Discussion paper series npv project = npv equity

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Discussion Paper Series: The Net Present Value
of The Firm is Equal to The Net Present Value of
The Equity
Discussions by Using the Paper “Applicability of the Classic WACC in
Practice” (2005, by M.A. Mian and Ignacio Velez-Pareja)
Note:
 IVP = Ignacio Velez-Pareja (Associate Professor of Finance at Universidad Tecnológica
de Bolívar in Cartagena, Colombia)
 Karnen : Sukarnen (a student in corporate finance)
Karnen
I am now on reading a paper with the title “Applicability of the Classic WACC in Practice”
(2005) (downloadable from http://ssrn.com/abstract=804764).
Just started, on page 5: I am a bit surprised about equation (1) and (2). The authors have put
"after-tax WACC" and "before-tax WACC".
Sukarnen
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I don't think it is correct to put the thinking into "after-tax" and "before-tax" for WACC. As we
know, it is all about Tax Shield (TS), whether we want to factor it into Free Cash Flows
(numerator) or discount rate (denominator).
As we discussed previously, and as you have enlightened it to me, behind WACC, there is a
strong assumption that "tax is paid in the year it is accrued", which assumption, we do
know, not correct!
I did remember, I discussed this "before-tax" and "after-tax" WACC with you, the terminology
that Peter DeMarzo and Jonathan Berk also used, and you are against it.
On the last paragraph of page 5/21:
“Under certain assumptions we can call the WACC_BT as the WACC for the Capital Cash Flow
(CCF).”
My comments:
1) The authors didn't put any footnote or any reference, what does it mean with "under certain
assumptions"? It is so ambiguous and it is not fair to leave it to the reader to fumble around.
2) I don't think we could refer it WACC_BT (before tax) for CCF. As we both know, Capital Cash
Flow (CCF) has included Tax Shield (TS), and accordingly, to avoid double counting, the
discount rate should not include TS discount rate anymore.
IVP:
Yes! You are right.
The problem of after or before tax is the same as when you say unlevered value of a firm
(V_unleved). In reality, it means with no tax effects. It means with no TS! That is a problem that
makes very difficult to explain the readers when writing a text for a book or a paper.

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And particularly when dealing with CCF! It has debt and taxes embedded in it and yet we say
we discount it with Ku (the unlevered cost of equity) or the "before" tax WACC.
What do you suggest to solve this semantical problem?
Karnen
Ok, we have predetermined debt schedule and the best way to deal with this situation is using
APV (=Adjusted Present Value), in which we separate FCF (hypothetical all equity) and TS, and
we apply discount rate to each part.
IVP
There is no better method. ALL of them yield the same answer.
Karnen
I am wondering which discount rate we are going to use.
You set the assumption about psi and use the one that fits the cash flow
 the first part FCF, assuming psi is Ku, then we use Ku - TS/VL_t-1.
 the second part, TS, assuming psi is Ku, then we use Ku.
IVP
NO. This formula Ku - TS/VL_t-1 is WACC for the FCF. In the APV FCF is discounted at Ku.
Just that simple. The TS are discounted at the psi you have assumed from the start
Karnen
As I know now, WACC_AT has incorrectly treated the TS in the same year it is accrued, do we
need still use it in the future?
IVP
That is true for the textbook formula, not for Ku - TS/VL_t-1. The idea in this formula is that you
include there the TS whatever the source (interest, adjustment to book equity if adjustment for
inflation are made, exchange losses in debt, dividends as in Brazil (see
http://papers.ssrn.com/abstract=1421509), etc.
When you have fixed or contractual CFD THAT makes the Ke (and WACC) change. You keep
the debt schedule as a given and you adjust Ke and/or WACC by D% or D/E.

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Karnen
The example shown under Tables 8 to 10 and the analysis is pretty much about reminding us
that if we use predetermined debt schedule, WACC_AT that is blindly applied will lead us to
incorrect value. There are strong assumptions behind WACC_AT.

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Since the debt repayment will follow certain schedule, it will mean D/V will keep changing from
year to year, and WACC needs to be recalculated each year - iteration, but this is easy to
handle using Excel. I believe the same idea is elaborated as well in your paper "Return to
Basics: Cost of Capital Depends on Free Cash Flow" (2008) (downloadable from
http://ssrn.com/abstract=1281451) that I have had read before.
Upon thinking about iteration and all formulas, this makes me wondering:
We have free cash flow, TS, WACC iteration recalculated and so it is not difficult to get Ku -
working backward. I have not yet tried it, but I will try it tomorrow, will we get different Ku each
period, like different WACC each period?
If we get the same Ku, for example, what does it mean? Is that correct Ku as per "market"? How
to validate this backward-iteration recalculation of Ku to the market rate?
I reworked Table 2, Table 3 and Table 4 of the paper "Applicability of the Classic WACC in
Practice" (2005) as demonstrated below.

Page 6

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From what I see, using correct discount rate aligned with the cash flows being discounted, will
result in the same value, in this case, $327.
What I am a bit confused, we know CCF = FCF + TS = CFE + CFD, right?
Why is NPV (derived from CFE) the same with that resulted from CCF and FCF? My
understanding to get NPV CFE = NPV CCF or NPV FCF - NPV Debt. or is it because NPV Debt
= 0? (note: I know all NPV Debt should be zero in practice assuming Kd is the market rate and if
we deal with the bankers, they love to use market rate, in other words, we never could win over
bank in such transaction). So in this case, NPV CFE will be the same with NPV FCF or NPV
CCF.
Thanks in advance for your confirmation.
IVP
Wow! You have arrived to something I am fighting for, for years (and perhaps I
mentioned in some of my messages)!
Haven't you heard that NPV project is different to NPV equity?‎Probably yes! That is deadly
wrong. More, some people say that it happens because of a kind of leverage and all that. The

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NPVs SHOULD Be identical! This happens IF value of debt is equal to book value of debt.
When debt is market value, say the firm has bonds traded in the market, both values might not
match and the difference in NPVs is the difference between market and book value of debt.
By the very same definition of NPV you should conclude they should be identical.
Karnen
All those CCF, FCF and ECF (or CFE) gave us the same NPV.
IVP
YES!
Karnen
Though the very assumption of constant D% is violated...why?
IVP
Not necessarily D% constant. It is nothing to do with identity of NPVs. Forget D% constant. I
answered your query in the same vein. I said that D% is either because you wish to optimize to
find Operating Cash Flow (OCS) or to assume that WACC or Ke is constant. Forget the idea of
constant D% (remember the paper on that). D% is achievable only of psi = Ku. AND Ke will be
also constant.
Karnen
Or you meant, we should check the PV instead of NPV? the example uses the predetermined
debt schedule, so the use of WACC for constant D% is not correct, otherwise it is computed for
each year (like your paper "Return to Basics : Cost of Capital Depends on Free Cash Flow"
(2008)).
IVP
I think you should think as the standard that D% is variable. Ke is adjusted by D%, and WACC
as well.
I don't follow what you try to say "Or you meant, we should check the PV instead of NPV?"
Karnen
I know what you meant there, but I refer to the paper.

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If that paper, the authors compute WACC_AT and WACC_BT (=Ku) and Ke (=Ku + (Ku-Kd)
D/E) using D% (assumed constant across 5 years), and applied to FCF and CCF and ECF,
resulting in the same NPV of $327. Knowing that the initial "initial investment" is different
($2,500 for FCF and CCF, and $1,793 for ECF), but NPV is the same, then PV should not be
the same, except for FCF and CCF (different amount for year 1, 2, etc.. but this is compensated
by different discount rate, so we end up with the same PV).
What confusing me, D% is not constant along all those years, as demonstrated in Table 6, but
how come we could use WACC_AT and WACC_BT with constant D%? Is the result of NPV of
$327 incorrect? From the Table 3 and 4, it is apparent we have pre-determined debt schedule
and not D% (for example, 25%, as shown in Table 1). I see inconsistent, but whether this
doesn't matter for NPV calculation?
To be honest, the paper is not clear, what it is trying to convey if we stop reading at Table 6....
What you said, to be honest, the first time I heard of...NPV projects should be the same with
NPV equity. Generally speaking, in valuation, we just pick up the book value of debt (especially,
this debt is from bank, and generally speaking, we seldom test it to using the going rate to arrive
at the "market" or "current" value of the debt).
So, tell me, in your valuation, do you always try to find the "market value" of the debt (though it
is not traded, for example, by using the current rate, instead of stated rate in the agreement)?
IVP
Well, the usual approach is to have CFE and FCF yielding inconsistent results, hence, NPV's
will not match. The inconsistency is the use of inconsistent WACC and Ke as you know.
I think on market value of debt if the firm is financially stressed. If it is a "normal" firm just BV of
debt.
In our model we assume that future debt will have an inflation indexed Kd. We calculate or
estimate future Kd as Rf + RPD (Risk Premium for Debt). You may ask how we do that. Well in
the MM model I sent you, debt is estimated that way. We have as inputs real interest rate,
inflation and a RPD. Rf is just (1+ireal)(1+infl).1 and RPD is estimated historically as lending
rate minus Rf. I thought this was a crazy idea, but rewriting my Spanish book I found some
interesting DBs, see:
 World Bank, 2014a ( http://data.worldbank.org/indicator);

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 World Bank, 2014b. World Development Indicators. WDI Archives.
(http://data.worldbank.org/products/wdi);
 International Monetary Fund (http://www.imf.org/external/data.htm).
These DBs have MANY indicators, more than you imagine and one of them I found, is the RPD!
So, I am now VERY confident that what I have been proposing for years is not crazy.
Regarding the "market" value of debt, it is the PV (not the NPV) of all future payments (principal
+ interest) from t=1 to t= N assuming all debt is contracted at t=0. If not, this is, that you have
some debt TODAY and you contract debt in the future the new contracted debt doesn't count
because it will be fully paid in the future. Hence, the only debt that is relevant is the one you
have unpaid today.
Karnen
Thanks for bringing me to World Bank data. I believe you are right regarding the RPD, I don't
see something logically wrong or weird...debt instrument is not much different from equity
instrument, and the way the required return is formed, I believe, also go through the same
process. I still remember there was a hot debate on LinkedIn Business Valuation group, and it
was said that the only difference between debt and equity is only the tax deduction for the
interest expense.
IVP
It is a CAPM without using betas. Rf + RPD (in terms of CAPM it would be Rf + Bd*MRP . I
disagree about the difference with equity.
Debt:
 Contractual, terms, defined principal, dates of payments, interest rate, Kd, etc.)
 Priority before equity (Interest paid before dividends, if liquidate in a bankruptcy, equity is
residual as ever.)
 Bank has guarantees (say collateral, insurance, co-debtor, etc.)
Equity
 Non contractual. Firms are not obliged by contract to pay dividends, nor payback initial
investment (it is expected that it does, but not an obligation).
 Residual.
 No insurance, no guarantee that will be paid dividends.

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That is the reason why Ke>Kd. These are the most critical differences between debt and equity.
Karnen
Debt vs equity - yeah you touched on legal stuffs, “form” stuffs...however looking at the finance
perspective, it is just the tax-deductible interest that matters..Yet, I don't say I don't agree with
what you put there...I have seen that before in standard corporate finance textbooks. You need
to read the one hotly debated at LinkedIn...amazing, how such simple stuff could drag so many
different views...I guess the world is overly populated.
Regarding the rest - I see your point, though this is not quite in line with what you put there last
night (Jakarta time), which you said under "normal" condition, you were suggesting to use "book
value of debt"...(I guess now we are in agreement to use market value of debt if possible,
though I know this should be 100% possible, since all we need is just the current borrowing rate
to get to the market value).
IVP
Listen, if it is possible to have market values for debt, you should use that. For sure. But the
issue for non- traded firms is a practical one. Market value for a stock is publicly available. Also
for public debt. BUT for private debt?...
The issue of the characteristic of debt, I see it more from the interest of view of risk compared
with equity. The issue of TS well, it is true, but it depends on EBIT+ OI (=Operating Income).
And there are other sources of TS as well. In any case, I don't try to disregard the fact that Kd is
subject of Tax. As I told you, in this world you can find everything. I can tell you that (as I said in
previous message) in Brazil they earn TS in a portion of dividends! Hence, the tax regime on
interest is not exclusive of interest
Karnen
By the way, as you mention abut "market value of debt" and in previous email, you touched on
that under "normal" condition, you suggest to use "book value of debt”, I see, if we use "book
value of debt" in the valuation, then we are a kind of mixing "market value of equity" and "book
value of debt" (=equity is the residual value if we use PV (not NPV, yes, you mentioned it
above) of FCFs (finite and terminal value) - book value of debt = "market value" of equity. Is this
apple to apple? or we just mix orange and apple?

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IVP
Yes, debt should be subtracted from PV of FCF and from TV at year N.
Karnen
There are pros and cons here:
Book value of debt - yes, we use it, because that's what contractual obligation of the company,
at the end of the day, that's what the company is obliged to pay contractually to the debt-
holder(s), either it is traded or not traded in bonds market, it is not relevant for the payment.
IVP
Agree.
Karnen
However, if we stick to the use of "market value", then what happens in the market cannot be
plainly disregarded. Forget the bonds market. Just look at the going/current borrowing rate. If
that's much lower than the stated rate in the loan agreement, it will be foolish for the company to
close his/her eyes off, without making much effort to [early] repay the existing loan, and file new
credit facility with lower interest rate. In practice, it is not really difficult, let alone, if it is a big
company, to switch from one bank to another bank, by asking new facility loan from other new
bank to repay the existing loan obtained from different bank. I've seen this many times. Even for
let's say, 25 basis point lower, the company is more than willing to remove existing bank loan
facility and go to another bank, without paying anything, other than notary fee for drafting new
loan agreement, insurance, etc.
IVP
Well, it depends on how the lending rate is defined. Usually it is defined as a base (risk free, or
CDs rate) plus some basic points. And this means that Kd is linked to inflation. Those extra
basic points are equivalent to the PRD. And of course, you can negotiate the Kd and (at least in
these times) banks are trying to buy debt from other banks at lower rates. In this sense, there is
a market value of debt. This has not been that way all the time. However, differences are not so
big to make a big difference in value.

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Karnen
So, somehow, seems to me both approaches above are acceptable, though I prefer using
"market value of debt" meaning we need to recalculate the implicit or supposed to be "the new
book value of debt" using current interest rate (which could be lower or higher).
IVP
It is desirable to use market value of debt whenever possible. In that case, NPV_equity is not
equal to NPV_firm. But remember, in case of market value of debt, the difference should be
exactly the very same difference between market value and book value.
The idea of identity of NPVs comes from the definition of NPV. I define NPV as follows:
Imagine the CF at any year. That CF is "responsible" to "pay" the following:
 Part of initial investment
 Cost of capital (WACC or Ke)
 A remaining quantity that is what creates value and contributes to the NPV
When using FCF, the cost of capital item 2 pays what debtor AND equity holders expect to
receive (in the case of debt is more than an expectation: it is a must). When using CFE, item 2
is just the cost of equity capital. The remaining, in the first case (FCF) is an excedent or excess
cash that belongs to the shareholder.
In the second case obviously that belongs to the shareholders.
See the value equation:
 VL = D + E
 NPV = VL - Capital invested = VL - (BVD+BVE)
 NPV = E - BVE
 VL = D + E
 NPV = VL - (BVD+BVE) = D+E - (BVD+BVE)
 When BVD = D then
 NPV = D+E - (BVD+BVE) = E - BVE
 If not equal, the difference will be D - BVD

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Karnen
Following your paper "Return to Basics: Cost of Capital Depends on Free Cash Flow" (2008),
there is no much different whether we value publicly traded firm or private firm. They are the
same. Even if we have the market value readily available of that stock from the trading floor, it is
not relevant anymore for D% in WACC. Just use the iterative process as you keep suggesting it,
to get the "market value" of t=1, t=2, etc. Am I right?
IVP
Well, DCF techniques try to mimic what the market does. That is the idea behind all those tools.
Market supposedly looks into the future, foresees the CFs and discounts them at a discount
rate. The fire test is forecasting a traded firm, discounting the CFs and getting today’s market
value! And of course, you have a starting point: the value of equity and debt today. Now the
question is if it makes sense to go over all that work to arrive to the actual price, given by the
market. Take into accounts that you KNOW what D% is TODAY but not tomorrow!
Karnen
The problem with the non-traded firms is that you have no reference to compare with.
IVP
In short, if you trust the market, it makes no sense to forecast and use DCF techniques for a
traded firm to check that the market price is correct. Agree?
If you try to find the value of a non-traded firm, you have to "sharpen your pencil" to get the best
estimate of value through forecasted CFs and discount rates and you have to live with that
because you don't have a market price to compare with.
This is what I see regarding valuation.
What do you think?
Karnen
For traded-firm valuation, the practice is diverse. I've seen that some took whatever the market
(stock market) gave him/her, on that he/she add/deduct on liquidity premium/discount, control
premium/discount, size premium/discount, etc. etc.. All those stuffs that might be subjective or
judgmental.

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However, some try to guestimate not the "market value" (since it is already there), but figure
out/work back to get the "market" Ke, and then use it as a discount rate to the FCFs that he/she
builds based on certain assumptions.
Or, if the transaction of buy/sell will take place through the stock market, an average of the last
50 days of trading prices......
IVP
Again, as I've ever said, the goal of valuation itself has justified which road that valuation expert
will take..
Karnen
I don't have "yes or no" answer. At the end of the day, it is the eye of the beholder and whether
his pocket will match whatever the price tag the valuation analyst will put it. They have created
so many names, "fair value", "fair market value", "market value", "fundamental/intrinsic value",
etc.
For non-traded firm....mostly will mimic the "market value" of the companies in the same
industry...I don't say it is "correct or not" to do.
However, somehow, I prefer your approach explained in the paper "Returns to Basic : Cost of
Capital Depends on Free Cash Flows"...iterative process will make us be clear about what
happens to the value at t=1, t=2, t=3...to see whether t=0 makes sense for both parties on
negotiation.
At the end of the day, the buyer buys the "future", or "prospects" of the company.. If you think
you could trust the market...you must be kidding...with its so many ups and downs and
"bubbles"....If you have time, buy the book "Random Walk the Wall Street" by Malkiel...a lovely
book to read...it's about just buying the index portfolio...nothing is more or less.
IVP
Then we agree that as a general rule, DCF method is not for traded firm! Now, in terms of
working backwards, you are assuming constant Ke! In reality, if you do that, the only "degrees of
freedom" you have is TV! You can estimate Ku from today Ke unlevering it. You forecast CFs
the best you can, and perform sensitivity analysis on TV. But in fact, this is a joke! Use as you
say, an average of prices.

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Remember the case I mentioned months ago of the transaction of the largest brewer un
Colombia some years ago. Market price 28 and they closed the deal at 42. That was all. Market
price to the trash!
Karnen
Interesting...though I was, am and will not be a big proponent for efficient market
hypothesis...Never take market price for granted. I guess, a positive side, market price contains
information, and this information is valuable, not the market price itself. In the presentation of
Prof. Damodaran last year, he reminded us that "price" is 'demand vs supply' (+market mood,
momentum, speculative, greedy, etc.), and value is not the same and probably will never be the
same with price. Value is driven by fundamental information about cash flows (amount and
timing and risk), growth of cash flows (projection remember) and quality of that growth...This is
what Prof. Damodaran keeps preaching.
I agree with you that consistent Ke is not easy to justify. markets never have that luxury...the
very existence of the market itself means constant is illusion.
Karnen
I am looking at the Table 6 and Table 7, and try to figure out what the authors want to tell me.
Table 7 is pretty much just a proof of CCF = FCF + TS = CFE and CFD.

Page 17
How about Table 6?
From what I see, this is to say that the same WACC of 8.5% being used across 5 years is not
correct, since it is clear from that Table 6, the D% is not constant across 5 years, something is
contrary with the way WACC of 8.5% is obtained. Am I correct?
In other words, faced with the pre-determined debt schedule, we are forced to use or recalculate
WACC for each year, or Ke is changing from year to year. Am I right?
Yet, sorry, D% is apparently not constant...but NPV of all those three methods, FCF, CCF and
ECF gave us the same results of $327. Why is so? On page 11/21 on top of the paper, it is said
"If the constant D/V ratio assumption is violated, all three discount factors will give different
NPVs even if the right combination of cash flow and discount factor is used.", but I thought the
example showed all giving us the same NPV. Am I missing something here?
IVP
I have to re-read that paper with the care and dedication you usually do.
It is true that given a loan schedule, then your D% will change and hence Ke and WACC. What
you cite seems to me it is a mistake or typo.
The condition for NPV_equity = NPV_project is not that D% be constant or variable. It is that the
cash flows are consistent and especially that Ke and WACC are consistent.
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