AJ Partners is a private equity investor which makes a $5 million investment in a venture capital firm today. AJ Partners expects to sell the firm in six years and believes there are three equally possible scenarios at termination:

1. expected earnings will be $20 million, and the expected P/E will be 10.

2. expected earnings will be $7 million, and the expected P/E will be 6.

3. expected earnings will be zero if the firm fails.

AJ Partners believes an IRR of 35% is appropriate.

Calculate

(i) The expected terminal value

(ii) The pre-money and post-money valuation

(iii) The PE firms fractional ownership in the venture capital firm