Bucky Inc. just paid a quarterly dividend of $0.51. They have been increasing their dividends by 2.0% per quarter and are expected to continue doing so. How much can they expect to receive for each new share of stock offered if investors require a return of 12% APR with quarterly compounding?

Round your answer to the nearest penny.

For example, $1,234.5678 is 1,234.57

Do not enter the $ sign. You can enter commas

We are given the following information:

- Quarterly dividend: $ D_0 = 0.51 $
- Dividend growth rate per quarter: $ g = 0.02 $
- Required return per year (APR): $ r = 0.12 $
- Compounding frequency: Quarterly, so the quarterly required return is $ r_q = \frac{0.12}{4} = 0.03 $.

The stock price is given by the **Dividend Discount Model (DDM)** for a growing dividend, which is:

\[
P_0 = \frac{D_1}{r_q - g}
\]

Where:
- $ P_0 $ is the price of the stock,
- $ D_1 $ is the dividend at the next period, which can be calculated as $ D_1 = D_0 \times (1 + g) $,
- $ r_q $ is the required quarterly return (0.03),
- $ g $ is the growth rate of the dividend (0.02).

### Step 1: Calculate $ D_1 $
\[
D_1 = 0.51 \times (1 + 0.02) = 0.51 \times 1.02 = 0.5202
\]

### Step 2: Calculate the stock price
\[
P_0 = \frac{0.5202}{0.03 - 0.02} = \frac{0.5202}{0.01} = 52.02
\]

Thus, the price of the stock is **52.02**.

Would you like further details or have any questions?

Here are 5 related questions you might explore:
1. How does the stock price change if the growth rate increases to 3% per quarter?
2. What happens to the stock price if the required return increases to 14% APR?
3. How would the model change for annual compounding instead of quarterly?
4. Can you calculate the price if dividends are expected to remain constant instead of growing?
5. How does inflation impact the interpretation of dividend growth models?

**Tip:** When using the dividend discount model, remember that the required return must always be higher than the dividend growth rate for the formula to work.

Bucky Inc. just paid a quarterly dividend of $0.51. They have been increasing their dividends by 2.0% per quarter and are expected to continue doing so. How much can they expect to receive for each new share of stock offered if investors require a return of 12% APR with quarterly compounding?

Discover how to calculate the stock price using the Dividend Discount Model when given a quarterly dividend of $0.51, a growth rate of 2% per quarter, and a 12% APR with quarterly compounding. This detailed solution walks through the key finance concepts and formulas used, including DDM and growth rate calculations. Perfect for college-level finance students.

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