How present value of tax shields be calculated

Question

I have two valuations of the company that we set as an objective. Within one of them, the present value of tax shields (D Kd T) computed using Ku (required return to unlevered equity) and, in one, by using Kd (required return to debt). The second valuation is too higher than the first one, but here which of the two is better?

Answer 1

Fernández (2001) demonstrates that discounting the tax shields along with the Ku and the WACC is not right. There are six habitual expressions to compute the value of tax shields that are frequently used. Just three of them are valid (they have a theoretical origin):

Myers (1974) and Modigliani-Miller (1963), while the company plans to return the existing debt without making a newest one; Miles-Ezzell (1980) while the company plans its debt proportionally to market value of shares; and also Fernández (2004), while the company plans its debt proportionally to book value of the assets or shares.

Fernández (2004): VTS = VA [D Ku T; Ku].

Miles-Ezzell (1980): VA[Ku; D T Kd] (1+Ku)/ (1+Kd)

Myers (1974) and Modigliani-Miller (1963): VTS = VA[Kd; D T Kd]. Other incorrect formulae to calculate the value of tax shields are:

Damodaran (1994): VA [Ku; DTKu – D (Kd – RF) (1–T)];

Practitioners: VA [Ku; DTKd – D(Kd – RF)]

Harris-Pringle (1985) y Ruback (1995, 2002): VA [Ku; D T Kd]

Myers (1974) has to be used only while it is possible to know with whole certainty the amount of the debt at any future instant. Miles y Ezzell (1980) has to be used only when the future debt is proportional to market value of the shares that we are not aware of any company which manages its debt in such a way. Fernández (2004) has to be used only when the risk of the future raise of the debt is the same to that of the FCF.