Hi, I am Karnen from Indonesia. I am currently reading your Corporate Finance textbook (third edition). Overall, I like the book. *(http://book.ivo-welch.info/home/)*

However, on Chapter 17 : Taxes and Capital Structure, page 550, seems to me you are indicating that all three valuation methods (APV, WACC and FTE) will not give us the same result.

You put there : *Properly applied, all three methods should provide similar – though not necessarily the exact same – answers.*

This statement of course is not right. All three valuation methods should give us the exact same answer (up to 0.00). This is very clear and proven already in many papers, which I enclose herewith for your reading.

1. Taggart (1991): Consistent Valuation and Cost of Capital Expressions with Corporate and Personal Taxes.

2. Papers written by Joseph Tham and Ignacio Velez Pareja (you could easily download their papers via ssrn.com). Both authors also wrote the book : **Principles of Cash Flow Valuation: An Integrated Market-Based Approach **(https://www.amazon.com/Principles-Cash-Flow-Valuation-Market-Based/dp/0126860408)** , **explaining in details how all those three valuation methods should result in the same value.

First, of course, we need to determine what the discount rate that we are going to use to discount the Tax Shield (could be Cost of Unlevered equity, Cost of Debt, etc.) then using the correct formula for Cost of Levered Equity, then all these three valuation methods will give us the exact same answer. No question about that.. Those authors have proven it.

I do hope there will be a revision to your Corporate Finance textbook in fifth edition.

Kind regards

**Prof. Ivo Welch:**

hi karnen—thanks for your note. how many of your MBA students will understand the nuances of the discount rate on the tax shield? and if there are any other imperfections in the market, such as investor market segmentation, how perfect will it remain?

/iaw

**Karnen:**

Dear Prof. Ivo,

Still I see, it is very important to state something correctly though students might not understand it when we said it. Some students will develop their curiosity and some don’t. However, for those students with growing curiosity, at least we have given them correct understanding early on. You could put that in the Companion to the book or Appendix.

I have gone through a handful of Corporate Finance textbooks (Stephen Ross & Jeffrey, Brealey & Myers & Allen, Brigham, Titman, Jonathan Berk & Peter DeMarzo, Ivo, etc.) and noted that it is Jonathan Berk & Peter DeMarzo explains away the concept of taxes and capital structure in a better way. You might need to look into their book, I guess, the best in the market. The concept of discount rate for Tax Shield is put there for students with higher curiosity.

I hope you don’t mind, if, I come back to you with more observation as I am reading more of your chapters.

Dear Prof. Ivo,

I sent herewith the Excel files, proofing all valuation methods (even 6 here) all leads to the same value (up to 0.00000000), so precise.

Again, the formulas were initially proposed by Taggart (1989), which paper I have ever sent it to you, and then elaborated more (using baby steps) by Ignacio Velez-Pareja and Joseph Tham.

Kind regards

Dear Prof. Ivo Welch,

I send you herewith the full-blown statements forecast including the Valuation using WACC. The assumption for the Tax Shield discount is Ku (Cost of Unlevered Equity). We could use simpler formula Capital Capital Flows (CCF) as suggested by RS Ruback (2000) in which both the Unlevered Cash Flows and Tax Shield are discounted using Ku. If used consistently, any methods will give us the exact answer, as long as we define the Tax Shield Discount and use correctly the formula for the Cost of Levered Equity.

In many corporate finance textbooks, many authors just jump to Income Statement and then build Free Cash Flows. Personally I found this a bit confusing to audience since it does not always tell us what happens to Balance Sheet and Cash Flow Statement.

The technique for balancing lies in the Cash Flow Waterfall.

Cheers

**Prof. Ivo Welch:**

hi S—I will take a look at your materials next quarter when I will be teaching the course again.

regards,

**Ignacio Velez-Pareja:**

Dear Karnen

Well, I think what we do in the model I sent days ago, is the same approach of the Cash Flow WaterFall. Could you give a look to that file?

From the Cash Flow Statement or Cash Budget Statement, that has 5 modules, I get directly the Cashflows as follows:

If you see the Module 3, it is what the firm pays to debt owners. Hence, the CFD (Cash Flow to Debtholders) is just the Net Cash Balance (NCB) of Module 3 multiplied by -1. The same with the NCB of Module 4: this NCB multiplied by -1 you get the CFE (Cash Flow to Equityholders). Hence the sum of CFE and CFD you GET the CCF (Capital Cash Flows) that is CFD+CFE. To get the FCF (Free Cash Flows), simply you subtract the TS (Tax Shield).

In the model, you have to define the TS as

In Excel

TS =Max(T*Min(EBIT+OI,FE),0) where OI is other income and FE is financial expense. With this formula you get three cases:

1) EBIT+OI (Other Income)>FE (Financial Expenses) ==> TS=T*FE

2) 0<EBIT+OI<FE ==> TS= T*(EBIT+OI)

3) EBIT+OI <0 ==> TS=0

Best regards

**Ignacio Velez-Pareja:**

Listen, my dear Karnen: I forgot to mention that they might be thinking on perpetuities and not in finite cashflows when they think of constant D or D%. Once they are freed from the perpetuities idea, they must realize the problem of constant debt/D%.

Again, if they are confronted with how do they forecast financial statements and how do they keep constant D/D% they will understand the issue.

Remember that value and cost of capital depend on cashflows. When I say that it means that say, Ke depends on the value of E and E depends on the CFE.

(*) Prof. Ivo Welch is J. Fred Weston Distinguished Professor of Finance and Economics

at the Anderson Graduate School of Management at UCLA.