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%

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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