Question

Sean-Ruben manage a $10.00 million mutual fund which has a beta of 1.05 and a 9.50% required return. The risk-free rate is 4.20%. Sean-Ruben now receives another $5.00 million, which he invests in stocks with an average beta of 0.65.    What is the required rate of return on the new portfolio? (Hint: You must first find the market risk premium, then find the new portfolio beta.)

Answer 1

Information provided:

Proportion of debt= 65%

Proportion of equity= 35%

Cost of debt= 9%

Information provided:

Amount invested in old portfolio= $10 million

Amount invested in addition to the portfolio= $5 million

Old portfolio’s beta= 1.05

Old portfolio’s required return= 9.50%

Risk free rate= 4.20%

Average beta= 0.65

The question is solved by first calculating the market risk premium

The required return is calculated using the Capital Asset Pricing Model (CAPM) which is calculated using the formula below:

Ke=Rf+b[E(Rm)-Rf]

Where:

Rf=risk-free rate of

Rm=expected rate of return on the market.

Rm- Rf= Market risk premium

b= stock’s beta

9.50%= 4.20% + 1.05*(x – 4.20%)

Market risk premium= 9.50% - 4.20%/ 1.05

                                         = 5.50%/ 1.05

                                         = 5%

The expected return of the addition to the portfolio is calculated as below:

= 4.20% + 0.65*5%

= 4.20% + 3.25%

= 7.45%

Expected return on the portfolio:

= 10*9.50% + 5*7.45%/ 10 + 5

= 0.95 + 0.3725/ 15

= 1.3225/ 15

= 0.0882*100

= 8.82%.

Therefore, the required rate of return of the new portfolio is 8.82%.

In case of any query, kindly comment on the solution.