The answer requires four steps:
Step 1: Calculate the post-money (POST) valuation, which is simply the pre-money (PRE) valuation plus the investment:
POST = PRE + INV = $6 million + $10 million = $16 million
Step 2: Calculate the private equity firm’s fractional ownership in the portfolio company:
f = INV / POST = $10 million / $16 million = 0.625
Step 3: If the founders currently hold 300,000 shares, the number of shares to be held by the private equity firm to have 62.5% ownership is:
Number of shares = 300,000 [0.625 / (1-0.625)] = 500,000
Step 4: Given the private equity firm’s $10 million investment and 500,000 shares, the share price is calculated as:
P = $10 million / 500,000 = $20.00
