$9.$ The total market value of equity for NNG Gas is $$10$ million, and the total value of its debt is $$4$ million. The treasurer estimates that the beta of the stock currently is $1\mathrm{.}4$ and that the expected risk premium on the market is $9$ percent. The T$-$bond yield is $2\mathrm{.}5\%.$

a$.$ What is the required rate of return on the stock?

b$.$ What is the beta of the company$$s existing portfolio of assets? The debt is perceived to be virtually risk free.

c$.$ Estimate the weighted average cost of capital assuming a tax rate of $21$ percent.

d$.$ Estimate the discount rate for an expansion of the company$$s present business.

e$.$ Suppose that company wants to diversify into the manufacture of rose$-$colored glasses. The beta of optical manufacturer with no debt outstanding is $1\mathrm{.}6.$ What is the required rate of return on NNG Gas$$s new venture? $($Assuming the company will not issue and additional debt.$)$