Final answer:
The expected stock price of Justus Corporation at the end of 3 years can be found using the Gordon Growth Model and CAPM formula to calculate the required rate of return and future value of the growing dividend. The required rate of return is 8.2%, and the dividend growth rate is assumed to be 9%.
Step-by-step explanation:
To find the stock price of Justus Corporation at the end of 3 years, we must apply the Gordon Growth Model which assumes a perpetuity of dividends growing at a constant rate. The formula for the Gordon Growth Model is P = D1 / (k - g), where P is the price, D1 is the dividend a year from now, k is the required rate of return, and g is the growth rate of dividends.
The required rate of return (k) is calculated using the Capital Asset Pricing Model (CAPM), which is k = risk-free rate + beta * (market risk premium). Substituting the given values, we get k = 4.6% + 0.9 * 4%, which leads to k = 4.6% + 3.6% = 8.2%.
Assuming the dividend grows at a rate of 9%, we can calculate P3 using the Gordon Growth Model to find the price of the stock at the end of 3 years. Substituting D1 = $3.00 * (1 + 0.09)^3 and g = 9% into the Gordon Growth Model formula, we get the predicted price at the end of 3 years.
Thus, to calculate the stock price at the end of year 3 (P3), the future value of the dividend at that time needs to be discounted back to present value using the required rate of return (8.2%) and then factoring in the growth rate to find P3. This calculation involves using the future value of the growing dividend and discounting it back to its present value to estimate the expected price.