Genenco is developing a new drug that will slow the aging process. In order to$$ succeed, two breakthroughs are$$ needed, one to increase the potency of the$$ drug, and the second to eliminate toxic side effects. Research to improve the$$ drug's potency is expected to require an upfront investment of $$10\mathrm{.}1$ million and take $2$years; the drug has a $6\%$ chance of success. Reducing the$$ drug's toxicity will require a $$30\mathrm{.}7$ million$$ up$-$front investment, take $4$years$,$ and has a $22\%$ chance of success. If both efforts are$$ successful, Genenco can sell the patent for the drug to a major drug company for $$2\mathrm{.}02$ billion. All risk is$$ idiosyncratic, and the$$ risk$-$free rate is $6\mathrm{.}3\%.$

a$.$ What is the NPV of launching both research efforts$$ simultaneously?

b$.$ What is the optimal order to stage the$$ investments?

c$.$ What is the NPV with the optimal$$ staging?