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.



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.


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)http://papers.ssrn.com/abstract=254587

(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: http://papers.ssrn.com/abstract=997435


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 http://ssrn.com/author=145648 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 ( http://cashflow88.com/decisiones/ejemplo_paso_a_paso.xlsx).


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


Potential dividends versus actual cash flows in firm valuation



I read the joint paper of Ignacio Velez-Pareja (IVP) with CA Magni, Potential Dividends vs Actual Cash Flows in Firm Valuation.

My comments:

There are no examples shown by authors how to get Actual Cash Flows…as this is about Forecast then there is such thing called Actual.

Probably what I capture from this paper. The authors want that the investment policy and payout policy for the excess cash is explicitly spelled out. Instead of assuming all Excess Cash be distributed as dividends.

The investment policy for excess cash will have the same impact as all distributed as dividends if the excess cash be put into zero NPV activities. For this statement. I am not really clear since in many valuation exercises during forecast mostly return is higher that WACC (abnormal then slowing down to normal or competitive margin).

Zero NPV activities also raise a question..as it is hard to imagine the company want to invest in such thing.

Excess cash in many cash be retained for “temporary” reason, for example, in Apple, to anticipate legal claims, to execute Acquisition, etc. Ultimately, it will go down to shareholders..this could be seen in Microsoft and Apple cases.

Excess cash should not be a norm in many companies. It could be high in certain period if there is a potential liquidity crises in financial market as management decides to keep the excess cash for a time being until the threat is lifted out.

As forecast is for long term view. Will this potential cash flow vs actual one will be a big difference to valuation? Or the error of not doing will have big impact? To answer this. Again I don’t see any example in numbers be shown by the authors.




The idea of that paper on potential dividends is simply that when calculating CFs you should take into account working capital including cash in hand and excess cash as ST investments if any.



I guess excess cash is not a spontaneous one, like Trade receivables or any operating cash.  This is a discretionary element. If it is considered too big, management could distribute it by increasing the payout ratio.




Yes, it can. But I wonder if you as analyst should decide that. It is a decision of the board of directors. 

If you are an analyst and forecast the CFs probably you don’t acummulate cash permanently. Hence, in general, cash and ST investments shoud be included in the working capital and forget the idea promoted by Damodaran of Potential Dividends.

When forecasting you can (as I do in my model) define a cash hold policy, a distribution policy (payment of dividends or Net Income), and a mechanism (see module 5 in our model) of investing temporary any excess cash that could be found. The policy IS NOT or SHOULD NOT to accumulate cash, in general. In any case, if the firm decides to hold cash it is a decision that destroys value and should be reflected in the CFs and hence in Value. 

In the model we have 5 modules: 

Module 1. Operating income and expenses

Module 2. Investment module

Module 3 Financing module: defines amounts of debt to be taken and payments of principal and interest

Module 4 Equity module:  amount od equity to be invested by owners and dividends payments

Module 5 Excess cash definition.

In Mod 3 and 4 we define the size of the deficit and we increase it by the amount of cash in hand, otherwise, your minimum end cash would be zero. Mod 5 defines if there is superavit that is decreased by the minimum cash desired. Otherwise the minimun cash in hand would be zero.

Minimum cash is defined by policy. The greater the cash in hand, the lower firm value. Defining the level of cash should be an issue to be formally studied. You can explore the firm history to see what final cash is compared, say with revenues or with expenses and based on that you define the policy as a % of one of them



Including excess cash into working capital movement comes with a cost. The amount of working capital then doesn’t make sense anymore…too big?

About the BOD (Board of Directors)’s decision, the shareholders could push the BOD to distribute the excess cash in dividends or share buy-backs. Remember FCF theory behind Acquisitions and Buy-outs in mid 1980s. The company holds too much cash.

Anyway, the issue is how to determine the elements of unlevered cash flows generated by the project, assuming that the project is financed entirely by equity.

Is excess cash of part of that?

Seems so..if this is generated by Operating Assets entirely.



Yes, few months ago I sent the complete model.

Except ST debt, you can model the project with 100% equity and this yields zero LT debt in Module 3. If you wish not to include ST, I will have to double check the model. I have to try it.

The behavior of the model is that when there is debt, then no excess cash to invest. It would make no sense to invest excess cash while paying interest on debt.



In reality, there is a cash called compensating balance in which company keeps paying interest on debt while keeping deposit in the same bank. Or, a company has a borrowing facility with a bank which loan facility requires the borrower to have their cash management be handled by the same bank lender, which means the borrower has to keep their current account and any excess money with the same bank.

So this is not uncommon thing.




Yes, that could be a condition from the bank. However, if the bank requires the same amount as collateral it makes no sense to borrow money from it.




November 2018