The Mcalhancy investment fund has total capital of $500 million invested in five

Question

The Mcalhancy investment fund has total capital of $500 million invested in five stocks: The current risk-free rate is 8 percent. Market returns have the following estimated probability distribution for the next period: Compute the expected return for the market. Compute the beta coefficient for the investment fund. (Remember, this problem involves a portfolio.) What is the estimated equation for the Security Market Line? Compute the fund's required rate of return for the next period. Suppose John McAlhany, the president, receives a proposal for a new stock. The investment needed to take a position in the stock is $50 million, it will have an expected return of 18 percent, and its estimated beta coefficient is 2.0. Should the firm purchase the new stock? At what expected rate of return should McAlhany be indifferent to purchasing the stock?

Explanation / Answer

a) Expected market return = Sum of P x MR

P

MR

P x MR

0.1

10%

1.00%

0.2

12%

2.40%

0.4

13%

5.20%

0.2

16%

3.20%

0.1

17%

1.70%

13.50%

Hence expected market return would be 13.50%.

b)Weight = Investment amount/ total investment

Beta of portfolio = sum of weights x beta

Stock

Investment (Billion)

Weights

Beta

Beta x Weight

A

160

0.32

0.5

0.16

B

120

0.24

2

0.48

C

80

0.16

4

0.64

D

80

0.16

1

0.16

E

60

0.12

3

0.36

Total

500

1

1.8

c)Equation of SML:

Rp = Rf + (Rm-Rf)xbeta

Rp     = 8% + (13.50% -8%)xbeta

Rp      = 8% + 5.50%Beta

d) Funds required return at beta =1.80

Rp = 8% + 5.50%Beta

Rp = 8% + 5.50%x1.80

      = 17.90%

P

MR

P x MR

0.1

10%

1.00%

0.2

12%

2.40%

0.4

13%

5.20%

0.2

16%

3.20%

0.1

17%

1.70%

13.50%

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