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:
The Stock, Investment Amt, And Stocks Beta Coefficient are as follows:Stock A 160 Million 0.5; Stock B 120 Million 2.0; Stock C 80 Million 4.0; Stock D 80 Million 1.0; Stock E 60 Million 3.0
The current risk free rate is 8%. Market returns have the following estimated probability distribution for the next period: Prob 0.1 Market Return 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 (Remember this involves a portfoliio)
C. What is the estimated equation for the security market line?
D. Compute the funds required rate of return for the next period.
E. Suppose John McAlhany recieves a proposal for a new stock. The investment needed to take a postion in the stock is $50 million-the expected return is 18%, 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 return of the market = 0.1(10%)+0.2(12%)+0.4(13%)+0.2(16%)+0.1(17%) = 13.5%

B. Overall beta = (160/500)0.5+(120/200)2+(80/500)4+(80/500)1+(60/500)3 = 1.88

C. SML return = 8% + Beta(13.5% - 8%) = 8% + 5.5%(Beta)

D. Required return =  8% + 5.5%(1.8) = 17.9%

E. For stock with Beta = 2, the required return should be = 8%+2(5.5%) = 19% > 18% expected return

So----> Don't buy this stock

McAlhany will be indifferent to purchasing the stock if expected return = 19%

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