145. A mutual fund manager has a $40 million portfolio with a beta of 1.00. The risk-free rate is 4.25%, and the market risk premium is 6.00%. The manager expects to receive an additional $60 million which she plans to invest in additional stocks. After investing the additional funds, she wants the fund's required and expected return to be 13.00%. What must the average beta of the new stocks be to achieve the target required rate of return?

1.763

Explanation:

Data provided in the question:

Beta of $40 million portfolio = 1

Risk-free rate = 4.25%

Market risk premium = 6.00%

Expected return = 13.00%

Now,

Expected return = Risk-free rate + (Beta * Market risk premium)

13.00% = 4.25% + (Beta * 6.00%)

or

Beta * 6.00% = 8.75%

or

Beta = 1.458

Now,

Beta of the total profile should be equal to 1.458

Thus,

Weight of $40 million portfolio = $40 million : [ $40 million + $60 million]

= 0.4

Weight of $60 million portfolio = $60 million : [ $40 million + $60 million]

= 0.6

therefore,

the average beta

1.458 = 0.4 * 1 + 0.6 * (Beta of $60 million portfolio)

or

1.058 = 0.6 * (Beta of $60 million portfolio)

or

Beta of $60 million portfolio = 1.763