Question: Is the Net Present Value (NPV) of Project will be equal to the NPV to Equityholders?

Prof. Peter DeMarzo (Stanford Graduate School of Business)


Hi Karnen,

We demonstrate this in Chapter 18 of the text (Corporate Finance), where we show that discounting FCF using WACC is equivalent to discounting Free Cash Flow to Equity using equity cost of capital.


That said, I find that in practice when people use the equity method the usually make mistakes in computing the FCF to Equity (because they don’t correctly account for the debt dynamics), so in that sense FCF/WACC or APV approach is generally much more reliable!

Ignacio Velez-Pareja:


Dear Karnen,

I understand that you are referring to NPVequity = NPVfirm. It is YES, you can see these papers:


Market Value Calculation and the Solution of Circularity Between Value and the Weighted Average Cost of Capital WACC (A Note on the Weighted Average Cost of Capital WACC)

(This has the original paper plus the published paper.)

Ignacio Velez-Pareja   Joseph Tham

Revista de Administração Mackenzie (RAM), Vol. 10, No. 6, pp 101-131 November-December 2009


Company Valuation in an Emerging Economy – Caldonia: A Case Study
Ignacio Velez-Pareja  Joseph Tham 

The Valuation Journal, Vol. 5, No. 2, pp. 4-45, 2010


Constructing Consistent Financial Planning Models for Valuation
Ignacio Velez-Pareja

IIMS Journal of Management of Science, Vol. 1, January-June 2010 (Inaugural Issue) pp 1-26


For proper WACC calculation Return to Basics: Cost of Capital Depends on Free Cash Flow
Ignacio Velez-Pareja

The IUP Journal of Applied Finance, Vol. 16, No. 1, pp. 27-39, January 2010


Applicability of the Classic WACC Concept in Practice
M. A. Mian Ignacio Velez-Pareja

Latin American Business Review, Vol. 8, No. 2, pp.19-40, 2007


Ignacio Velez-Pareja (in commenting the reply from Prof. Peter DeMarzo):

I understand their problem. Apparently, they use variable WACC and hence, variable Ke, BUT the problem is with the CFE calculations. Hard to believe.

Well, I read the part of Chapter 18 (of Corporate Finance textbook by Jonathan Berk and Peter DeMarzo).

They show the simple case (that when modeling and reality is not that simple) where they assume constant leverage.

They say that NOT assuming constant is a problem to find the amount of debt. It depends on how they make the financial forecasting. Using my methods (that we have discussed at lenght), you forecast financial needs! Trying to act as a blind user of the FCF departing from an Income Statement the analyst have NO CLUE of what is going on related to the financing of the firm. How come they could say that (either explicitly or implicitly) in a Corporate Finance book? Isn’t that relevant for managing the firm? That makes no sense.

What do you think?

I forgot to tell you that they cheated because they use the value from the value of FCF method to calculate debt. That is not serious. You have to define debt for each method independently. They also define interest from results obtained for the FCF. And they do this for APV and for PV(ECF).

Sorry for not telling you before… I forgot. That is a real failure and lack of academic rigor.

Haven’t you seen the step by step example where I define value for each method independently?

In short, to have in a forecast a constant leverage at market prices is the most difficult task. They show that as if it were very easy and it is not. You should read a paper I have about that:


I am not really against using constant leverage. Some companies have not always ups and downs of its market value of equity. So in certain periods it might work well. I don’t think valuation is about being accurate. Saying that we could give numbers that are reliable, will be questioned easily. This happened all the time with reports produced by big boys in finance. It might read as fraudulent.

However, being transparent and consistent might be good to use as you suggested in your papers.

Ignacio Velez-Pareja:

I am not against using constant leverage neither. The issue is to do it correctly. The issue is if you wish to use the tool just to do a blind and quick valuation without really knowing how things will be happening, if you wish to have a real managerial tool for tracking something relevant as leverage and if you wish to track down what is going on in the firm to achieve the goal of some given leverage.

With a tool like the one proposed by most textbooks like Corporate Finance (Jonathan Berk & Peter DeMarzo), you will never achieve that. Unless you just need a quick and dirty way to arrive to a magical number… like a NPV today to say yes or not to accept or reject the project.

Tell me which is the managerial tool for doing that tracking proposed by corporate finance textbook writers?

Going back to the use of FCF and WACC, they are just saying look, the only reliable method is it. The others (APV, CFE) are like self fulfilling prophecies! They “show” that the methods have identical results, because they depart from the first value (from FCF) to define the variables of the second (APV and CFE) and, Bingo! they yield the same result! That is cheating, my dear friend.

Going back to the beginning of our exchange of ideas, remember that you started it with the question of telling them about NPV equity identical to NPV firm. Yes, it is true but doing what they do is not the proper way to proof it. See, please,

V = D + E (mkt values)
NPV = V – Bvalue Assets
NPV = PV(CFD) + PV(CFE) – D – Ebv
NPV = PV(CFE) -Ebv = PV(FCF)- Book Value Assets only if D=PV(CFD).


Go to pages 629-640 (of Corporate Finance textbook by Jonathan Berk and Peter DeMarzo).

Ask them what should we do if we decide to use ONLY the APV or the CFE method. Assume that we say ok, we in our firm value ONLY with CFE because them and Velez-Pareja and Tham have shown that all methods yield the same results. Shall we, as suggested in those pages, do it with FCF first to estimate debt?

I insist, doing that is not that simple.

Please download this (bilingual) example:

I use it to teach my students how to calculate Values and NPV’s with different methods and I show they are all independent from each other (this means that discount rates, say, Ku, Ke, WACC and values are estimated independently for each method). And they match. For constant leverage, it is a little more difficult and it is explained in the paper I sent these days.

If you construct a set of financial statements it is almost impossible to get constant leverage in terms of market value.

Book value constant leverage may be possible. Even this may not be easy.

In fact as an exercise it would be good to try and construct a set of consistent financial statements with constant leverage, based on market value.

If you can do this, then you have truly understood valuation!!


“Market value” for many companies is an elusive concept, easier said than having the same measuring line falling into an agreement among many people.

Constant leverage  I believe no such thing in this real world, except in Excel and math world. As long as it doesn’t oscillate too high or too down, we need to bite it off as relatively constant. Of course, relatively constant could be read as constant.

Joe Tham (co-author of Principles of Cash Flow Valuation with Ignacio Velez-Pareja)

We try to measure market value. Sure it is elusive. Based on the assumptions we try to estimate market value.

In our models we DO NOT have constant leverage.

In our models, we use variable leverage.

You should make your argument against authors who ASSUME constant leverage.

Please read our approach carefully and check that you understand our principles.

However, in our models we can construct ANY kind of leverage, constant or variable.

Please check if other authors can do VARIABLE leverage.

We need no approximations in our models.

We use the exact leverage that you specify.

Why bite off as approximate when it is NOT necessary?

Please ask your other friends.

Ignacio Velez-Pareja:

Dear Karnen,

Well, almost all of our papers on valuation relate to variable leverage. However, I have to say that it is not previously defined (a predefined leverage is possible and that would be a generalization of the constant leverage case as in the paper I sent you these days). It is the result of the interaction of cash flows, values, debt levels, Ku and Kd when you use the popular Ke formulation (Ke_t = Ku_t + (Ku_t – Kd_t)D_t-1/E_t-1), for instance. Notice that Ke at t depends on value at t-1 and it is there where circularity appears.

If you go to my page you can search there for papers like WACC depends on FCF, or A Note on the Weighted Average Cost of Capital. In addition, ALL that is in the CFV book that you have read so carefully, comes from those initial papers. The same regarding the step by step example I sent you few days ago (


Another finance professors that I sent him up your papers, seems to me does’t really catch up your ideas and talking something that might be preached many times in the current textbook.

I believe and suggest you need to publish your corporate finance textbook in English. Nowadays it’s becoming rarer for people to read papers in the midst of so many papers published and it becomes harder for us to separate gold from dull.

Will try to look back at your excel file.

Ignacio Velez-Pareja:

I see what you mean. However, all the ideas in CFV book has been taken from papers we developed prior to that book. The Spanish book is based on the ideas published in the CFV book; at least what we have related to the financial model and the cost of capital. This Spanish book is an improvement to the CFV book in the sense that we have made an effort to explain step by step, for instance, the development of the financial model. Yes, that might be interesting to translate it into English.

Yes, most papers deal with finite cash flows that is what happens in reality. Do you work with perpetuities in your consulting activity?

Tell me which papers you or your colleagues don’t understand. I will try to explain them.

What I can say is that the underlying ideas in our papers/books are the M&M ideas. For instance, we use an equilibrium equatios for cashflows and values:


VUn + VTS = D + E


  • FCF = Free Cash Flows
  • TS = Tax Shield
  • CFD = Cash Flow to Debtholders
  • CFE  = Cash Flow to Equityholders
  • VUn = (Market) Value of Unlevered Firm
  • VTS = Value of Tax Shield
  • D = (Market) value of Debt
  • E = (Market) value of Equity

These two previous equations are from M&M papers.

The same happens with the fomulas for WACC and Ke. They have been developed in CFV book and in a previous paper.

Part of the problem is that we think that many people doesn’t have clear ideas on what the tax shields are. If that is not clear, tehy will not understand the derivations of general expressions for different cost of capital. These formulas are derived based upon the two equation above and a basic tenet of finance: PV_t = (PV_t+1 + CF_t+1)/(1+ i_t+1)

This formula is in some of the recent messages I sent you.

I wish to understand why finite is harder to understand than perpetuities. To me, perpetuities are an oversimplification and at the same time, a Pandora Box, because you might find some surprises…

Best regards


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