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# SML Fund: required rate of return; should new stock be purchased?

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An investment fund has total capital of \$500 million invested in 5 stocks:

STOCK INVESTMENT STOCK'S BETA COEFFICIENT
A \$60 million 0.5
B \$120 million 2.0
C \$80 million 4.0
D \$80 million 1.0
E \$60 million 3.0

The beta coefficient for the fund can be found as a weighted average of the fund's investments. The current risk-free rate is 6%, whereas market returns have the following estimated probability distribution for the next period:

PROBABILITY MARKET RETURN
0.1 ---------- 7%
0.2 ---------- 9%
0.4 ---------- 11%
0.2 ---------- 13%
0.1 ---------- 15%

a. What is the estimated equation for the Security Market Line (SML)?
b. Compute the fund's required rate of return for the next period.
c. Assume that Jose Croesact, the fund's president, receives a proposal for a new stock. The
investment needed to take a position in the stock is \$50 million, it would have an expected
return of 15%, and its estimated beta coefficient is 2.0. Should the new stock be purchased?
d. At what expected rate of return should the fund be indifferent to purchasing the stock?

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#### Solution Preview

a. What is the estimated equation for the Security Market Line (SML)?
The expected market return is
E(Rm)=SUM(Pr*Rm)=.1*7+.2*9+.4*11+.2*13+.1*15= 11
And the Security Market Line is
E(Rstock)=Rf + (Rm-Rf)*Beta = 6+(11-6)*Beta = 6 + 5 Beta (%)

b. Compute the fund's required rate of return for the next period.
The fund's beta coefficient is the weighted average of the fund's investments
*However, there might be some type error in your question: the sum of ...

#### Solution Summary

The solution presents a quality narrative to understand the concepts and then shows the formulas used to compute the answers.

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