$(12\%$;$2\%$ for each subquestion$)$ Company ABC has non$-$dividend$-$paying equity $($Et: equity value at time

t$)$ and zero$-$coupon debt $($Bt: debt value at time $t$; promised payment at time $T$ is $$250$ million$).A_t$ is the

asset value of the firm at time $t.$ The firm has $20$ million shares outstanding in the stock market, and the

stock price is $$\frac{4}{?}$ share. $A_0=$$$280$ million, $r_c=2\%($continuous time$),$ and $T=5$ years.

$($a$)$ Find the $($implied$)$ asset volatility.

$($b$)$ Find the continuously compounded bond yield $(\%)$ and credit spread $(\%).$

$($c$)$ What is the current value of risk$-$free debt?

$($d$)$ Calculate the quasi debt$-$to$-$asset ratio $d=(B\frac{e^{-rT}}{A_0}).$

$($e$)$ If the government is willing to provide debt guarantee $($i$.$e$.,$ a put option$)$ to protect the firm from

bankruptcy, what is the current value of debt guarantee?