unlever the beta when there is preferred stock

Dear all, My query is the following (hope one of you could help): I'd like to take into account preferred stock when unlevering equity beta & then relevering the asset beta to a new equity beta, appropriate to the target cap. structure. If I pick Hamada hypothesis (existing tax shield & null debt beta, not arguing on these hypothesis it's just for this example): unlever with ßl =ßu(1+(DV/EV(1-t)+PSV/EV) ) relever with ßu = ße/((1+ (1-t)* DV/EV+PSV/EV)) PSV = preferred share value ; EV = equity value ; DV = Financial Debt value Im using gross debt in the beta & then in WACC weights computation.

When using these formulas, the higher the Preferred shares value, the lower the unlevered beta. PSV is considered as a levering resource (debt without tax benefit). Given that it doesn't belong to common equity shareholders, it doesn't follow market prices (fixed dividends), and add a mandatory cost before paying dividends to common equity holders I suppose it may be sound. Still, would this be consistent if PSV represents a significant portion of cap. structure ?

I sometimes see that PSV is simply included in debt (with tax bias), which doesn't look satisfactory to me, unless it allows tax benefit (rare cases). In other cases, PSV is purely ignored in the unlevering/relevering beta formula. This would, in contrary, result in an increase of the beta of assets. Would it be consistent ?

Thank you Best regards