An entrepreneur seeks $12 million from a VC fund. The entrepreneur and fund managers agree that the entrepreneur's venture is currently worth $30 million and that the company is likely to be ready to go public in four years.
At that time, the company is expected to have a net income of $9 million. Comparable firms are expected to be selling at a price/earnings ratio of 25.
Given the company's stage of development, the venture capital fund managers require a 40 percent compound annual return on their investment. What fraction of the firm will the fund receive in exchange for its $12 million investment?