Final answer:
The average beta required for the new stocks added to the portfolio to achieve the desired required return of 19.0 percent is 1.75, as calculated using the rearranged Capital Asset Pricing Model formula.
Step-by-step explanation:
To determine what the average beta should be for the new stocks to be added to the current portfolio, we need to use the Capital Asset Pricing Model (CAPM) formula: Expected Return (ER) = Risk-Free Rate (Rf) + Beta (β) × Market Risk Premium (MRP). The formula can be rearranged to solve for beta: β = (ER - Rf) / MRP. Given that the mutual fund manager has a $40.0 million portfolio with a beta of 1.25, the risk-free rate is 5.0 percent, and the market risk premium is 8.0 percent, and after the additional investment of $10.0 million the required return is set at 19.0 percent, we calculate the beta needed for the new investment.
The current portfolio's expected return is calculated as follows:
ER (current) = Rf + β (current) × MRP
ER (current) = 5.0% + 1.25 × 8.0%
ER (current) = 5.0% + 10.0%
ER (current) = 15.0%
The required return after the new investment is 19.0%, which is 4.0% higher than the current portfolio's return. For the entire portfolio worth $50.0 million to have a required return of 19.0%, the new stocks must have a sufficient beta to raise the overall portfolio beta to that level. Using the CAPM formula, we calculate the beta for the new funds (β new):
β (new) = (ER (entire portfolio) - Rf) / MRP
β (new) = (19.0% - 5.0%) / 8.0%
β (new) = 14.0% / 8.0%
β (new) = 1.75
Thus, option (c) 1.75 is the correct answer for the average beta required for the new stocks to achieve the targeted required return of 19.0 percent.