Imagine that Adaptec is contemplating a project that requires a $3.75 billion initial outlay and features an NPV of $466 million. The firm is all-equity financed and has $1 billion in cash that it plans to invest in the project. Adaptec’s current market value of equity is $6.68 billion. Adaptec’s investment bankers have advised the firm’s financial managers that they could raise the $2.75 billion by issuing new equity. However, Adaptec has no capacity for debt. If the firm issues new equity, then the new shareholders would come to hold 28.5 percent of the firm, which is conditional on adopting the project they estimate to be worth $9.569 billion. The investment bankers have computed the NPV of the project to be about $227 million, not the $466 million computed by Adaptec’s managers. 

Adaptec’s managers have concluded that their firm is undervalued in the market and that its intrinsic value would be about $13 billion if it adopts the project. In addition, the managers have concluded that the new shareholders merit 21.2 percent of the firm for their $2.75 billion investment. Nevertheless, the investment bankers have made it clear that unless Adaptec’s managers agree to give up 28.5 percent of their firm, they will not be able to raise the $2.75 billion. Assume that flotation costs are zero. Suppose that Adaptec has no debt capacity and has to rely on external equity. What value of BPV would the managers of Adaptec compute if they adopted the project and financed it with equity?