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. (


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. (

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 Both authors also wrote the book : Principles of Cash Flow Valuation: An Integrated Market-Based Approach ( 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.



Why it is so important to have an assumption that debt is risk free and the interest rate on debt is the risk free rate?

I keep noting that many corporate valuation textbooks and papers have such explicit assumption.

This assumption is also part of MM Theory.

If debt is risk free that Kd = Rf, which in many cases, analysts will use government bonds as a reference. Why is not using corporate bonds since we are valuing firm (public or private)?

Will this assumption be used because we want to use Book Value of Debt instead of Market Value of Debt? If the Debt is not risk free, what is the impact to WACC or firm valuation?

Kd is only assumed at risk free is a lot confusing.

Kd should be Risk Free + Business Risk Premium

Ke = Risk Free + Business Risk Premium + Financial Risk Premium

Then how come we assume away Kd = Risk Free only?

Risk free debt is very common assumption though I don’t know why is so important to stress this.

See Hamada (1972) paper. He has this assumption as well, risk free here means default free..if this is what it means, then government bond or AAA corporate bonds will be the representative of Default free debt.

Hamada model assumes that tax shield is riskless ( is default risk free or riskless the same?) and thus each period’s tax deduction arising from interest payment shud be discounted back to date 0 at the risk free rate. This implies beta of debt tax shield in the Hamada model is zero.

I resolved this risk free rate assumption for debt.

Risk free here means default risk free, but still includes business risk premium.

Why is default risk free assumption crucial?

It is because we are going to use EXPECTEd rate of return to discount EXPECTED cash flows.

To be EXPECTED rate of return, then it should be default risk free, otherwise it becomes PROMISED rate of return.

For example, a bank wants to lend  $100 with expected rate of return of 10%, then the actual interest rate the bank will charge the borrower will depend its default probability. The higher the prob % then the higher the promised interest rate it will be charging.


Ignacio Velez-Pareja (Columbia)’s comments

In fact, Kd = Rf + Debt Risk Premium. You can see that in the DB from World Bank. It was a surprise for me because in our model (the xls model I sent you) I said that Kd was estimated as in CAPM: Rf + DRP (debt risk premium). I know that we have been using the wording Kd as risk free, but that is not exact. ANY debt has a risk, but it is lower that the implied risk in Ke





Note: Karnen in Italics


I can’t see under Tax Shield (TS) discount rate = Ku, then Ku = pre-tax WACC, or D/(D+E) Kd + E/(E+D) Ke?

I found a side note in my Stephen Ross Corporate Finance textbook (7th Ed., the book I read during my master study) showing Ku = WACC without corporate tax.

(1) WACC = D/ (D + E) * Kd + E/ (D+E) Ke

(2) Ke = (Earnings before Interest EBI – Kd* D)/E

Incorporating (2) into (1), we will have

WACC = (kd*D + EBI – Kd*D)/(D + E)

Since under unlevered situation D= zero, then


EBI/E here is Ku!

However you gave me one statement that the above is correct only under TS discount rate is Ku….here I don’t get it..???

What is the relationship between TS discount rate for WACC pretax with Ku?

I guess your statement probably is unintentionally wrongly said?

Ignacio Velez-Pareja:

Yes, it is valid for any value of discount rate for TS.

My comment on Ross derivation is this: one thing is to design WACC without taxes and another thing is that a situation without taxes means D=0.

Let’s see

Let’s see this


Adjusted WACC applied to the FCF

Let WACCAdji be the adjusted WACC that is applied to the FCF in year i. Then we have

VLi-1×WACCAdji  = Di-1×Kdi – TS+ ELi-1×Kei                                (24)

VLi-1×WACCAdji  = VUni-1×Kui + VTSi-1×yi – TS                            (25)

VLi-1×WACCAdji  = (VLi-1 – VTSi-1)×Kui + VTSi-1Xyi – TS              (26)

VLi-1×WACCAdji  = VLi-1×Kui – (Kui – yi)×VTSi-1 – TS                   (27)

In equation 27, if not taxes, we obtain,

WACCAdji  = Kui                     (28)

However, when there is no taxes, FCF and FCF are identical. Remember


When no taxes, TS =0 and


And WACC for FCF = WACC for CCF = Ku.

From (24)

VLi-1×WACCAdji  = Di-1×Kdi – TS+ ELi-1×Kei

BUT, if no taxes , then

VLi-1×WACCAdji  = Di-1×Kdi + ELi-1×Kei

and WACCAdj =  KdiD%i-1 + Ei-1%XKe = Ku

I would not say that D=0. What we want is to define WACC BEFORE Taxes, BUT it doesn’t mean that it is WITHOUT debt.

In short, I think that Ross approach depart from the assumption that no taxes implies no debt and that is wrong.



Yes, I guess you are correct. WACC pretax can’t be read as no Debt.

Today I got time to go thru again Corporate Finance textbook by Jonathan Berk and Peter Demarzo (B&DM). I believe their teaching on valuation is correct, which mean they are not departed from what you have in your books. However, they further said that TS discount rate will be Ku if only the Debt Equity ratio is being kept constant, meaning that Debt and Equity will be kept adjusted at t=1, t=2, etc following the target D/E ratio. If it is permanent debt, then Kd will be appropriate for TS discount rate. Bottom line, Berk and DeMarzo (B&DM) recognized and even put that in their book that the relationship between Ku and Ke will be determined by which assumption we put for TS discount rate.

Ignacio Velez-Pareja:

Yes, I agree

HOWEVER, the idea of constant debt or D%, is borrowed from the original idea of perpetuities.

But, let’s accept it. How do you implement that in practice? Let’s see.


Karnen: yes, I agree with you 100%. This constant D/E ratio is not observable in the reality. most companies are very careful in using debt, though technically, its tax savings and financial leverage is enticing. From finance book we know, this financial leverage increases the risk of the cash flows. So long the ROA, or EBIT level could support the cost of debt, theoretically, EPS will be levered much higher than that without debt. 


If you use a model like the one I have sent to you, it is very easy to implement the idea of constant debt. You just set LT + ST debt constant and equity will contribute to any LT investment/deficit up to the value needed. The procedure would be to discount the CFs with the proper formulas for Ke and WACC.

If D% is constant the solution is a little bit more complicated: it yields another source of circularity because D will be D% times total value and you have to somehow, apportion ST and LT.



 I guess, in reality, people confuses Debt Constant (=permanent debt, the one that M&M uses) and Debt % constant. The latter creates circularity.


Personally, I am choosing Debt with Scheduled Payment. In this cases, separately valuing the FCF and then added on that the value of TS will make more efficient to handle the TS. Again this will necessitate us to put explicitly the discount rate for TS. From B&DM, sounds to me the authors will support Kd as the discount rate for TS in the case scheduled payment of Debt could be detailed. only in the case in which the firm adjusts its debt continuously to maintain a target debt to value ratio, then it is reasonable to expect the risk of the interest tax shield will equal that of the firm FCF.


On the other hand, I wonder if B&DM will offer the proper formulae for Ke and WACC for each world: Kd and Ku as discount rate for TS. Do them?


Karnen: yes, though the way they present it not always easy to follow. Your book is better. Yet, I guess, each finance scholar would like to have his/her own way of presenting the concept. Similar to M&M proposition, I noted that each corporate finance textbook is not always having the same idea in explaining it away.

By the way, you should buy B&DM book, it is a good book indeed, the best of all corporate finance textbooks in the market so far. I always use both your book/papers and B&DM book as my anchor in case I am confused with something related to valuation.

Would you like to to play with the model and try to work under the two assumptions as I mentioned above? [Karnen: sure…have tried it anyway…I like your approach. B&DM approach is assuming constant D%, which I believe in reality, it’s not easy to apply.]


By the way, I just came to realize that it is why you keep saying that there is a strong assumption behind traditional WACC formula, that is EBIT will be sufficient to cover the interest expense, meaning that EBIT > interest expense for the company to enjoy full Tax Savings = Kd (1-T). In situation, which EBIT < Interest expense, then traditional WACC is not working, and that’s well known formula can’t be used. Is there anyway that if that traditional WACC with its Kd(1-T) could handle the situation in which EBIT < interest expense? Or is it really a very special case in which EBIT > Interest expense that we could only use this Traditional WACC?


I am re-reading your paper now: Returns to Basics: Are You Properly Calculating Tax Shields.

I guess, not many people/readers really appreciate the contents of your papers in which you keep saying traditional WACC has a very strong assumptions. Even the Berk&Peter Demarzo do not say anything about this assumption and keep using the example in which the EBIT > Interest Expense.

Ignacio Velez-Pareja:

See this:

In next table I show how to handle the TS.

OI = Other income, FE Financial expenses, TS = tax savings


No Debt With debt TS= Change in taxes
0 FE
Impuesto = T×(EBIT+OI) Impuesto = T×(EBIT+OI – FE) T×FE
Tax = T×(EBIT + OI) Tax = 0 T×(EBIT+OI)
Case 3 EBIT+OI < 0 EBT=EBIT+OI< 0 EBT <EBIT + OI – FE <0
Tax = 0 Tax = 0 0


This situation can be expressed as


This means

TS = Maxim(T ´ Minimum(EBIT+OI, FE), 0).

In Excel: =Max(T*Min(EBIT+OI;FE);0)

In this way you can model the TS.


Thanks for the table. Yet, can we still use traditional WACC in situation in which EBIT less than Interest expense?



Ignacio Velez-Pareja:

Well, that is the problem with traditional WACC. It works only for the case when EBIT >FE!!!

The case you are mentioning IS NOT case 1.

When psi=Ku the formula is

WACC = Ku – TS_t/V_t-1

See that when you are in this formula with case 1, you end up with traditional WACC. SEE: WACC = Ku – TxKdxD_t-1/V_t-1, but Ku =KdxD%_t-1 + KexE%_t-1


WACC_t= KdxD%_t-1 + KexE%_t-1 – TxKdxD_t-1/V_t-1,

WACC_t= KdxD%_t-1 + KexE%_t-1 – TxKdxD%_t-1

Identical to traditional WACC.

The new formula above is much better than the traditional one because you can cover ALL 3 cases plus include ANY other sources of TS. The best example of this is the losses in exchange when you have a loan in foreign exchange and the above mentioned cases.

It is a more general formula. Follow?


Other sources of TS not related to Kd might be bank commissions paid at the issue of the loan and for only one time and similars. There are banks that charge a commission using the loan or a fine for not using a loan and so on. There is an interesting case in Brazil where they have part of dividends paid as a deductible expense, hence you earn tax shields on that.


Thank you for the clarification. I see your points…

Unfortunately many corporate finance textbooks, instead of giving us general WACC formula, they teach a very special case…The problem with this teaching, we, as the reader (and new baby in finance), swallow it and use it to the general case….The right way, it is supposed to be the book teaching the general approach and bring it to specific situation, instead of the other way around.

Jakarta, Sept-Oct 2018








Readers, this article is pretty good, reminding us that pre-tax and post-tax discount rate is not the same.

Ignacio Velez-Pareja:

I agree with the paper. The reason is simple.  Debt creates value through tax savings. See the cashflows and value equations.
V_unlevered + VTS = D + E
If you disregard taxes, you lose VTS
FCF = Free Cash Flows
TS = Cash Flow from Tax Shield
CFE = Cash Flow to/from the Equityholders
CFD = Cash Flow to/from the Debtholders
VTS  = Value of Tax Shield
D = Debt (Book value)
E = Equity (Market value)