A pharmaceutical company may be valued at $$200$ million if it gets FDA approval for a key drug being developed, or $$70$ million otherwise, and both scenarios are equally probable. The pharmaceutical company is considering investing $$15$ million in a new project with $$22$ million safe return next year. Using a discount rate of $10\%,$ the NPV of the new investment opportunity is $$5$ million $($calculated as $-15+22/1\mathrm{.}1=5).$

The pharmaceutical company neither has the $$15$ million available internally, nor can it borrow the $$15$ million. To invest in this project, the pharmaceutical company will need to issue equity. What percentage of the company $($with the new investment$)$ must be sold off to new shareholders to finance the $$15$ million investment? The correct answer is $9\mathrm{.}7\%$