Question

a. 17. You have been managing a $4 million portfolio that has a beta of 1.5 and a required rate of return of 13%. The current risk-free rate is 5.5%. Assume that you receive another $1 million. If you invest the money in a stock with a beta of 1.75, what will be the required return on your $5 million portfolio? 10.75% b. 11.50% c. 12.25% d. 12.75% e. 13.25% I 18. A stock is exnected to nay lividend of $50 at 1.

Answer 1

Given

Portfolio $4 million

Beta = 1.5

Required rate of return Rp= 13%

Risk free rate Rf= 5.5%

Now, using CAPM model equation, let us calculate the market risk premium Rm

Rp = Rf + beta *(Rm-Rf)

13% = 5.5% + 1.5 * (Rm- 5.5%)

7.5% = 1.5 *(Rm- 5.5%)

(Rm- 5.5%) = 7.5%/1.5 = 5%

Rm = 5%+ 5.5% = 10.5%

New portfolio = $4 million + 1 million = $5 million

Beta of $1 million stock added = 1.75

New beta = [(1.5 * 4 million) + (1.75 *1 million)]/ 5 million = 1.55

Now, required return of new portfolio

Rp = Rf + beta *(Rm-Rf)

Rp = 5.5% + 1.55 *(10.5%-5.5%)

Rp = 5.5% + 1.55 *5

Rp = 5.5% + 7.75%

Rp= 13.25%

Answer: option e. 13.25%