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KPE, the public vehicle, has a net asset value of $22.25 a share, but to the frustration of the partners at KKR, the share price has steadily dropped since the unit was listed in April 2006.
The shares, which peaked at about $25 soon after they listed, have lost 48 per cent of their value in the past year, and closed at $10.50 on Friday.
KKR hopes the value of the firm once it lists on the NYSE will be between $15bn and $19bn.