A company's assets will have a value, one year from now, equal to $$45$

millions if the economic conditions are good or to $$8$ millions if the conditions

are bad, and the two scenarios are equally likely. The company currently has

no debt and, after one year, it will terminate its operations. Today $($that is one

year before terminating its operation$),$ the company has decided to go through

with a recapitalization issuing a zero coupon bond with face value $$10$ millions

and maturity one year and buying back its own shares with the proceeds. The

expected return required by bond holders is $5\mathrm{.}45\%.$ In case of bankruptcy there

will be estimated direct bankruptcy cost for $$564,000$ and indirect bankruptcy

costs for $$789,000.$ The return on levered equity after the recapitalization will

be $15\%.$ At the moment $($that is before the recapitalization$)$ the company has

$100,000$ shares outstanding. Assume no taxation.

$($a$)$ What is the value of levered equity? $[15,217,391\mathrm{.}30]$

$($b$)$ What is the amount of money raised from bond holders when the bond

is issued? $[7,893,314\mathrm{.}30]$

$($c$)$ How many shares will be bought back? $[34,154\mathrm{.}36]$