Kelly Enterprises' stock currently sells for $35.25 per share. The dividend is projected to increase at a constant rate of 4.75% per year. The required rate of return on the stock, rs, is 11.50%. What is the stock's expected price 5 years from now?a. $40.17b. $41.20c. $42.26d. $43.34e. $44.46

To calculate the expected stock price 5 years from now, you can use the Gordon Growth Model (also known as the Dividend Discount Model). The formula for the price of a stock with dividends that grow at a constant rate is given by:

P0 = D1 / (rs - g)

where: - P0 is the stock's current price, - D1 is the dividend next year, - rs is the required rate of return, and - g is the growth rate of the dividends.

However, since we want to find the price 5 years from now (P5), we will use:

P5 = D6 / (rs - g)

First, we need to find out the expected dividend 6 years from now (D6). Knowing that the dividend is growing at a constant rate (g), we can calculate D6 from the current dividend (D0) using the formula:

D6 = D0 * (1 + g)^6

We don't have the current dividend (D0), so we can't calculate D6 directly. However, the current stock price already factors in the expected growth of the dividend at the constant rate, assuming the market is efficient. We can work backward to estimate the current dividend (D0) implied by the current stock price (P0), the growth rate (g), and the required rate of return (rs):

P0 = D0 * (1 + g) / (rs - g)

Using the given data: P0 = $35.25 g = 4.75% or 0.0475 rs = 11.50% or 0.115

Rearrange the formula to solve for D0:

D0 = P0 * (rs - g) / (1 + g)

Now, calculate the current dividend (D0):

D0 = $35.25 * (0.115 - 0.0475) / (1 + 0.0475) D0 ≈ $35.25 * 0.0675 / 1.0475 D0 ≈ $35.25 * 0.064452

D0 ≈ $2.27 (approx)

Next, calculate D6 using the growth rate:

D6 = D0 * (1 + g)^6 D6 = $2.27 * (1 + 0.0475)^6 D6 ≈ $2.27 * 1.315342

D6 = $2.98 (approximately)

Finally, calculate the expected stock price five years from now (P5):

P5 = D6 / (rs - g)

 P5 = $2.98 / (0.115 - 0.0475)

 P5 = $2.98 / 0.0675 

P5 = $44.15.

This is not one of the options given, so it's possible that there has been a rounding error during the calculation or the original dividend was different. However, based on the calculated figures, the closest option given is:

e. $44.46