If a stock has a βof 1.5, the return on the market is 10 %,...

If a stock has a $\beta$ of $1.5,$ the return on the market is $10 \%,$ and the riskfree rate of return is $5 \%,$ what expected rate of return should this stock offer according to the Capital Asset Pricing Model? If the expected value of the stock is $\$ 100,$ what price should the stock be selling for today?

Key Concepts

Capital Asset Pricing Model (CAPM)

The CAPM is a foundational financial model used to determine the expected return of an asset based on its sensitivity to market risk. It relates the risk of an asset, measured by its beta, to the overall expected market return above the risk-free rate, thereby providing a benchmark for evaluating whether an asset is fairly priced based on its risk level.

Beta

Beta is a measure of an asset's volatility in relation to the market as a whole. A beta greater than one indicates that the asset is more volatile than the market, while a beta less than one means it is less volatile. This coefficient is a key input in the CAPM, as it adjusts the market risk premium to reflect the asset's specific risk relative to the market.

Risk-Free Rate and Market Risk Premium

The risk-free rate is the return on an investment with zero risk, serving as a baseline for evaluating investment returns. The market risk premium is the additional return investors expect for taking on the risk of investing in the market instead of a risk-free asset. Together, they are used in the CAPM to calculate the extra return demanded for bearing the asset's additional risk over the risk-free investment.

Discounted Cash Flow (DCF) Valuation

DCF valuation is a method used to determine the current price of an asset based on its expected future cash flows. By discounting the expected future value back to the present using the appropriate rate of return (in this case, the CAPM-derived expected return), investors can assess whether the current market price reflects the asset's true value and potential for returns.

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