Sisters Corporation expects to earn $6 per share next year. The firm’s ROE is 15% and its plowback ratio is 60%. The firm’s market capitalization rate is 10%.

Required:
Calculate the price with the constant dividend growth model.

Note: Do not round intermediate calculations.



Calculate the price with no growth.



What is the present value of its growth opportunities?

Note: Do not round intermediate calculations.



To solve this problem, we will use the following formulas:

1. **Constant Dividend Growth Model (Gordon Growth Model):**
   \[
   P_0 = \frac{D_1}{r - g}
   \]
   where:
   - $P_0$ is the current price of the stock,
   - $D_1 = \text{Earnings per share} \times (1 - \text{Plowback ratio})$ is the dividend for the next year,
   - $r$ is the market capitalization rate (required rate of return),
   - $g = \text{ROE} \times \text{Plowback ratio}$ is the growth rate of dividends.

2. **Price with No Growth (Zero-Growth Model):**
   \[
   P_0 = \frac{D_1}{r}
   \]
   where $D_1$ is the dividend per share for the next year, assuming no growth.

3. **Present Value of Growth Opportunities (PVGO):**
   \[
   PVGO = P_0 (\text{with growth}) - P_0 (\text{no growth})
   \]

---

### Step 1: Find the growth rate $g$
Using the ROE and plowback ratio:
\[
g = \text{ROE} \times \text{Plowback ratio} = 15\% \times 60\% = 0.15 \times 0.60 = 0.09 \text{ or } 9\%
\]

### Step 2: Calculate the dividend per share $D_1$
The dividend is calculated from the earnings and plowback ratio:
\[
D_1 = 6 \times (1 - 0.60) = 6 \times 0.40 = 2.4
\]

### Step 3: Calculate the stock price with growth using the Gordon Growth Model
\[
P_0 = \frac{D_1}{r - g} = \frac{2.4}{0.10 - 0.09} = \frac{2.4}{0.01} = 240
\]

### Step 4: Calculate the stock price with no growth
With no growth, we simply use:
\[
P_0 (\text{no growth}) = \frac{D_1}{r} = \frac{2.4}{0.10} = 24
\]

### Step 5: Calculate the present value of growth opportunities (PVGO)
\[
PVGO = P_0 (\text{with growth}) - P_0 (\text{no growth}) = 240 - 24 = 216
\]

---

### Final Results:
1. **Price with the constant dividend growth model:** $P_0 = 240$
2. **Price with no growth:** $P_0 = 24$
3. **Present Value of Growth Opportunities (PVGO):** 216

Would you like more details or have any questions?

Here are 5 related questions:
1. What happens to the stock price if the ROE increases to 20%?
2. How would the price change if the plowback ratio is decreased to 40%?
3. How does the market capitalization rate affect the stock price under this model?
4. What are the limitations of the constant dividend growth model?
5. How can the PVGO help in investment decision-making?

**Tip:** The dividend growth model assumes constant growth forever, which may not be realistic for all companies.

Sisters Corporation expects to earn $6 per share next year. The firm’s ROE is 15% and its plowback ratio is 60%. The firm’s market capitalization rate is 10%. Calculate the price with the constant dividend growth model. Calculate the price with no growth. What is the present value of its growth opportunities? Note: Do not round intermediate calculations.

Calculate the stock price of Sisters Corporation using the constant dividend growth model. Learn how to determine stock price with growth, no growth, and the present value of growth opportunities (PVGO) using detailed formulas like the Gordon Growth Model. Given: $6 earnings per share, 15% ROE, 60% plowback ratio, and 10% market capitalization rate. Ideal for undergraduate finance and MBA students.

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