Email exchanges among:
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.
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.
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.
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.
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.
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?
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?
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?
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).
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.
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?
Let me comment on Rauf note below, please.
Hello, KarnenThanks 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 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.
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.
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.