General Systems, a computer manufacturer, announces that it will be acquiring FastWorks Software. You know the following $$

$$ General Systems had a levered beta of $1\mathrm{.}09$ prior to the merger. The firm has a market value of equity of $$12$ billion and $$16$ billion in debt outstanding.

$$ FastWorks Software had a levered beta of $1\mathrm{.}30$ prior to the merger. The firm has a market value of equity of $$6\mathrm{.}00$ billion and $$6\mathrm{.}00$ billion in debt outstanding.

a$)$ Estimate the unlevered beta of the combined firm.

b$)$ If you were told that the combined firm$$s levered beta will be $1\mathrm{.}270$ after the acquisition, how much debt did General Systems use to acquire FastWorks? $[$You can assume that General Systems will assume Fastworks$$ existing debt$].$ Both firms have a $40\mathrm{.}00\%$Tax rate

$1.$ Unlevered beta for General Systems

$2.$ Unlevered beta for Fast Works

$3.$ Combined value of merged firm $($in $bn$)$

$4.$ Unlevered beta of combined firm

$5.$ Debt$-$to$-$equity ratio after the merger $($in decimal form. i$.$e$.,50\%$ is $0\mathrm{.}5$ not $50)$

$6.$ Debt$-$to$-$capital after transaction $($in decimal form$)$

$7.$ Dollar value of debt in the merged firm $($in $bn$)$

$8.$ Dollar value of debt in existing companies $($in $bn$)$

$9.$ New debt issued to finance the transaction $($in $bn$)$