AJ Partners is a private equity investor which makes a $5 million investment in a venture capital firm today. AJ Partner

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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
firm’s fractional ownership in the venture capital firm