Questions: Problem 7-1 Stock Values [LO 1] The RLX Company just paid a dividend of 2.80 per share on its stock. The dividends are expected to grow at a constant rate of 6.75 percent per year, indefinitely. Assume investors require a return of 12 percent on this stock. a. What is the current price? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. b. What will the price be in four years and in sixteen years? Note: Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.

To solve this problem, we will use the Gordon Growth Model (also known as the Dividend Discount Model) which is used to determine the present value of a stock that is expected to grow dividends at a constant rate indefinitely. The formula for the Gordon Growth Model is:

\[ P_0 = \frac{D_0 (1 + g)}{r - g} \]

where:

• \( P_0 \) is the current stock price
• \( D_0 \) is the most recent dividend payment
• \( g \) is the growth rate of the dividends
• \( r \) is the required rate of return

Given:

• \( D_0 = \$2.80 \)
• \( g = 6.75\% = 0.0675 \)
• \( r = 12\% = 0.12 \)

First, we calculate the next year's dividend (\( D_1 \)):

\[ D_1 = D_0 (1 + g) = 2.80 \times (1 + 0.0675) = 2.80 \times 1.0675 = 2.989 \]

Now, we can calculate the current price (\( P_0 \)):

\[ P_0 = \frac{D_1}{r - g} = \frac{2.989}{0.12 - 0.0675} = \frac{2.989}{0.0525} = 56.93 \]

So, the current price is:

\[ \text{Current price} = \$56.93 \]

To find the price in the future, we need to calculate the dividend at that future time and then use the Gordon Growth Model again.

First, calculate the dividend in four years (\( D_4 \)):

\[ D_4 = D_0 (1 + g)^4 = 2.80 \times (1 + 0.0675)^4 = 2.80 \times 1.2973 = 3.6324 \]

Now, calculate the price in four years (\( P_4 \)):

\[ P_4 = \frac{D_4 (1 + g)}{r - g} = \frac{3.6324 \times 1.0675}{0.12 - 0.0675} = \frac{3.8751}{0.0525} = 73.81 \]

So, the price in four years is:

\[ \text{Price in four years} = \$73.81 \]

First, calculate the dividend in sixteen years (\( D_{16} \)):

\[ D_{16} = D_0 (1 + g)^{16} = 2.80 \times (1 + 0.0675)^{16} = 2.80 \times 2.9387 = 8.2274 \]

Now, calculate the price in sixteen years (\( P_{16} \)):

\[ P_{16} = \frac{D_{16} (1 + g)}{r - g} = \frac{8.2274 \times 1.0675}{0.12 - 0.0675} = \frac{8.7821}{0.0525} = 167.30 \]

So, the price in sixteen years is:

\[ \text{Price in sixteen years} = \$167.30 \]

• The current price is \$56.93.
• The price in four years is \$73.81.
• The price in sixteen years is \$167.30.