BigCo’s Chief Financial Officer is trying to determine a fair value for PrivCo, a non-publicly traded firm that BigCo’s

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BigCo’s Chief Financial Officer is trying to determine a fair
value for PrivCo, a non-publicly traded firm that BigCo’s is
considering acquiring. Several of PrivCo’s competitors, Ion
International, and Zenon are publicly traded. Ion and Zenon
have price-to-earnings ratios of 20 and 15, respectively. The
Ion’s and Zenon’s earnings per share are projected to grow by 10%
and 15% per annual, respectively. BigCo estimates that next year,
PrivCo will achieve earnings per share of $4 per share and its
earnings per share is expected to grow at 20%. To gain a
controlling interest in the firm, BigCo expects to pay at least a
40% premium to the firm’s estimated market value. What should BigCo
expect to pay for PrivCo per share?