Final answer:
To find the new required return on a stock with an increased beta of 2.25, we use the CAPM formula with the original risk-free rate and the calculated market return based on the original required return and beta. Calculating the original market return is done by reversing the CAPM formula, and then we use that market return to find the new expected return with the increased beta.
Step-by-step explanation:
The question pertains to the calculation of a new required return on a stock based on the Capital Asset Pricing Model (CAPM). This model suggests that the expected return on an asset is a function of the risk-free rate, the asset's sensitivity to market movements (beta), and the overall market return. The formula to calculate the required return is:
Required Return = Risk-free Rate + (Beta * (Market Return - Risk-free Rate))
We're given that the original beta is 1.64, the risk-free rate is 4.0%, and the required return is 16.30%. If the beta increases to 2.25, we need to calculate the new required return using the same risk-free rate and assuming the market return (which is implied by the original data) remains constant.
To find the original market return, we can reverse the CAPM formula:
Market Return = (Required Return - Risk-free Rate) / Beta + Risk-free Rate
Substituting the known values:
Market Return = (16.30% - 4.0%) / 1.64 + 4.0%
This would give us the original market return, which we would then use to calculate the new required return with the higher beta of 2.25.
New Required Return = 4.0% + (2.25 * (Market Return - 4.0%))
The result of this calculation would give us the new required return on the stock if its beta increased to 2.25 with other conditions remaining unchanged.