You have the following initial information on which to base your calculations and discussion:

Debt yield $=2\mathrm{.}6\%$

Required Rate of Return on Equity $=12\%$

Expected return on S&P$500=10\%$

Risk$-$free rate $($rF$)=1\mathrm{.}5\%$

Inflation $=2\mathrm{.}5\%$

Corporate tax rate $($TC$)=30\%$

Current long$-$term and target debt$-$equity ratio $($D:E$)=1$:$3$

a$.$ What is the unlevered cost of equity $($rE$*)$ for this firm?$)$

Assume that the management of the firm is considering a leveraged buyout of the above company. They believe that they can gear the company to a higher level due to their ability to extract efficiencies from the firm$$s operations. Thus, they wish to use a target debt$-$equity ratio of $3$:$1$ in their valuation calculations.

b$.$ What would the required rate of return for the company equal if it were to be acquired under the leveraged buyout structure $($i$.$e$.,$ what would the estimated firm WACC equal to under a debt$-$equity ratio of $3$:

c$.$ Following the acquisition. The CEO of the firm has requested that you evaluate a potential investment in a new project. The proposed project requires an initial outlay of $$7$ billion. Once completed $(1$ year from initial outlay$)$ it will provide a real net cash flow of $$550$ million in perpetuity following its completion. It has the same business risk as the company$$s current activities and is funded under the same capital structure following the acquisition.