The McAlhany Investment Fund has total capital of $500 million invested in five

Question

The McAlhany Investment Fund has total capital of $500 million invested in five stocks:

Stock A: Investment $160 Million Stock's Beta Coefficient 0.5
Stock B: Investment $120 Million Stock's Beta Coefficient 2.0
Stock C: Investment $ 80 Million Stock's Beta Coefficient 4.0
Stock D: Investment $ 80 Million Stock's Beta Coefficient 1.0
Stock E: Investment $ 60 Million Stock's Beta Coefficient 3.0

The Current risk free rate is 8 percent. Market returns have the following estimated probability distribution for the next period:

Probability Market Return
0.1 10%
0.2 12%
0.4 13%
0.2 16%
0.1 17%

A. Compute the expected return for the market
B. Compute the beta coefficient for the investment fund.
C. What is the estimated equation for the security market line?
D. Compute the fund's required rate of return for the next period
E. 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%, 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

expected market return = 0.1*10 +.2*12 + .4*13 + .2 *16 +.1*17 = 13.5%

return on stock A = rf + (rm - rf)*a

= 8% + (13.5-8)*.5 = 10.75%

similarly, return on stock B = 19%

return on stock C = 30%

return on stock D = 13.5%

return on stock E = 24.5%

with a beta coefficient of 2, return on stock B is 19%

and the new investments beta is also 2 and its retrun is 18%

hence it will not purchase the new stock

at 19% expected arte of return the McAlhany be indifferent to purchasing the stock, since then it would be same riskier as security of beta 2

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