Final answer:
Using the CAPM formula, the expected return is calculated at 13.5%. Based on this, the intrinsic value of the stock is $14.76. Since the market price is $15, which is higher than the intrinsic value, you should not consider purchasing the stock.
Step-by-step explanation:
According to the Capital Asset Pricing Model (CAPM), the expected return on a stock can be calculated using the formula: expected return = risk-free rate + beta x (market return - risk-free rate). In this case, you have a stock with a beta of 2, a risk-free rate of 1.5%, and an expected market return of 7.5%. Plugging these values into the formula gives us an expected return of 1.5% + 2 x (7.5% - 1.5%) = 13.5%.
To evaluate whether you should purchase the stock, calculate the stock's intrinsic value by discounting the expected price in one year plus the dividend by the expected return. The intrinsic value can be found using the formula: intrinsic value = (expected price + dividend)/(1 + expected return). Plugging in the expected price of $16 and the dividend of $0.75, we get: intrinsic value = ($16 + $0.75)/(1 + 0.135) = $14.76.
Given that the current price of the stock is $15 and the intrinsic value you calculated is $14.76, the stock is overvalued based on your expectations and the CAPM. Therefore, you should not consider buying the stock as the market price is higher than what the CAPM model suggests its value should be. The correct answer to the initial question is option (a).