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

Stock Investment Stock's Beta Coefficient

A $$160$ million $0\mathrm{.}3$

B $120$ million $1\mathrm{.}2$

C $80$ million $1\mathrm{.}8$

D $80$ million $1\mathrm{.}0$

E $60$ million $1\mathrm{.}3$

Kish's beta coefficient can be found as a weighted average of its stocks' betas. The risk$-$free rate is $7\%,$ and you believe the following probability distribution for future market returns is realistic:

Probability Market Return

$0\mathrm{.}1-29\%$

$0\mathrm{.}20$

$0\mathrm{.}414$

$0\mathrm{.}229$

$0\mathrm{.}146$

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

ri $=7\mathrm{.}0\%+(6\mathrm{.}1\%)$bi

ri $=9\mathrm{.}0\%+(5\mathrm{.}1\%)$bi

ri $=7\mathrm{.}0\%+(7\mathrm{.}6\%)$bi

ri $=9\mathrm{.}3\%+(6\mathrm{.}1\%)$bi

ri $=9\mathrm{.}3\%+(7\mathrm{.}6\%)$bi

$-$Select$-$

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

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Suppose Rick Kish, the president, receives 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 $15\%,$ and its estimated beta is $1\mathrm{.}4.$ Should Kish invest in the new company?

The new stock

$-$Select$-$

be purchased.

At what expected rate of return should Kish be indifferent to purchasing the stock? Round your answer to two decimal places.

$\%$