POST money valuation--short problem

A private equity firm makes a $10 million investment in a portfolio company and calculates that the firm’s investors should hold 1,000,000 shares at a price of $15.00 per share using the IRR approach. The founders of a portfolio company currently hold 300,000 shares. The appropriate post-money (POST) valuation is: A) $15 million. B) $13 million. C) $19.5 million. Your answer: B was incorrect. The correct answer was C) $19.5 million. Since we have no information on exit value or the IRR rate, but the share price and number shares held by each party is given, the post-money valuation (POST) is calculated as: POST = shares price x total number of shares = $15 × (1,000,000 + 300,000) = $19.5 million. While this makes perfect sense, I did it another way and got the wrong answer and cannot figure out why these two methods yield different results. I did: POST = INV/f = 10/f spe = (se) x f/(1-f) 1M = 300K x f/(1-f) 3.333 = f/(1-f) 3.333 - 3.333f = f 3.333 = 4.333f .769 = f which checks out if you plug it back into the equation. POST = 10/f = 10/.769 = 13M

just did another problem and realized fraction can be much more simply calculate by doing spe/(spe + se) = 1/1.3 = .769 answer still comes out to 10/.769 = 13M