A venture with 2 million total common shares - 1.4 million owned by the entrepreneur and 0.6 million by an angel investor - had a post-money value of $8 million after its last (and only) round of outside financing. The company has run into some developmental delays and needs to raise additional capital. A new investor offers $500,000 in exchange for 200,000 new common shares.

a.     If there is no ratchet agreement, what will be the post-money value after the $500,000 investment? How much is the entrepreneur's stake worth? 

b.     Now assume the angel investor's agreement includes a ratchet provision. Under the terms of the ratchet, the angel investor will receive enough new shares for free so that his average cost per share is the same as that of any new investor. Given your answer to part (a), and including the impact of the ratchet, what price per share would the new investor seek, and how many new shares would the existing angel investor receive? Now how much is the entrepreneur's stake worth?