$(15$ points$)$ Dong Hwa is a renowned ideal resort that currently has $$10$ billion in cash. Dong Hwa has decided to use this cash to repurchase shares from its investors and has already announced the stock repurchase plan. Currently, Dong Hwa is an all$-$equity firm with $2\mathrm{.}5$ billion shares outstanding. Dong Hwa's shares are currently trading at $$40$ per share. $(1)$ How much is the market value of Dong Hwa's non$-$cash assets? $(2\mathrm{.}5$ points$)(2)$ After the repurchase, how many shares will Dong Hwa have outstanding? $(2\mathrm{.}5$ points$)(3)$ With perfect capital markets, what is the market value of Dong Hwa's equity after the share repurchase? $(2\mathrm{.}5$ points$)(4)$ With perfect capital markets, what is the market price per share of Dong Hwa's stock after the share repurchase? $(2\mathrm{.}5$ points$)(5)$ If the market is not perfect and investors consider the stock repurchase carrying a signal of undervaluation of the shares, and the mispricing is believed to be as the function of $4$ dollars $*$ number of shares repurchased. What will be the market value and share price of Dong Hwa after the announcement of repurchase? $(5$ points$)$