times (1 + g) = 2 \times (1 + 0.06) = 2 \times 1.06 = 2.12
\]

Now, plug $ D_1 $, $ P_0 $, and $ g $ into the formula for $ r_e $:

\[
r_e = \frac{2.12}{42.4} + 0.06
\]

\[
r_e = 0.05 + 0.06 = 0.11
\]

So, the cost of equity $ r_e $ is approximately **11%**, which corresponds to **g. 11**.

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Would you like a more detailed explanation or have any other questions?

Here are some related questions you might be interested in:
1. How does the growth rate of dividends affect the cost of equity?
2. What are the limitations of the Gordon Growth Model?
3. How would a higher stock price impact the cost of equity?
4. What other models can be used to estimate the cost of equity?
5. How would a decrease in dividend growth rate affect the cost of equity?

**Tip:** The Gordon Growth Model is best suited for companies with stable and predictable dividend growth rates. For companies with more volatile dividends, alternative models like the Capital Asset Pricing Model (CAPM) might be more appropriate.

Learn how to calculate the cost of equity using analysts' estimates, dividend growth rate, and current stock price. Solve the problem step-by-step with a detailed explanation of the Dividend Discount Model and Gordon Growth Model. Suitable for finance professionals and graduate-level students.

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