Prove that an outsider will not pay more than ((1-alpha)) times the value he expects the firm

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Prove that an outsider will not pay more than \((1-\alpha)\) times the value he expects the firm to have-that is, he will not pay the value \((1-\alpha) V^{*}\), but only \((1-\alpha) V^{0}\), for the fraction \((1-\alpha)\) of the shares.

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