John Ford starts a firm Bestafer and Bob Strong is the venture capitalist. The situation is as follows: John Ford, CEO of Bestafer, Inc., sought to raise $5 million in a private placement of equity in his early stage dairy products company. Ford conservatively projected net income of $4 million in year 5, and knew that comparable but more mature companies traded at a price earnings ratio of 20x. The venture capitalist, Bob Strong, has a 50% target rate of return. Ford has 1,000,000 shares. (There is expected to be no debt or available cash at the investment horizon.)

But now: Bob Strong of Kennebunk Capital liked Ford's plan, but thought it naive in one respect: to recruit a senior management team, he felt Ford would have to grant generous stock options in addition to the salaries projected in his business plan. From past experience, he felt management should have the ability to own at least a 15% share of the company by the end of year 5 (at t=5). That is, management will be rewarded with stock options that Strong feels will result in these managers (not including Ford) owning 15% of all shares as of t=5. (Those shares will not be issued at t=0)

Given these beliefs, how many shares should Strong insist on today if his target rate of return is 50%? (The assumption here is that a wise venture capitalist will anticipate this 15% management pool at the time of the financing.) Assume that $5 million must be invested now.