LBO Financial Modeling Question

For context: I did two self-study modeling courses (one with Corporate Finance Institute, one specifically related to LBOs, and both models have the same approach for post-close ownership calculation, which confuses me. I understand how it's calculated, but not why (and neither explained)

Using a hypothetical scenario to explain what confuses me, and let's assume no fees for simplicity's sake:

  • $10M enterprise value as purchase price

  • Seller rolls 20% ($2M)

  • $4M of debt.

  • Fund contribution of $4M.

  • Post-close equity value in this case would be $6M.

The way the two models calculate common share ownership is as follows: The seller has $2M of the $6M post-close equity value, and the sponsor has $4M of the $6M. This means the seller has 33% ownership, and the fund has 66% ownership. Then, when you sell the Company five years later, the seller gets 33% of the proceeds, and the fund 66%.

The way the 33% / 66% is calculated is clear and simple. That said, to me it does not make sense. If the company is bought for $10M, and the seller rolls 20%, shouldn't the seller ownership be 20% (based on enterprise value), rather than 33% (based on equity value)?

Using the house analogy, if I buy a house for $1M, and have a mortgage of 80%, I still own 100% of the house, no matter how much leverage is used.

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