Step 1: Calculate the price with the constant dividend growth model (Gordon Growth Model)

The Gordon Growth Model formula is given by:

$P_0 = \frac{D_1}{k - g}$

Where:

• $P_0$ = Price of the stock
• $D_1$ = Dividend next year
• $k$ = Market capitalization rate (required rate of return)
• $g$ = Growth rate of dividends

1.1 Calculate $D_1$ (Dividend next year)

The firm expects to earn $6 per share next year, and the plowback ratio is 60%. This means that 40% of the earnings are paid as dividends.

$D_1 = (1 - \text{plowback ratio}) \times \text{earnings}$ $D_1 = (1 - 0.60) \times 6 = 0.40 \times 6 = 2.40$

1.2 Calculate the growth rate $g$

The growth rate $g$ is given by:

$g = \text{ROE} \times \text{plowback ratio}$ $g = 0.15 \times 0.60 = 0.09 = 9\%$

1.3 Calculate the price $P_0$

Using the Gordon Growth Model:

$P_0 = \frac{2.40}{0.10 - 0.09} = \frac{2.40}{0.01} = 240$

Thus, the price with the constant dividend growth model is $240.

---

Step 2: Calculate the price with no growth

If there is no growth, the company would pay out all of its earnings as dividends, and the price would be the earnings divided by the market capitalization rate. The formula in this case is:

$P_0 = \frac{E_1}{k}$

Where:

• $E_1$ = Earnings next year
• $k$ = Market capitalization rate

$P_0 = \frac{6}{0.10} = 60$

Thus, the price with no growth is $60.

---

Step 3: Calculate the present value of growth opportunities (PVGO)

The Present Value of Growth Opportunities (PVGO) is the difference between the price with growth and the price with no growth:

$PVGO = P_0 (\text{with growth}) - P_0 (\text{no growth})$

$PVGO = 240 - 60 = 180$

Thus, the present value of its growth opportunities is $180.

---

Summary of Answers:

1. Price with the constant dividend growth model: $240
2. Price with no growth: $60
3. Present value of growth opportunities: $180

Would you like further details or have any questions on these calculations?

---

Related Questions:

1. How does the plowback ratio impact the growth rate and stock price?
2. What is the effect of increasing the ROE on the stock price?
3. How would a change in the market capitalization rate affect the price of the stock?
4. What happens to the price if the firm changes its dividend payout ratio?
5. How can the Gordon Growth Model be adjusted for non-constant growth?

Tip:

The plowback ratio (retained earnings ratio) significantly affects the firm’s growth rate. Higher retention means more earnings are reinvested, leading to higher growth rates and higher stock prices.