Blackstone is contemplating a leveraged buyout of MGM Mirage. MGM$\text{'}$s $1\mathrm{.}2$ billion shares currently trade at $$\frac{11}{?}$ share, and the company has $$12$ billion in long$-$term debt, $$2$ billion in excess cash, and $$3$ billion in short$-$term liabilities that are due immediately. Blackstone is offering $$\frac{18}{?}$ share to existing shareholders and plans to finance the buyout using $$20\mathrm{.}6$ billion of debt to with an interest cost of debt, rd$,$ equal to $13\%,$ and $$2$ billion of equity financing. The interest expenses $($in billions$)$ under the buyout plan are reported separately for old and new debt below. After increasing the incentives of the managers with increased equity stakes in the firm, Blackstone projects that MGM will generate free cash flows of $$3$ billion next year $)=(1$ and that these cash flows will grow at $5\%$ a year thereafter. Blackstone plans to sell MGM after $4$ years $)=(4,$ and anticipates the new owners will maintain a target $DN$ ratio of $0\mathrm{.}50$ following the sale. With this $\frac{D}{N}$ of $0\mathrm{.}50,$ MGM$\text{'}$s cost of debt will drop back to $8\%.$ In your below analysis of this LBO, you should assume that MGM$\text{'}$s unlevered cost of equity, ra$,$ equals $15\%.$ You should als$$assume the corporate tax rate faced by MGM is $35\%.$ Please express all values in billions of dollars.

$\backslash$table$[[$Year$,1,2,3,4,],[$Interest expense $($Old debt$),0\mathrm{.}5,0\mathrm{.}5,0\mathrm{.}5,0\mathrm{.}5,],[$Interest expense $($New debt$),3\mathrm{.}0,3\mathrm{.}0,3\mathrm{.}0,3\mathrm{.}0,]]$

With the LBO, what is the PV$($interest tax shields$)$ for years $1-4?$

$2\mathrm{.}94$

$3\mathrm{.}64$

$2\mathrm{.}15$

$3\mathrm{.}99$