Final answer:
Stock X should sell for $35.71 today, calculated using the Gordon Growth Model and the CAPM to find the required rate of return, considering the given market conditions and Stock X's specific characteristics.
Step-by-step explanation:
The value of Stock X today can be determined using the Gordon Growth Model (also known as the Dividend Discount Model), which calculates the present value of an infinite series of future dividends that grow at a constant rate. Given that Stock X paid a dividend of $2.50 yesterday and is expected to grow at 7% indefinitely, we can use this model to calculate its price. We also need to calculate the required rate of return for Stock X considering its response to market changes, known as the Beta (in this case, it responds twice as much to the market, so its Beta is 2). This, along with the risk-free rate from Treasury bills (8%) and the market yield (11%), will allow us to use the Capital Asset Pricing Model (CAPM) to find the required rate of return.
The CAPM formula is Required Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate).
Substituting the given values,
we get Required Return = 8% + 2 * (11% - 8%)
= 14%.
Using the Gordon Growth Model,
the price of Stock X = Dividend per share / (Required Return - Growth rate) = $2.50 / (14% - 7%) = $2.50 / 0.07
= $35.71.
Therefore, Stock X should sell for $35.71 today.