I have made 5 videos showing the consistent formulas that we need to use for Tax Shield discount rate, Ke (Cost of Levered Equity), which will give us the same computed value result.

In those videos, I use the assumption of TS discount rate being discounted at Ku (Cost of Unlevered Equity).

In a nutshell, we need to be consistent in which formulas to use..otherwise, the resulted value will not be the same…trust me!

Kd that should be used in the WACC for CCF Kd WITHOUT (1-Tax). Once we apply this, it is so easy to see that the WACC is now Ku….. This is why Ignacio Velez-Pareja (the co-author of the Principles of Cash Flows Valuation book) kept saying that the simplest thing to do the valuation if we don’t have much time, we just apply Ku as the discount rate to CCF.

No circularity….and we have more time to focus on building the better forecast for FCF and TS.

Now I could see WACC applied to FCF is not the best option…easily leading to incorrect TS which might not always be there for the company at tax loss situation, and the constant leverage assumed.

Notes from Ignacio Velez-Pareja: (Note: I put in italics)

For clearness, when you wish to use the name WACC. it is better to say WACC for the FCF or for the CCF. For Ku as discount rate for TS, in the first case, it is Kd(1-T)D%+KeP% or BETTER, Ku-TS_t/V-t-1. Please throw out the first formula for WACC for the FCF to the trash. In the second case, CCF, WACC is Ku = KdD%+KeE%. Throw out the last formula  to the trash. Just use Ku and that’s all.

We have 5 methods: 3 of them have circularity and 2 don’t. No circularity: APV and PV of CCF at Ku. Circularity: PV of CFE at Ke, “general ” WACC and textbook WACC. 

You are 100% right when you say that using Ku and CCF gives you time to devote to make a better forecast and models. 

Please notice that Ku = KdD%+KeE% is true ONLY when Ku is the discount rate for TS. Look at the other tabs/sheets for other discount rates (Kd, Ke or any number) and see the formulas you have worked on in the case of Ku as discount rate of TS and the others. Try calculating Ku = KdD%+KeE% for each case and you will notice that the ONLY case when it is identical to Ku is when Ku is the discount rate for the TS.

In the literature, it seems to me that people mix cases (discount rate for TS) even for perpetuities. For perpetuities, the case of Ke is as follows:

  1. For Ku Ke = Ku + (Ku-Kd)D/E for finite cash flows AND perpetuities.
  2. For Kd, in general, and for finite CFs: Ke= Ku + (Ku-Kd)[Dt-1/Et-1 – VTSt-1/ Et-1] .  For perpetuities. remember that VTS = KdDT/Kd=DT, hence, Ke= Ku + (Ku-Kd)[Dt-1/Et-1 – (KdDT/Kd)t-1/ Et-1] = Ku + (Ku-Kd)[Dt-1/Et-1 – (DT)t-1/ Et-1]. And then you have the popular Ke formulation for perpetuity (that many wrongly use for finite CFs): Ke= Ku + (Ku-Kd)[Dt-1/Et-1 – (KdDT/Kd)t-1/ Et-1] = Ku + (Ku-Kd)(1-T)Dt-1/Et-1
  3. Those many that use (or used) Ke=Ku + (Ku-Kd)(1-T)Dt-1/Et-1 were authors such as Brealey and Myers, just to mention one pair of Holy Cows in finance books. 


Back to my videos, in the next videos, I will use the TS discount rate at Kd (Cost of Debt).


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