"Address the limitations of traditional methods such as CAPM $($Capital Asset Pricing Model$)$ and Discounted Cash Flow Analysis in valuing a company's stock price in non$-$stationary market conditions. Particularly, discuss the consistency of the beta coefficient in determining the cost of capital and the selection of the risk$-$free rate. Also, evaluate how these traditional models can or cannot integrate non$-$financial factors $($e$.$g$.,$ company management, brand value, industry trends$).$ Lastly, discuss the alternative models used in stock valuation and the advantages and disadvantages of these models compared to traditional methods."