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 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?


First, MM WACC is the most used method, we could say 100% being used in valuation reports in Indonesia. I guess, this method becomes so popular because ALL corporate finance textbooks will start teaching the valuation chapters by showing that most well-known MM theory and their formula.

Though I know after many years graduated from corporate finance school, many books, including Berk & DeMarzo (https://www.amazon.com/Corporate-Finance-4th-Pearson-Standalone/dp/013408327X), didn’t tell us, the way MM WACC is shown, is misleading:

Kd(1-Tx) D/V + Ke E/V

By linking (1-Tx) to Kd, though it is simple to tell the story to new babies, this is not right, this tax shield basically will be going to Equity holder. It should be written:

Kd D/V + [ Ke E/V – Kd.Tx.D/V]

Second, MM WACC has a couple of strong assumptions:

  1. The Company could exploit 100% tax shield, which we know now, this is not right. OECD and other tax jurisdictions (see the list enclosed) has limited the capability of the company to exploit the tax shield by either using balance sheet approach (DER is limited to certain x, for example, in Indonesia tax jurisdiction, DER for tax calculation is max 4x. Meaning, all tax shields coming from debt above DER 4x, will not be recognized for tax purposes, the Company in calculating the corporate income tax, the interest will not be enjoying the tax deduction]
  1. It is “a must” to assume away how much we want to put the ratio of D/V and E/V (one of them will be the residual, depending we start with D/V or E/V first]. This D/V (or E/V) creates circularity, and could only be used in limited cases, so this is not general formula.

D/V in many cases, will depend the company profile itself.

Under project finance financial modeling, D/V seldom to be stabile. We will assess the strength of projected cash flows during the project term (10 – 50 years), and “sculpt” the debt to follow the pattern of the cash flow, and along the way, the debt will be paid down. The Debt amount will be high in the early years of project finance and then down. Theoretically, MM WACC should not be used, Myers- APV is a good one to go. We assess TS separately instead of lumping it into WACC. But of course, this TS discount rate is another big issue to say, how much we want to put there?

For mature company, in many cases, what we see, stabile  book D/E ratio, though this doesn’t automatically we could say, we will have one rate for D/V. For mature company, they will keep debt balance the same, unless, they have new projects. Debt itself may means working capital loan, investment loan, and trade finance loan. So this really depends on the company’s situation. Some could have a stabile debt balance and some couldn’t have. For example, trade finance loan might be up and down dependent upon whether the company has import activities during certain period.

Third, continuously adjusted debt (introduced by Harris-Pringle) or Annually Adjusted Debt (by Miles-Ezzel), though good for academicians, I never it is used in reality. The company could be quite crazy to keep changing their loan balance from year to year.

This book (https://www.amazon.com/Principles-Cash-Flow-Valuation-Market-Based-ebook/dp/B001P81GQS), gave me a couple of fresh things, among others:

Tax Shield (TS) discount rate assumption is so critical if we want to get the consistent results among many approaches (MM-WACC, general WACC, CCF, APV, etc.) But once we talk about TS discount rate, this is never-ending battle, which rate is to use? Myers-APV is also problematic to apply since we do need to decide Ku (cost of unlevered equity), which is not observable in share capital market.

The discount rate being used under “finite” and “perpetual” is different, though in many corporate finance textbooks, probably for the pedagogic purposes, the authors make (try hard) to simplify the chapters and the teaching…just use the perpetual formula to teach (Note: this is not totally wrong, since if you start teaching valuation by using MM theory, then 100% you will get into that very famous formula for perpetual situation. Unfortunately, not many finance authors tell us that this “perpetual” formula is only applicable under very special condition and not a general one. In many cases, they justify their “perpetual” formula by saying that the company lives forever, shares could be exchanged forever, etc…

The book strictly keeps coming back to TS discount that should be explicitly stated. Many corporate finance textbooks, including Berk and DeMarzo, shy away from this. Though in several parts of the book of Berk and DeMarzo, I read, they are in support for the use of Ku or Kd (Under “Leverage and the Cost of Capital” section of Chapter 18, whether the company maintains target leverage ratio, or not).

Joseph Tham to Mattia Landoni (http://www.mattialandoni.com/)

Dear Mattia, 

For perpetuity:

Ke = Ku + (Ku – Kd)*(D – Vts)/E for the case Kts = Kd

So one can interpret the term (1 – T) as the adjustment for effective debt.

Due to my ignorance I have never read this interpretation of the term (1 – T)

Interesting and thought provoking.


Yes, but one of the many sources of confusion is that typically people start from a perpetual firm with constant debt, so that

D – Vts = D(1-T)

and the formula for Ke is

Ke = Ku + (Ku – Kd)*D(1-T)/E


But then if you have a different case, e.g., a 1-period firm, the formula becomes

D – Vts = D(1 – T Kd / (1-Kd))

Ke = Ku + (Ku – Kd)*D(1 – T Kd / (1-Kd))/E


Many people do not realize that the formula for Ke should change this way, they use the former version everywhere, and in many cases underestimate Ke significantly. So it is helpful to explain it as D – Vts, even though it’s only for the special case Kts=Kd.

Mattia, could you give me a clue (hint?) on how we develop annual state prices that correspond to the appropriate discount rates? I am lost!!

It’s super simple. One way is that you derive them aprioristically as the prices of Arrow-De breu securities from the utility function of the representative investor in a general equilibrium model.

The second way is, you define a large number of relevant future time-state paths – e.g. a binomial tree with future values of the market portfolio – and for every time-state you derive your best guess of CF from an asset. You do that for many assets whose value is observable. Then, the state prices are the ones that minimize the distance between observed prices and model prices across all assets. Usually people do this using an S&P500 index fund and its option chain, which gives you many assets without having to work a lot to get the cash flows.


Hi Joseph and all,


Many people still saw (1-T) is the favourable adjustment to the effective rate of Kd, since this is shown after Kd in the formula. This sounds logical since there is interest tax shield. Yet, what many don’t tell us, from where this traditional WACC came from. It is in deed “simplified” version. I believe, the finance teacher should write  traditional WACC as :


Kd D/V + (Ke E/V – Kd.T.D/V)


Though mathematically it is simpler, yet this has lead the wrong idea that Ts belongs to debt-holders and not to equity-holders.


Under MM theory, they have no obligation to show the above formula, and instead using the simpler one, since their emphasis of cash flows is Free Cash Flows.


Well put, thanks and nice to meet you all by the way.


Kd D/V + (Ke E/V – Kd.T.D/V)


Also note that, by definition,


Kd D/V + Ke E/V == Ku,


So the above can be written as (and Jonathan Berk and Peter DeMarzo does)


Ku – Kd.T.D/V



Dear Prof. Peter DeMarzo,

I read Chapter 17 : Does Debt Policy Matter? Brealey Myers Allen, where it is said,

Capital structure can be irrelevant even when debt is risky.

Do you agree with that above statement?

One of strong assumptions of the MM propositions is Debt is default risk free, so cost of debt will be only related to time premium (and no default risk premium).

Prof. Peter M. DeMarzo:

Yes of course, risky debt does not change MM, as we explain in Chapter 14 under Figure 14.1.  See the figure in that chapter, which includes risky debt. (https://www.pearson.com/nl/en_NL/higher-education/subject-catalogue/finance/corporate-finance-4e-berk-and-demarzo.html?tab=table-of-contents)


I noted that it is Stiglitz (1969) and Rubinstein (1973) that have shown that the conclusions concerning the total value of company do not change as compared to the findings derived by Modigliani and Miller under assumptions about free of risk debt (Modigliani and Miller 1958, 1963, 1966. Note: MM 1958 assumed away distress by allowing the firm to issue risk-free debt). However, the debt cost will be changed.


Stiglitz J (1969) A re-examination of the Modigliani–Miller theorem. America Economic Review 59 (5):784–793  and its Comments on Stiglitz’s Reexamination of the Modigliani Miller Theorem by David T. Whitford (1980)

Rubinstein M (1973) A mean–variance synthesis of corporate financial theory. Journal of  Finance 28:167–181


Peter M. DeMarzo:

Yes, those are useful references on the topic.  I will suggest adding them to further readings.


Reading both of those papers, Stiglitz and Rubinstein took different route in incorporating risky debt into the cost of capital. Stiglitz used a state preference framework and Rubinstein applied a mean-variance approach. However, both authors gave us the same results that risky debt has no impact on value, the same conclusion gave by MM Proposition. Those 2 papers are not really easy to follow, yet, the simple idea in the assumptions of MM Theorem that there are no costs to bankruptcy i is much simpler. Meaning without the bankruptcy cost, then it doesn’t make much different whether the firm could issue debt at risk-free rate or at riskier one.


Dear Prof. Ivo Welch (*),

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

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

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

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

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

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

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

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

Kind regards

Jakarta, 16 November 2018

Prof. Ivo Welch:

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






Dear Prof. Ivo,

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

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

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


Dear Prof. Ivo,

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

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

Kind regards


Dear Prof. Ivo Welch,

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

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

The technique for balancing lies in the Cash Flow Waterfall.



Prof. Ivo Welch:

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



Ignacio Velez-Pareja:

Dear Karnen

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

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

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

In the model, you have to define the TS as

In Excel

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

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

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

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

Best regards

Ignacio Velez-Pareja:

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

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

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

(*)  Prof. Ivo Welch is J. Fred Weston Distinguished Professor of Finance and Economics
at the Anderson Graduate School of Management at UCLA.