unlever beta with 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 debt without tax benefit. Given that it doesn't belong to common equity shareholders & it doesn't follow market prices (fixed dividends), 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.
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 ? I suppose less han the formula above, but the higher the beta the lesser the risk of over-valuating ?
Thank you
Best regards
Hi ManoftheShadow
Under your assumptions (debt and preferred beta = 0; tax shield same risk as debt), your equations are correct.
It would certainly be wrong to include preferred in the debt component. As you correctly point out, preferred dividend payments are not tax deductible.
However, the zero-beta assumptions are highly questionable, especially in the case with debt AND preferred. You point out one of the reasons why. Working with this assumption can lead to SEVERE bias (see for a discussion and solution of this issue: https://www.tebu-finance.ch/forum/firm-valuation/how-to-avoid-bias-when…)
The risk of preferred is between the risk of debt and the risk of equity. Hence, the beta of preferred will not be zero. If you don't know the respective betas, try to figure out what return the respective providers of capital expect to earn. For example, what's the return the preferred stockholders expect to earn? If this return is around, say, 6%, the risk-free is 2% and the market risk premium is 4%, the beta of preferred will be approximately 1: (6% - 2%)/4%.
We have uploaded an excel file that allows you to unlever and relever betas of firms with preferred stock without the zero-beta assumption:
https://www.tebu-finance.ch/forum/firm-valuation/unlevering-and-relever…
If you alternatively set beta debt and preferred to zero, you will see by how much your unlevered and relevered betas deviate.
Hope this helps. tebu finance
Thank you so much, really really helpful! I actually never saw on any book before this way to present the return formula to get the implicit beta: implicit beta = (expected return - Rf)/MRP. It is very useful!!.
The excel files on the link are also excellent too, thanks. I scrutinised them and it would seem you use the following formula to unlever the beta in an existing tax shield hypothesis: (beta of debt * Debt value *(1-t))/(assets - VTS) + (Beta Ps * Ps value)/(assets-VTS) +(Beta Equity * Equity value)/(assets-VTS) with VTS = Value of Tax Shield
I see some very interesting points in this formula you use. And I hope you can elaborate some of the choices you made (see below): - VTS is substracted from the asset denominator, whereas the tax gain is kept in the beta of debt => how do you explain this reasoning? - unlevered beta obtained is not corrected from cash => does this mean this is the Firm unlevered beta, hence the denominator (Assets - VTS) in the formula to unlever is to be considered as Firm Value - VTS (operating + non-operating assets - VTS)? => If we changed to a non-existing tax shield, we would just remove the *(1-t) and the -VTS in the formula?
Thank you so much, Kind regards
Hi, I am glad this helped. For your additional questions, you may be interested in the following appendix (http://vlp.tebu-finance.ch/courses/course/view.php?id=5§ion=7).
The unlevered betas are factually corrected for cash. What you have to do is assume that the firm's debt is actually its net debt, that is, interest bearing debt minus excess cash. It all goes through.
you should break convertibles into implied debt component and conversion option value (equity component) then use the adjusted debt/equity ratio for your WACC calculation
starts on pg 58 http://people.stern.nyu.edu/adamodar/pdfiles/ovhds/dam2ed/discountrates…
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