Summer Co. expects to pay a dividend of $4.00 per share—one year from now—out of earnings of $7.50 per share. If the required rate of return on the stock is 15 percent and its dividends are growing at a constant rate of 10 percent per year, calculate the present value of growth opportunities for the stock (PVGO). (Hint 1: b =1- Dividend/Earnings) (Hint 2: you will need to re-arrange g=ROE x b to get ROE!) Group of answer choices $50 $80 $30 $26

**Step 1: Calculate Retention Ratio**
Given formula:
b = 1 - \frac{D}{E}
Given values:
D = \ (D1)
E = \
Substitute values:
b = 1 - \frac{4.00}{7.50}
b = 1 - 0.5333
b \approx 0.4667

**Step 2: Calculate Return on Equity (ROE)**
Given relationship:
g = ROE \times b
Given growth rate:
g = 10\% or 0.10
Substitute retention ratio:
0.10 = ROE \times 0.4667
ROE = \frac{0.10}{0.4667}
ROE \approx 0.214 or 21.4\%

**Step 3: Calculate Stock Price ( P )**
Using Gordon Growth Model:
P = \frac{D_1}{r - g}
Given values:
D_1 = \
r = 15\% or 0.15
g = 10\% or 0.10
Substitute values:
P = \frac{4.00}{0.15 - 0.10}
P = \frac{4.00}{0.05}
P = \

**Step 4: Calculate PVGO**
Using PVGO formula:
PVGO = P - \frac{E}{r}
Given values:
P = \
E = \
r = 15\% or 0.15
Substitute values:
PVGO = 80.00 - \frac{7.50}{0.15}
PVGO = 80.00 - 50.00
PVGO = \

Answer:
The present value of growth opportunities (PVGO) for the stock is approximately $30.