It is December $2021$ a private equity group called Magna is considering a leveraged buyout of FG$.$FG generated $$4\mathrm{.}5$ billion in revenue in $2021.$ Revenue is expected to grow at $8\%$ for five years. As an analyst at Magna, you have obtained the following additional assumptions for FG for the next five years

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$5-$year revenue growth forecast $8\%$

Operating expense $(\%$ of sales$)*68\%$

Tax rate $20\%$

Capex $(\%$ of sales$)5\%$

Depreciation $(\%$ of sales$)3\%$

Working capital $(\%$ of sales$)5\%$

Shares outstanding $($millions$)850$

Cash balance $0$

$*$Including depreciation expense

In addition, you have the following information about the LBO

$$ The purchase multiple will be $4$x EBITDA

$$ The acquisition will be financed with $25\%$ equity and $75\%$ debt. The LBO debt financing will be a term loan that carries an interest rate of $6\%$

$$ The debt covenants require that half of the free cash flow to equity holders generated each year must be used to pay down the term loan principal. The rest of the cash flow can be disbursed to equity holders each period

$$ The private equity group expects to exit the investment at $5$x EBITDA

Answer the following questions

a$.$ What is the value of equity at exit?

b$.$ What is the IRR earned by the LBO?