New studies find that there is potentially a new variant of the corona virus, variant D$,$ that may emerge next year $($year $1).$ The chance for this to occur is $44\mathrm{.}49\%.$ If it does not occur, the existing vaccines will stop the pandemic. If it occurs, however, none of the existing vaccines will work and new vaccines are needed.

n$.$Vac is a start$-$up devoted to developing a new vaccine, Vac$-$D$,$ against variant D$.$ Current data shows that Vac$-$D has a $99\%$ efficacy rate against variant D$.$ Hence, if variant D occurs next year, Vac$-$D will be able to fully stop it$.$

n$.$Vac has spent $$500\mathrm{.}00$ million in developing Vac$-$D and needs to spend another $$334\mathrm{.}00$ million this year $($year $0)$ to finish its development. The production cost of Vac$-$D will be $$11\mathrm{.}60$ billion to meet global needs if variant D does emerge, which will generate a revenue of $$24\mathrm{.}58$ billion from government purchases. Both production cost and revenue will materialize in year $1.$ If variant D does not emerge, Vac$-$D will not be produced and will be worth nothing. The governments have also committed a subsidy of $$4\mathrm{.}54$ billion for next year $($year $1),$ independent of whether or not Vac$-$D will be produced. There will be no future cash flows after year $1$ for n$.$Vac.

C$.$Vax is a spinoff from an existing biotech company, whose sole product is a successful vaccine against the current strands of corona virus. C$.$Vax has no debt. Its shares are currently traded on NASDAQ with a total market value of $$5\mathrm{.}00$ billion. Its value will go up by $61\mathrm{.}86\%$ next year if variant D emerges, but will drop by $26\mathrm{.}08\%$ if variant D does not hit.

Ignore corporate taxes. The risk$-$free interest rate is $1\mathrm{.}00\%.$

a$)$ What is the cost of capital for C$.$Vax?

b$)$ What is current market value of n$.$Vac?