Ch $08$: End$-$of$-$Chapter Problems$-$LPK $-$ Risk and Rates of Return

You plan to invest in the Kish Hedge Fund, which has total capital of $$500$ million invested in five stocks:

Kish's beta coefficient can be found as a weighted average of its stocks' betas. The risk$-$free rate is $3\%,$ and you believe the following probability

distribution for future market returns is realistic:

a$.$ What is the equation for the Security Market Line $($SML$)?($Hint: First determine the expected market return.$)$

I. $r_i=3\mathrm{.}0\%+(11\mathrm{.}0\%)b_i$

II$.r_i=6\mathrm{.}0\%+(9\mathrm{.}5\%)b_i$

III. $r_i=3\mathrm{.}0\%+(11\mathrm{.}9\%)b_i$

IV$.r_i=6\mathrm{.}5\%+(11\mathrm{.}0\%)b_i$

V$.r_i=6\mathrm{.}5\%+(11\mathrm{.}9\%)b_i$

b$.$ Calculate Kish's required rate of return. Do not round intermediate calculations. Round your answer to two decimal places.

C$.$Suppose Rick Kish, the president, recieves a proposal from a company seeking new capital. The amount needed to take a position in the stock is $$50$ million, it has an expected return of $14\%,$ and its estimated beta is $1\mathrm{.}4.$ Should kish invest in the new company? Should the new stock be purchased or not purcahsed?

D$.$ At what expected rate of return should kish be indifferent to purchasing the stock?