The Cross-Term in a Value Bridge, Explained

The cross-term equals (ΔEBITDA) x (ΔMultiple). It arises because when both EBITDA and the valuation multiple change, the simple additive decomposition, EBITDA growth at entry multiple and multiple expansion at entry EBITDA, leaves a residual. The cross-term captures the interactive effect of both drivers changing simultaneously. Without it, the sum of the two primary effects understates the total enterprise value change.

Two common allocation methods:

1. Conservative (operational bias): Allocate the entire cross-term to EBITDA growth, essentially valuing the EBITDA delta at the exit multiple. Multiple expansion is then measured at entry EBITDA only. This highlights operational improvement.
2. Proportional: Split the cross-term between EBITDA growth and multiple expansion based on the relative size of each primary driver (e.g., if EBITDA growth contributes 60% of the combined primary effect, it receives 60% of the cross-term). This treats both drivers symmetrically.

I prefer the proportional method because it avoids arbitrary bias and gives a balanced view of where returns came from. However, I acknowledge the conservative method is common when sponsors want to emphasize operational value creation to LPs. In an interview, I clearly state the method chosen and verify the sum.

Follow-up pressure:

• If EBITDA declined but the multiple expanded, the cross-term would be negative. How would you allocate a negative cross-term under the proportional method, and what does that imply about the sources of return?
• A sponsor reports a 3.5x MoIC and says 80% from operations using the conservative method. If the cross-term was large and you reallocate it proportionally, how might the operational contribution change?
• Does the allocation method affect the total equity value creation in the bridge? Why or why not?