I got this email from Mike Adhikari informing me about the Advanced Growth Model that he introduced as a better model compared to over-simplified capital structure assumption in the Gordon Growth Model.

Hello Sukarnen:

Capitalization 2.0 will be released at the NACVA Conference on June 5th, 2019.

The current single-period capitalization method, and the method used to calculate the terminal value in the multi-period DCF are used when the business is growing at constant rate. These methods implicitly assume that, after the willing buyer buys the business, the capital structure of the business will remain constant, and that the debt principal will not be amortized (i.e. debt will never be repaid.)

Capitalization 2.0 eliminates these assumptions. It considers that even when the business is growing at a constant rate, the debt principal may have to be paid down, and hence the capital structure will change.

Current methods use Gordon Growth Model (GGM) formula, whereas Capitalization 2.0 uses the newly developed Advanced Growth Model (AGM) formula. Typically, GGM formula overvalues a business by 10-50%

Unlike the GGM formula, the AGM formula is complex; hence, a spreadsheet of AGM formula can be downloaded (free for a limited time) from the website www.AltBV.com.

Upon visiting his website, I got two papers that I could downloaded, as enclosed, and the summary of the differences in the results between Gordon Growth Model vs Advanced Growth Model, as follows:

I think this Advanced Growth Model concept is interesting as the capital structure assumption is on of the critical assumption in all valuation models. The issue, can we assume away, the capital structure to be constant, and no principal debt repayment in the long-term?


June 2019

2 Articles by Mike Adhikari:

Article: Advanced Growth Model Reduces The Risk of Overvaluing From ‘Constant WACC’ Assumptions

Advanced Growth Model 0609 BVUpdate

Article : WACC as used in capitalization formula causes overvaluation


Raul Ibragimov:

Hello Sukarnen

Regarding the statement “…  constant WACC is making more sense than variable WACC …”, I disagree, moreover, I would say the constant WACC is an artificial construct. One may reasonably assume that the risk of firm’s assets (i.e. Ku) stays unchanged, but Ke and WACC will vary due to cash flow fluctuations and changes in the debt level.
The “AGM Model to challenge constant WACC” is dubious. In the background section the author mentions a setting where the debt is to be paid down and at the same time he assumes constant return expectations by the equity holder. These are confusion. When debt is paid down or held for n periods while the cash flows grow at a rate g, the leverage and hence the cost of equity Ke (expected return) would definitely change. A model based on incompatible assumptions makes no sense, so, going into subsequent algebra would be a waste of time, unless there’s an intention to write a reply.
There are two surprising statements on the second page. Saying “WACC ignores debt principal repayment” is a manifestation of not knowing the true mechanics of FCF-WACC valuation. See the writings of Ignacio and Joe to clear that out. Another one is arguing that debt has value other than its tax shields. What Mike Adhikary means, I wonder? He doesn’t consider any debt subsidy, neither does he differentiate between the contractual interest rate on debt and the cost of the debt capital.
Ignacio Velez-Pareja:
Hello, you all!
The debate is very “simple” to define: Ke and WACC depend on cashflows!!!!
Why? Let’s see what happens with Ke, for instance.
Ke = Ku + (Ku-Kd)D/E D and E are at t-1 and Ke and Ku and Kd at t.
E is the PV of CFE from t to N at Ke. This generates circularity but that is a different problem.
Constant Ke and WACC could exist forcing D to be a constant % of V at any time. Karnen has worked this case. Karnen, could you explain the cases you have been working on?
Yes, constant WACC and/or Ke are a construct and it doesn’t make more sense. What is usual in a firm is to contract loans as needed and the repayment of those loans define the level of debt and leverage. In practice, it makes no sense to ask the bank to repay or acquire new debt almost at random. Banks need some certainty in their cashflows. If debt is public debt, the situation is worse. To put bonds in the market is not an easy task that can be done, say, on a monthly base, not even on a yearly base!
Agree with Rauf. People try to adjust theory to their particular interests.
Joseph Tham:
We have always assumed that consistency is a strong and persuasive argument.

Forget taxes. In a world with perfect capital markets, if financing is simply equivalent to slicing a pizza, then it is possible to slice the pizza with no loss in value.
This means that the sum of the divided pizza must equal the whole pizza. No more, no less. We can illustrate this with the simplest two period example. Forget perpetuities. QED
Rauf Ibragimov:
As far as I see, the point Sukarnen introduced to discuss was not the constant vs variable WACC debate (which would be strange iin this consistency lovers club), but Adhikary’s new formula to substitute Gordon’s growing perpetuity. My comments go to that.
I dare say, that the statement “Ke and WACC depend on cashflows!!!!” is impresise. Take the setting of no debt, then Ke=WACC=Ku irrespective of CFs. Actually, Ke and WACC depend on Ku and debt level, the latter causes varying leverage and TSs contribution => varying Ke and WACC
Joseph Tham:
Growing cash flows in perpetuity?
I insist that we need to think about finite cash flows. Perpetuity is inflexible.

Even a 1000 years is not a reasonable approximation to perpetuity. I am stuck at this nonsensical assumption. This is my fundamental psychological barrier. Has always been.
Ignacio Velez-Pareja:
OK, Rauf, thanks for your comments and precision, however, under no debt and constant inflation, yes, WACC is constant and does not depend on CFs. Even with variable inflation, WACC doesn’t depend on CFs…
Joseph Tham:
If inflation is variable, then the nominal WACC may vary but the real WACC will be constant. Agree?

However, suppose the risk of the cash flow changes for some exogenous reason from years 5 to 10. Then the cost of capital real from years 5 to 10 may be different from the first five years. Agree in principle?
Ignacio Velez-Pareja:
If inflation is variable, then the nominal WACC may vary but the real WACC will be constant. Agree?
IVP: Yes, agree in general terms. The nominal cost of debt and equity   would be constant
However, suppose the risk of the cash flow changes for some exogenous reason from years 5 to 10. Then the cost of capital real from years 5 to 10 may be different from the first five years. Agree in principle?
IVP : Yes, in general, yes…
Then what?


It is common now for us to read the news about the Series funding that are received by start-up companies.

For example, GoJek, one of the most popular ride-hailing app in Indonesia, had even received up to Series F funding up to March 2019, as shown below.


Source: https://www.crunchbase.com/organization/go-jek/funding_rounds/funding_rounds_list#section-funding-rounds (accessed on 5 June 2019).

The purpose of Series A, Series B, etc. funding might be different, which for example,

Series A  ==> Optimize

Series B ==> Build

Series C ==> Scale

Source: https://www.investopedia.com/articles/personal-finance/102015/series-b-c-funding-what-it-all-means-and-how-it-works.asp (accessed on 5 June 2019).

These funding rounds provide outside investors the opportunity to invest cash in a growing company in exchange for equity, or partial ownership of that company.

Founder of the start-up company is an entrepreneur, and though he/she needs capital to build assets to generate as higher as possible the cash flows in the future, yet, he/she needs the capital at the lowest possible costs. The capital funding from the outside investors will translate, in most cases, to the equity or partial ownership of the company or venture. In other words, he/she, in exchange of the capital funding, sell the partial ownership of the venture to outsiders.

This Series Funding will provide a way for the entrepreneur to obtain the capital at lowest cost, while the business is growing its cash flows and its valuation.

It means, that the ownership cost that he/she has to sell, will go down, along with the higher valuation.

For example, if the percentage of ownership to sell will decrease compared to the funding needed, when the valuation is higher, as demonstrated below.


Knowing this relationship, then the entrepreneur could “TIMING” the funding needed, meaning that he/she does not have to raise the capital at one time, but could split it into some stages, while at the same time, he/she works with his/her team to grow the business and to bring more cash flows in the future or to reduce the uncertainty with regards to the business.

For example, if the business needs a total of USD 5 mio, then the funding could be broken into some Series.

If this US$ 5 mio is to be raised one time in the beginning while the valuation of the business might be not that high, for example, US$ 10 mio, then it means he/she has to sell an equity stake of 50%. Yet by timing the cash needed and funding raising, to 5 years, the equity ownership going out of the door to the outside investors could be much lower, depending the increase in the business valuation, as displayed below.

Under this simplified valuation example, it is shown that if the entrepreneur could “timing” the funding raising, then he/she will just have to release approximately 34% equity ownership instead of 60%.

Accordingly, this Series Funding is making financial sense for start-up entrepreneur.



It is known that cost of capital is market-driven, comparable to other investments of similar risk.

If this is the case, then we only know what WACC is as of now. Meaning that constant WACC is making more sense than variable WACC, since we will never know the cost of capital known in advance for Y2, Y3, Y4, Y5, etc?


Email exchanges among:

Joseph Tham

Raul Ibragimov

Ignacio Velez-Pareja


Joseph Tham:

For a given debt-equity ratio D/E, the only value of KTS for which the value of the return to levered equity KE is constant occurs when we specify that the value of KTS is equal to the unlevered equity return KUn.

For any value of KTS that is different from KUn, it is not possible for the value of KE to be constant, given the assumption that the regular standard debt-equity ratio is constant.

Please see attached note.

Joseph Tham ConstantLeverageImpossible_V1


Dear Joe,

Once you mentioned about Ku, this always intrigued me.

Ku conceptually, everybody knows that, is independent of leverage. However, the problem with Ku is, it is unobservable (and nobody can’t really be sure) in the market. Many will suggest the lever-unlever process, and in many books (including Damodaran’s internationally used corporate finance and investment books), Hamada model is being suggested for this lever-unlever process. Unfortunately, the assumption behind Hamada model (1972) is not really well explained in many of those books. I guess, well, Hamada model became a big reference since his paper is the first of the kind of explaining the relationship between leverage and equity beta, and even people call Modigliani-Miller-Hamada model when they are talking about this. Hamada formula assumes that Kd is the discount rate for TS and it is the perpetuity context with its (1-T) in the equation, which we know now that this can’t be applied to finite cash flow context.

Any comments?

Joseph Tham:
Hi Karnen,
Let me briefly respond to your excellent question.
Sure, Ku is unobserved, and it is an empirical problem. I FULLY AGREE.  My response will focus only on FINITE CFs. it may be the case that results from CFs in perpetuity do not apply to finite CFs, but I care MORE about finite CFs.
If we assume that Kts = Kd, it is okay but with finite CFs, the D/E is not constant and thus Ke is not constant. As the text by Berk and DeMarzo show, with finite CFs, and Kts = Kd, we must use the effective debt-equity ratio, and I am pretty sure that it is not constant. Will have to double check.
However, if we assume that Kts = Ku, then for finite CFs, D/E is constant and Ke is constant. In the finite CF, with Kts = Ku, there is no (1 – T) factor for the D/E.
These are my brief comments.

Raul Ibragimov:

Dear Karnen,

A widespread use of Hamada model in the lever-unlever process is puzzling, since its two assumptions – (1) debt is perpetual, (2) debt is risk free – do not hold in any realistic settings. Implications of this inconsistency could be amazing, you may give a look to a simple numerical illustration in the note attached, if you wish.

Probably, if one relies on the unlevering idea, it could be reasonable to use the standard (Harris-Pringle) formula assuming Kts=Ku instead.



Hi Raul,

I like it when you said …debt is risk free – do not hold in any realistic settings. I did remember in the wonderful book written by Joe and Ignacio, they have this assumption as well. They keep putting this assumption about Kd = Risk Free in many of their papers. I agree with you, this assumption is not realistic at all, unless we use it to discount “promised” cash flows (for government bills/bonds, or Triple A bonds in certain cases), instead of “expected” cash flow.

However, you suggested here to use Harris-Pringle formula instead, which as far as I know, their formula is built with the assumption that the debt level is being kept adjusted continuously to the growth of the investment. This latter assumption, again, is not realistic either in the corporate setting.

Thanks for the paper, I will take time to read it through.

Ignacio Velez-Pareja:

Well, you are discussing something that is too theoretical for me. I will write below from a practical point of view.

Although it is must to mention the unlevering and levering betas, I never use that for obvious reasons, in practice, we don’t have a significant market to do it with local stocks. Damodaran does it and estimates (and offers) unlevered betas with a hodgepodge of information from “emerging markets” and the procedure to arrive to betas (in general) is not elemental. He includes information from previous years and most recent information to arrive to the betas he offers.

We also double check with the investors their perception of risk.

We usually don’t use levered betas.

With that unlevered betas we estimate Ku. From that, you know how we proceed: when calculating PV of CFs we calculate the Ke that usually is not constant due to the implicit unlevering/levering procedure. For this reason it makes no sense to me to talk about “the” Ke.

Perpetuities are used only for the Terminal value. However, when teaching TV I confess, even to my students, that I am ashamed. Why? After insisting on detailed forecasted financial statements and on being aware of the correct cost of capital, etc., then I have to propose a perpetuity that is full of crazy assumptions…

After explaining the implications of the perpetuities and warnings about g and G, the “formula” I use is

TV = NOPLAT(1+G)(1-g/ku)/(G-WACC)

WACC is defined as Ku – KdTD%. Here D% is initially defined as a given value, but it implies a circularity between D% and TV (D% = D_N/TV) so we set that circular relationship.

Kd? We assume the expected cost of debt as the contractual Kd.

In short, we devote most efforts to the forecasting model from where we derive CFs. More than the effort we devote to the refined details of CoC. Most of value drivers are implicit in the CFs.

Joseph Tham commenting Ignacio Velez-Pareja: I think if we forecast CFs out to 15 years, it should reduce the impact of the TV calculation.

Rauf Ibragimov:

Thanks, Karnen, for your comments.

Sure, continuous debt rebalancing is not realistic. One may pick a discreet leverage adjustment version of Miles and Ezzell, if it feels better. “More general” refined models need Vu and Vts as inputs, which are unobservable as well. Finding a compromise between the theoretical rigor and practical convenience is an everlasting issue with no one for all receipt. Always a matter of benefits, costs and common sense.

What is your preferred choice, Karnen?


Hi Rauf,

Thanks for the email.

To be honest, I don’t have any preference. I don’t believe there will be one model that fit all sizes.

I guess, before going to lever-unlever mechanism, normally, during the training of Financial Modelling, I will teach the participants to determine first about whether in the model, they want to use:

  • Pre-determined debt level; or
  • Periodically adjusted debt level.

For example, in the Corporate Modelling, the company has had a history, we have their balance sheet, income statements and cash flow statement. And normally, we assume that it last definitely (though virtually they might end up be in bankruptcy or being purchased). Some historical analysis will give us an idea about their leverage policy. If this company is a public listed company, then this is much better. For this Corporate Model, pre-determined debt might work better. In building the model, though we have the value assessment of the company, yet, the main focus is more on ROI, ROE and EPS.

Other model, such as Project Finance, the project practically does not have history. Everything is from the scratch. Such project is characterized by alternative time phases that have different risk level. The fact for the modelling, there is no history on cash flows exist and the project has a defined lifetime. The main focus will be on the cash flows accruing (or to be flowing) to equity holders and lenders. We will “sculp” the debt level to be aligned with the cash flows pattern which in many cases, will be coming after the Commercial Operation Date, a couple of months/years after the project got kicked-off. For such modeling, Periodically adjusting debt level will be more appropriate.

For continuously adjusting debt level, I don’t believe this model, and I’ve never seen one in practice doing this.

In the wonderful book by Joe and Ignacio (Principles of Cash Flow Valuation), they gave us the formula for return to levered equity (page 276) under finite context, which formula to use will depend on the assumption being used for Tax Shield. Though all this formula is consistent mathematically, however, what I don’t really feel right even up to now: can we value Tax Shield separately using different discount rate assumption?

Tax savings from Tax Shield is not exactly the same like cash flows from other items that we know so far;

  • cash flow from operations
  • operating cost savings
  • opportunity costs (such as vacant land, that in the model, we could assume what if rented out to market)

All those cash flows are coming from the interaction with the third-party, which in many cases, there is a market for that. There is a supply and demand, resulting in the “price” that we could tag it.

Yet, for tax shield, the interaction is more with the government, and we do know, there is no market for such interaction. This is one-way. There is no pricing at all that we could build.

If this is the case, then  why we bother valuing Tax Shield? Even if we want to do that, we are faced with very problematic and debatable issue, which discount rate we want to use? There could be from A to Z that at the end, no one could be too sure to say. Empirically, we could not test that as well.

Pablo Fernandez model seems to me said that the value of Tax Shield is the Value of the Company paying (more) tax vs the Value of the Company paying (less) tax due to leverage presence. This conceptually might be right, as it is not possible (in my opinion), to value or to price Tax Shield separately.

What do you think?

Raul Ibragimov:

Hello, Karnen

Thanks for your extensive explanations.

Generally, i agree with the procedure you describe, and it immediately brings us to the tricky issue of Ku. One my look for comparables, and the next step she will have to decide on the unlevering formula. Which one? Any consistent expression for finite CFs needs knowing Vts (and Kts) or Vu, and the choice of a particular formula depends on an explicit answer on Kts. The issue seems unavoidable. Any ideas, how to deal with it, Karnen?

Many would use Damodaran’s industry unlevered betas, pretending the issue of Kts doesn’t exist. However, Damodaran applies Hamada’s model for unlevering/relevering procedure, and its validity is questionable.
How to proceed? Some compromise based on a common sense? What do you think?
Hi Rauf,

For lever and unlevering process, I shall take the route as suggested in the Chapter 19 of Jonathan Berk & Peter DeMarzo’s corporate finance textbook (now, 4th Edition, 2017).

In that chapter 19, unlevering beta will be:

Beta_unlevered = E/V * Beta_levered + Net Debt Value/V * Beta_Debt

In other version, we could write it:

Beta_levered = Beta_unlevered + (Beta_unlevered – Beta_debt) * D/E;

Or, if assumed away Beta_debt is small, or negligible, then we end up with a simpler one:

Beta_unlevered = Beta levered/ (1+D/E)

For comparables, Beta_levered and D/E as suggested by many practitioners might be better to use the sector or industry, instead of company level as there is quite “noise” in the stock market. But this is not always followed by me, since if the comparables are around 5-7 companies, I prefer using them.

Once this Beta_levered is obtained, we go to CAPM formula to determine the cost of the levered equity.

How about you? Which formula you use in the lever-unlevering process? Love to hear that as well.

Raul Ibragimov:

Dear  Karnen,

Looks we are in agreement, I’ll follow about the same route. Just note, that the formula Beta_unlevered = E/V * Beta_levered + Net Debt Value/V * Beta_Debt you mentioned (and its Beta_levered counterpart) is Harris-Pringle’s version under continuous debt rebalancing (Kts=Ku) assumption. Robustness and simplicity are advantages obtained at a cost of minor retreat from the theoretical rigor. When it comes to a real world pro forma modelling and CF valuation, I’d prefer CCF and accept Kts=Ku for the same reason, in some cases APV could be more informative.

Do Ignacio and Joseph share this point of view, I wonder?

Ignacio Velez-Pareja

Let me comment on Rauf note below, please.

Hello, Karnen

Thanks for your extensive explanations. Generally, i agree with the procedure you describe, and it immediately brings us to the tricky issue of Ku. One my look for comparables, and the next step she will have to decide on the unlevering formula. Which one? Any consistent expression for finite CFs needs knowing Vts (and Kts) or Vu, and the choice of a particular formula depends on an explicit answer on Kts. The issue seems unavoidable. Any ideas, how to deal with it, Karnen?

Yes, you have to define in which world you want to “live”. Let be practical: as Karnen said, adjusting debt is a good idea but in practice it might not be possible. Actually, the most common and probable situation is the one with variable D and D% for many reasons. Hence, I would think we are on the safe side if we consider that Kts= Ku. A plus of this decision is that formulas for Ke and for WACC are the simplest ones. Just one example: if you value with CCF, you only need Ku.

Many would use Damodaran’s industry unlevered betas, pretending the issue of Kts doesn’t exist. However, Damodaran applies Hamada’s model for unlevering/relevering procedure, and its validity is questionable.

Betas from Damodaran are much more than levering/unlevering. He adds some historical information from 5-10 previous years.

Yes, I have many questions about betas from Damodaran. Remember we (in Colombia) are part of emerging markets and you should know what that hodgepodge is (and it is not clear to me if we have a solution of this): in Emerging markets he has Colombia (about 20 firms much less industries (9) because many are from identical industry), Peru, Ecuador, Argentina, Mexico, etc with the same problems. To these countries, add Eastern Europe, Africa, South Asia, etc. plus India and China. Hence, when I get an unlevered beta from Damodaran, I don’t know what is really inside. I mean, the industrial code has about 100 industries. In Colombia, our Stock index has 20 stocks: 10 of them permanent and other 10 will be changed every 3 months; total firms in the stock exchange is 68 firms. In total, out of 100 industries, our index covers only 9 and one of them is the financial industry. 

This said, I wonder why would not be “valid” to ask the investor what is her expectation of say, Ku, and trying to push his estimation to the minimum. I have tried a methodical approach of that interview with the investor and when I make a reverse check with the implicit beta in the guesstimate and the one from Damodaran the results are not identical of course, but I never have found differences of 3x-5x or similar… Our main source of consulting in valuation is the non-traded firms. This means that the direct access to the investor is something normal during the consulting process. Remember that CAPM was a very clever approach to “guesstimate” the expected return of an investor to which you don’t have direct access. 

On the other side of the problem, I think we should put more effort on defining our CFs instead on the cost of capital, because most value drivers are there and not in the Cost of capital. Remember that what you get from the stock exchange are reactions of a market and traders that base their “offers” on very light fundamental analysis and they don´t even imagine what the CFs would be. Instead, CFs come from lots of variables such as prices, volume, increases in prices an costs etc. I believe that our attention should be at where value is. 


Dear Ignacio and Rauf,

It’s always quite glad for me to read all your valuable comments. It really adds my understanding.

I just want to add something the reason as to why I took this Harris-Pringle formula when I use the market data to calculate the Beta_unlevered.

I am faced with three choices with regards to the assumption on the leverage policy of those comparables or the industry data. I could assume away their leverage policy:

a) keep the permanent debt level

b) annually adjusted debt level

c) continuously adjusted debt to maintain a target leverage ratio

Some empirical papers found out that the industry’s leverage policy is reasonably sticky, which means that the leverage ratio does not change much or significantly from period to period. I then prefer using the target leverage ratio assumption in running lever-unlever process. As a consequence, if we assume that  there is a target leverage ratio, it is also equally reasonable to assume that the risk of the tax shield will be the cost of unlevered equity (Ku). Again, as a consequence of the latter, we could say that KTs = Ku, as long as the cost of capital is constant along the way. This brings us to what exactly our friend, Joe, said, in the beginning of these long email exchanges, which I quoted again below:

For a given debt-equity ratio D/E, the only value of KTS for which the value of the return to levered equity KE is constant occurs when we specify that the value of KTS is equal to the unlevered equity return KUn.

For any value of KTS that is different from KUn, it is not possible for the value of KE to be constant, given the assumption that the regular standard debt-equity ratio is constant.

(Note: I do hope, Joe will know now that I was a good listener to what he wrote before.)

However, having a continuously adjusted debt, is somehow, troubling me, since I know this is not realistic in corporate life. Yet, I guess, having a target leverage ratio, will not mean that it will be “constant” over or all the time.  The company might set a periodical schedule to adjust their leverage ratio along the way.

This sounds a bit a compromise for myself for practical reasons.

Having Ku as KTs will surely simplify many things in calculating the valuation, which will lead us to the compressed APV, or CCF.

Personally, I buy this idea that KTs = Ku. Most of the corporate finance books including MM will use Kd as the KTs, yet, I am not too sure this is 100% correct, since the risk of the tax shield is just based on a portion (which might be much smaller) of the whole debt payments, and additionally, this risk of tax shield is quite associated with the fluctuated marginal tax rate of the company.

Having said that, it is not that easy as well to sell this idea to the market as Ku is again, unobservable.

Raul Ibragimov:

Hello Ignacio and Karnen,

All sounds like a meeting in the club of fellow believers :)) And that is great!

No sure, there’s a choice other than saying good bye to the academic rigor fetishism when entering the real world with its uncertainty and complexities. Though we can’t go ahead without a reasonable estimate of Ku, I agree with Ignacio, building a sound CFs forecast is always the core. 


Hi Raul,

Personally I am quite glad to know you now, though only via email. For Ignacio, the chance to exchange emails with him started a couple of years ago is really eye opening. After one or two email exchanges back in 2012 something, he just forwarded me his book for me to read. And that book wow is really good…I do hope it gains wider audience. Many concepts I got from this book. I will be grateful to ever read this book and got many opportunities to discuss with Ignacio. He is such great teacher and I do hope I had had ever sit on one of his classes. He is a kind of quite open minded finance scholar.

About Ignacio’s point to Cash Flows..that’s exactly the same point being used by Jonathan Berk and Peter DeMarzo to close their chapter 13. A very strong reminder before entering Part V Capital Structure of their book.

Prof. Ivo Welch also reminded the readers of his Corporate Finance textbook that the error being made in Cash Flows has much bigger impact to value compared to the error in discount rate. He gave example even to emphasize this point.

Ignacio Velez-Pareja to Karnen : Thanks, Karnen for those compromising comments from you. I am sure you are too generous with me.

Raul Ibragimov to Karnen:

Thanks, Karnen. It was a pleasure exchanging ideas with you.

I like the new generation textbooks by Berk-DeMarzo and Welch you mention. Would it happen I teach a course in corporate finance, I would suggest them as the core readings.

The Cash Flow valuation book by IVP-JTh is one of the top few in its field, and I am happy to have a chance to communicate and learn from the authors.

April 2019


Email exchanges in March 2019 among:

Joseph Tham, Carlo Alberto Magni, Rauf Ibragimov, Karnen and one Respondent



FCF is easier to sell than CCF to corporate audience. People love tp hear “free cash flows”. I guess it might be the reason it is so popular and Stern was the big sponsor in their book The Quest of Value.

FCF is the project cash flows..without concerning too much on TS. Many finance decisions at corporate life, they are more focused on whether ROA is higher than Kd when the financing decision comes up. TS becomes limited now since the tax authority limit debt to equity for max 4x. So we cannot exploit lnterest TS too much.

CA Magni:

I see FCF as unnatural for the following reasons:

1) It is not the cash flow which is distributed to capital providers. It is only a part of the distributed cash flow (the one which does not depend on the capital structure)

2) the textboook WACC method assumes that a firm rebalances its leverage ratio. This is a strong assumption, most firms do not rebalance the leverage ratio (even more so if one is evaluating a single project rather than a firm).

Rauf Ibragimov :

The next moment a firm engages in the external financing transactions or retains cash, the FCF (as it is basically defined) becomes an artificial construct. CCF (as defined by Ruback) incorporates the tax advantage of debt, so it is an improvement (though, limited, as it builds on the FCF) in measuring cash available to satisfy existing claims. An advantage of the CCF approach in valuation could be no circularity and absent need to periodically recalculate the discount rate, however, forecasting CCF requires an explicit financing plan. The latter could be advantage as well, since implicit in the FCF-WACC approach is a generally unrealistic assumption of a constant leverage (market values) financing policy

As with the daily goods, consumer preferences follow the size of the marketing budgets for competing offers


FCF is designed to be the same no matter the capital structure. That is the point of it. Force people to not get confused and forget MM.

Using FCFE discounted at the cost of equity gives you the same results, if you do it right. If you know what you are doing, I do not advocate one or the other method. If you are going to do FCFE please avoid:
  1. Feeling that debt is cheaper than equity because Ke > Kd
  2. Forgetting to account for net proceeds from issuance of debt – very easy in a growing perpetuity firm model with constant leverage, something you are likely to use for residual value in a DCF valuation model
  3. Forgetting the MM theorem in any other way

Further to the point:

1)…….. as I stated, my favorite approach is state prices.
 FCF is needed to do either WACC or APV, so if one doesn’t like the constant leverage assumption of WACC, that doesn’t eliminate the need to define FCFFCF is the cash generated by the firm’s operations that is available to distribute to investors. It is not a part of the cash flow distributed to investors; it could be more OR less than what is distributed to investors in any given period, and typically more in the long run.
 I teach three valuation methods: FCF-WACC, FCF-APV, and FCFE (which I assume is what we are calling “CCF” here. I could teach a fourth if it existed and if I learned of an example in which it is clearly superior.) More often than not I observe that my undergraduate student become confused when they do FCFE with time-varying debt.
Both FCF discounted at WACC, and FCFE discounted at Ke, have an assumption of constant leverage. If you don’t agree, you appear to be forgetting the MM theorem. That is why I like FCF with APV – no confusion. You get separate estimates of the value created by financing and the value created by operations.
Nonetheless, the thing that started this whole discussion is a table in Berk-DeMarzo showing that you can do FCF-WACC with time-varying leverage; it’s just hard work. The same hard work is necessary if you want to use FCFE discounted at Ke.


Finally, the constant leverage assumption is necessary and reasonable in certain situations. If I write down a DCF to value a firm in years 1-10, and I need a residual value for years 10-1000, I assume constant leverage. As Keynes would say… “what do you do, sir?”

Carlo Alberto MAGNI  wrote:

The FCF is one “part” of the CCF,  the TS being the other part:


Obviously, as you imply, either part of CCF may be positive or negative.

I agree that APV creates no confusion: both parts are discounted at the respective risk-adjusted rates of returns, and there is consistency in the both ratios in the following sense: The unlevered cost of assets (denominator) reflects the risk of FCF (numerator), and the discount rate for TS (denominator) reflects the risk of TS.

Precisely for this reason I do not like FCF-WACC method: it does not preserve consistency between numerator and denominator and turns an unlevered cash flow into a levered value. I see the WACC as a plug which is necessary to make the leap from unlevered perspective to levered perspective. While mathematically correct, it is conceptually unsatisfying and difficult to digest.

In contrast, CCF is discounted at a rate which is significant, because it is the mean of the discount rate for FCF and the discount rate for TS. This is rather natural, given that CCF may be viewed as a portfolio of FCF and TS. Further, since the discount rate for CCF is also equal to the average of cost of equity and cost of debt, we have two different perspectives for conceptualizing it: investment perspective and financing perspective, respectively. This reinforces its significance.


I thought CCF was another word for CFE or FCFE. I had never heard about CCF. I see now that we were talking about different things.

If you define CCF as FCF + tax shield, and the appropriate discount rate as a weighted average of the unlevered cost of capital Ku and whatever appropriate rate for the tax shield Kts, then this sounds very similar to APV – I would call it “APV without keeping the pieces separated”. I suppose I have nothing against it, but before I teach it to my students as a fourth method, I need to be convinced that it has distinct advantages over APV.

Joseph Tham:

Apparently simple,

May be difficult to apply,

Used for matching,

Effective as a check on consistency,

Potentially useful,

Practically difficult to estimate

Apparently simplistic,

Practically unknown,

Totally ignored and neglected,

Definitely simple,

Superior to the FCF,

Poorly marketed

Usefulness is underestimated

May be confusing for accountants


CA Magni:

Indeed, one may  view the CCF method as a reframing of the APV method, where the two components, FCF and TS, are merged together into one single cash flow (the CCF) which represents is the cash flow which is distributed to investors. For this reason, It is also called “compressed APV”.

Investment perspective

VL = CCF/x = Vu+VTS = FCF/ku+TS/k^T


x=(ku Vu+ kT *VTS)/(Vu+VTS)

Financing perspective

VL = CCF/x = E+D = CFE/ke+ CFD/kd


x=(ke E+ kd D)/(E+D)

In finance textbooks the expression “CCF method” is mainly used with alongside the assumption kT=ku. This implies

x=ku=(ke E+ kd D)/(E+D)

so that V=CCF/ku.

The latter version has been introduced by Ruback.

Joseph Tham:

Hmm. The disadvantages of CCF do not readily come to mind. However, in the spirit of full disclosure, we must confess that we not unbiased assessors since we have been unsuccessfully peddling the CCF over two decades!!!

CA Magni:

I prefer CCF as intuitively much simpler than APV. I explain CCF in my lectures, not APV.

Joseph Tham:

Would you have a detailed financial example that would demonstrate clearly the superiority of CCF? I fully support Mattia’s skepticism. He is not happy with my hand waving and nontechnical explanations, understandably.