Discussion paper series - “Cost of capital depends on free cash flows and conditions for constant leverage”, and “constant leverage and constant cost of capital”

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Discussion Paper Series:
“Cost of Capital Depends on Free Cash Flows
and Conditions for Constant Leverage”, and
“Constant Leverage and Constant Cost of
Capital”
An old joke of a former student that met his finance professor?
He said to his teacher, hey you were my teacher 20 years ago and I saw your tests and they
have the same questions you used to apply to us in the quizzes and exams.
How come? Everybody will know the answers!
The professor replied: Yes, they are the same questions. The new thing is that answers change
Sukarnen
DILARANG MENG-COPY, MENYALIN,
ATAU MENDISTRIBUSIKAN
SEBAGIAN ATAU SELURUH TULISAN
INI TANPA PERSETUJUAN TERTULIS
DARI PENULIS
Untuk pertanyaan atau komentar bisa
diposting melalui website
www.futurumcorfinan.com

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Karnen = Sukarnen (a student)
IVP = Ignacio Velez-Pareja (valuation advisory, authors of many papers and books)
Karnen:
Hi Ignacio,
I copied from Damodaran's holy sermon:
While the temptation is to go with book values for debt and equity, you should steer away from
them. There are three alternatives you can employ.
 Use the industry average market debt ratio, obtained by looking at publicly traded
companies in the sector, to estimate the cost of equity and capital.
 Use an estimated market value of equity, based upon applying a multiple (say a PE
ratio) to your private company’s earnings to arrive at a debt to equity ratio.
 Use your DCF estimates of equity and debt value to compute your cost of capital. Since
you will need the cost of capital to arrive at these estimates, this will create circularity in
your valuation. If you are willing to use the iteration function in Excel, you should be still
able to work with the circularity.
By the way, I am reading now your paper : Cost of capital depends on FCF and conditions for
constant leverage.
I have finished up reading your paper: Returns to Basics Cost of Capital Depends on Free Cash
Flow.
Interesting! Changing FCF somehow has an impact to WACC...circularity due to D/V factor in
the WACC calculation.
IVP: Yes! They are not independent!
Karnen:
However......
If you sit as an investor...in the market...if people asked you how much rate of return you expect
to get from a stock investment. Mostly people will see on the going rate and historical returns (if
you are lucky to have that)...and you said this is your "expected", "required", "minimum", rate of

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return. I don't think not many people will say, "well,....it depends of the cash flow projection".
Probably because it is not easy to have it and the "market price" somehow you believe that it
has incorporated the free cash flow projection and WACC as expected by the market in the
aggregate. So ...the going market rate is what we use in the valuation analysis. There might be
a disconnection between the market rate and the rate from the PV of projected cash flows. Then
what does that difference mean?
IVP:
Yes, you are right! However, what people have in their mind is what they expect to earn in an
investment and usually they don't differentiate if their investment "has debt". I would say what
they expected is Ku without knowing it. This said, I take that expectation as Ku and use CCF
and that is it. The only adjustment needed is for inflation if I don' expect changing inflation.
Karnen:
I guess, Ignacio, this is all about the valuation purpose, to identify those stocks "undervalued" or
"overvalued"....
IVP: No, it is about valuation of firma and projects.
Karnen:
It means it will be ok to have a market rate to discount the projected free cash flow...
IVP: See above about CCF!
Karnen:
What do you think?
Note : Though I understand your paper, but still I am confused, as so many people in the market
don't use such interconnections between FCFs and WACC...They call it "benchmark WACC" so
it is not necessary to be "internal" as your paper indicated so, but as "benchmark" means
"external comparison"....
IVP: See above again . it is Ku!

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Karnen:
The way I see in your paper, is like INTERNAL rate of return calculation. We could easily get
IRR without even knowing market rate, and just change the cash flows ups and downs to get
the IRR that we want to see.
IVP: You can do that, but I don't like it.
Could you please give me the link of Damodaran's holy sermon? :-)
Listen, Damodaran lists those three options as equivalent and they are not. The first two imply
to use constant D/E and Ke. And this is what he uses in his books! The problem is the same!
Those D/E are point estimates at t=0. What happens with t>0?
Dear Karnen, your vocation is to be an academician! I never have seen a Finance teacher (Not
to say a consultant) that studies more than you do! Chapeau!
Remember all formulae for Ke? Well, the ONLY one that could stand in a constant D/E setting is
when you Assume Ku as discount rate of TS! Would you smile?
Karnen:
Hi Ignacio,
Thanks.
Will send it tomorrow as I keep Damodaran's papers or presentations in my external HD.
I started reading your paper "Constant Leverage and Constant Cost of Capital"
You started in the abstract by stating that under perpetuity context, constant D/E is a special
case, it is only under kd as the discount rate for TS, that constant D/E will make ke and WACC
will be constant as well. So this is a very special situation. Once it is not, then we don't and we
can't assume D/E constant away.
I am trying to look at the formula in your Principles of Cash Flow book, Table A.2.1 (page 79).
Formula for WACC is similar for either kd or ku as the discount rate for TS. The difference will
be only on the ke, which under kd as the TS discount rate, then we have (1-T).

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IVP:
Be careful. The Ke with the (1- t) is only when you have perpetuities! For finite cash flows you
have term with VTS that depends on TS. Hence, you don't have the beauty of Ke = Ku + (Ku-
Kd)D/E. It is in this case where Ke might be constant given that you design D in order D/E be
constant.
When Ku is the risk of TS the formula for perpetuities is the same as for finite.
In short, what we say in the paper is that when CFs is finite, the only possibility to have constant
D/E is assuming Ku as risk of TS. With perpetuities, it could be either Ku or kd.
I look forward to receiving the holy paper by Damodaran.
Karnen:
Hi Ignacio,
Need to confirm:
Under perpetuity context of the FCF, constant D/E will result in constant ke and WACC. This
prevails either under kd or ku as the discount rate for TS "as long as" we consistently use the
formulas as shown in Table A2.1 and Table A2.2, for ke and WACC.
IVP: Yes!
Karnen:
The above is true because we don't have V(TS) in that formula. The only difference in the
formula, as you said above, is we have (1-T) in the ke formula for kd as TS discount rate. As far
as we use the correct formula, then constant D/E will give us constant ke and WACC.
IVP : Yes!
Karnen:
But...
We cannot say the same thing as above, when we are facing "finite cash flows" situation.
IVP: Yes!

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Karnen:
Constant D/E will give us constant ke and WACC only when ku as the discount rate for TS. Yet,
constant D/E will not give us constant ke and WACC when TS discount rate is kd, because we
have V(TS). This V(TS) happens in the "finite cash flows" and it will change depending upon
whether the company could have EBIT(t)>i(t). In other words, it is not always possible to realize
the TS when EBIT(t) is not enough to cover i(t), then in this case, V(TS) could be zero.
IVP: Not need to be zero. Just having VTS yu cannot grant that (Ku-Kd)D/E + VTS/E are
constant. THE Problem is VTS!
Karnen: Am I following your paper and book correctly?
IVP: YES!
Karnen: One more, once we have V(TS), in addition to whether EBIT(t) > i(t), we need to
specify the discount rate for TS as well.
IVP: Well, you have to specify the risk of TS in order to know which formulation you will use. If
Ku, then Ke = Ku + (Ku-Kd)D/E, if Kd and finite you will have Ke = Ku + (Ku-Kd)D/E + VTS/E
etc.(writing without checking the exact formula )
Karnen: Though I have not yet tried in Excel and finish reading your paper "Constant leverage
and constant cost of capital", I guess, to be consistent, kd should be used as TS discount rate in
the case we have V(TS) in the formula.
IVP: NO! The final recommendation is that in order to get constant Ke and constant WACC you
need to assume Ku as discount rate for TS. Not Kd!
Karnen: I believe your paper "Constant Leverage and Constant Cost of Capital" will explain it
away for my guessing above.
Karnen:
Hi Ignacio,
I copy from your paper : Constant Leverage and Constant Cost of Capital
Practitioners frequently assume that the risk (and corresponding discount rate, ψ) of the interest
tax shield is the cost of debt, Kd. This is done explicitly when, for example, the APV method is
applied, or implicitly, if popular formula Ke= Ku + (Ku−Kd)×(1−T)×D/E (Ku, the cost of unlevered
equity; T, corporate tax rate; D and E are market values of debt and equity, respectively) is used

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to estimate the cost of equity capital. As Taggart (1991) and Tham and Velez-Pareja (2002,
2004) prove, this formulation is valid only for a fixed (in perpetuity) dollar amount of debt, thus
under constant leverage assumption it could be applied only to perpetual cash flows.
You mentioned above "fixed dollar AMOUNT OF DEBT"...As this is "perpetuity" context, are you
saying about "permanent debt" (meaning that the amount of debt is forever there) or "debt/value
that is forever"?
IVP: Yes, I have seen authors that use the formula for perpetuities in finite case! You can see
some papers by IVP-JTh, about the inconsistencies in B&M books.
What the paragraph you cite is correct and says the same as I have telling you: Ke= Ku +
(Ku−Kd)×(1−T)×D/E is correct only for perpetuities.
Karnen:
Ignacio, you said:
Well, you have to specify the risk of TS in order to know which formulation you will use. If Ku,
then Ke = Ku + (Ku-Kd)D/E, if Kd and finite you will have Ke = Ku + (Ku-Kd)D/E + VTS/E etc.
(writing without checking the exact formula).
So, for VTS above under kd and finite, [the correct one ke = ku + (ku-kd)D/E - (ku-kd) VTS/E],
we need to use kd as the discount rate to get the value of TS, right? And even doing that, still,
constant leverage assumption (D/E) will not end up in constant ke and WACC...is this you are
saying?
IVP: Yes, because VTS. You can grant D/E constant but not VTS/E constant. Am I right?
Karnen:
Ignacio, when you refer to unlevered equity or beta in Damodaran's website, is the link that you
are talking about?
http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/Betas.html
IVP: Yes, that is it. However, as the pages say, you can have that in xls format. Also, you can
find total beta. Another issue is that you can find betas by geographical areas, for instance, US,
Europe, emergent countries, including India and China, these two separated and MANY other
indexes such as multiples, P/E EBITDA, etc.

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Karnen:
ke = ku + (ku-kd) x (1-T) x D/E
I know this is only valid under perpetuity and kd is the TS discount rate.
IVP: THAT is for perpetuity. Yes.
Karnen:
As your Table A2.1 (page 79 of your book) said that, but my confusion...D/E.
D here is "permanent amount of debt", or constant D/E, or in perpetuity context constant D/E will
mean D here permanent Debt amount?
I guess so
IVP: Not necessarily. What you have to do it to keep constant D/E and that doesn't imply
constant debt.
Karnen:
Yes, that what I meant.
I am a bit confused since the paragraph said ...
IVP:
You have to use a kind of Solver in order to set that as constant changing Debt.
Karnen:
Valid only for a fixed (in perpetuity) dollar amount of debt.
IVP:
The problem is that E changes, V changes and E = V-D.
Karnen:
Then why you use "fixed (in perpetuity) dollar amount"?
IVP:
In the case of perpetual D and E are constant.

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Karnen:
Then in this case D/E constant, not necessarily "permanent D amount"
IVP:
Yes although you could do what I suggest above, but perpetuities you assume D/E constant.
See the formulation for WACC = Ku - KdTD% (D% is constant and equal to D/V).
Karnen:
Yes, that's what I am thinking of.
IVP:
Then we agree?
Karnen:
I guess the sentence over there in the paper is a bit confusing..since it is mentioned about the
"amount".
IVP:
Probably it is and you are right.
Karnen:
In my head...in the perpetuity, we could assume (a) permanent debt - this is what M&M used, or
(b) constant D/E meaning that the company keeps adjusting its leverage to maintain a constant
D/E.
I guess, the paper should refer to constant D/E instead.
IVP: But in perpetuity at the end of the day is the same.
May 2015
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