futurum paper discussion series constant leverage and constant cost of capital, a common...

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Paper Discussion Series : “Constant Leverage

and Constant Cost of Capital, a Common

Knowledge Half-Truth” paper with Ignacio Velez-

Pareja

Note:

IVP : Ignacio Velez-Pareja

Karnen : Sukarnen (a student)

Karnen:

Hi Ignacio,

I spent a while reading your paper "Constant Leverage and Constant Cost of Capital", now on

page 5.

Sukarnen

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I guess, the message of this paper is to say that under perpetuity situation, we could have the

luxury of assuming constant leverage (D/E) and constant cost of capital at the same time,

regardless whatever assumption we have for TS discount rate. But...this luxury is gone, when

we step into finite cash flows situation.

Constant leverage and constant cost of capital doesn't work when we use Kd as TS discount

rate.

Still, I have something trying to get further clarification from you:

On page 5, it is said that when the TS discount rate = ku, WACC depends on TS and it will be

constant when taxes are paid when accrued....

You said as well:

From these calculations we can conclude that for finite cash flows, leverage and cost of capital

are constant when:....

2. Taxes are paid when accrued.

5. Interest rate on debt is equal to the (market) cost of debt, Kd

My questions:

Why "taxes are paid when accrued" is so important for this assumption? When you said "paid",

is that "paid in the same year it is accrued"? As far as I know, corporate income tax is calculated

once a year, usually, at year end, after closing of the books, and the company always pays that

corporate income tax liability in the following year (usually within Jan-March of the following

year).

Interest rate on debt is equal to the (market) cost of debt..Is this market at t=0? How about t=1,

t=2, etc.?

Under WACC (FCF), you have Ku(i) - TS(i)/VL (i-1)....Is this formula working under "permanent

debt amount", meaning that D/V could be changing every year, since "Debt amount" stays the

same?

Thanks as usual


IVP:

Dear Karnen

As usual, you have done a very detailed reading of the paper. Great.

See below, please. (Note: the sentences in italics represent Karnen’s email above)

I spent a while reading your paper "Constant Leverage and Constant Cost of Capital", now on

page 5.

I guess, the message of this paper is to say that under perpetuity situation, we could have the

luxury of assuming constant leverage (D/E) and constant cost of capital at the same time,

regardless whatever assumption we have for TS discount rate. But...this luxury is gone, when

we step into finite cash flows situation.

IVP: Except if you assume Ku as discount rate of TS.

[Karnen: Agree]

Constant leverage and constant cost of capital doesn't work when we use Kd as TS discount

rate.

IVP: It does!

See, WACC = Ku - TS/V and Ke = Ku + (Ku-Kd)D/E. In other scenarios such as Kd, you have

VTS involved in Ke and WACC. And it is that what restrict having constant D/E. However, you

should read a paper on OCS with finite CFs and non-constant D/E!

[Karnen: The reply is confusing. I said Kd as TS discount rate, but you gave me the formula for

Ku as the TS discount rate. Can you kindly take a look again? Kd as the TS discount rate, under

finite cash flows, displays VTS_t-1 for ke formula, which makes it is not possible to have

constant cost of capital for constant leverage, am I right?]


IVP:

What I am trying to say is that when Ku is the risk of TS, WACC and Ke depends ONLY on D/E.

When the risk is Kd, they have involved more VTS that depends on future TS hence it is very

difficult, say impossible to obtain a constant Ke and/or WACC. Follow?

[Karnen: Follow, Sir..Just an addition, now I am not too worried about constant or non-constant,

the key in valuation is to use the right Ke and WACC formulas aligned with its TS discount

assumption.]

IVP:

Yes, you are right. The idea of constant D% has two purposes:

1. To "aid" or support Those that wish to use a constant WACC out from the thing air. (You are

not now in that group).

2. To look for an optimal capital structure, OCS.

This is what I see in this issue

[Karnen: ....agree. However, Optimal Capital Structure is like holy grail...business is so

dynamic, I am not too sure the world could agree on "one" optimal capital structure. It might end

up a very wide range of D%. But I could live with that notion.

It is so dangerous when we could assume that there is only "one" optimal D% in this very

complex world.]

IVP: Read the draft of the paper [that is “Optimal Capital Structure for Finite Cash Flows”] and

we can discuss that after your reading.

[Karnen: under Ku as the TS discount rate for finite cash flows for WACC_FCF, I noted we

have TS_i. Will the existence of TS_i make constant leverage non-constant cost of capital?]

IVP:

Remember what the role of TS in WACC: Ku-TS/V = KdD% + KeE% - KfTD% only D/V hence

you can keep D/V constant somehow. Imagine you are trying to find the optimal capital structure


(OCS) using Solver. You have a single variable per period to optimize. In the case of Kd as the

risk of TS you have D/V and VTS/V (or D/E and VTS/E).

[Karnen: yes, follow, good explanation...]

Still, I have something trying to get further clarification from you:

On page 5, it is said that when the TS discount rate = ku, WACC depends on TS and it will be

constant when taxes are paid when accrued....

You said as well:

From these calculations we can conclude that for finite cash flows, leverage and cost of capital

are constant when:....

Taxes are paid when accrued.

Interest rate on debt is equal to the (market) cost of debt, Kd

My questions:

Why "taxes are paid when accrued" is so important for this assumption? When you said "paid",

is that "paid in the same year it is accrued"? As far as I know, corporate income tax is calculated

once a year, usually, at year end, after closing of the books, and the company always pays that

corporate income tax liability in the following year (usually within Jan-March of the following

year).

IVP:

Precisely for the reason you mention. Using textbook WACC assumes taxes are paid the SAME

year and as you correctly say, taxes are paid NEXT year.

Let me show a very Mickey Mouse example.

Assume you have a loan for one year at 30% per annum.

T= 0 CF = +1000 T= 1 CF = -1300.


When u uses WACC with (1-T), you have Kd (1-T), right? The CFs after taxes (Tx = 40%) would

be

T=0 +1000 T=1 -1300 + 120 = 1180. Right? IRR? IRR = 18%. Kd(1-T) =? 30%(1-40%) = 18%.

Right? This means that the WACC formula works

Now assume you pay taxes next year. One thing that has to be very clear: TS are really earned

when YOU PAY the taxes, not when they are accrued!

Under this assumption, we have

T=0 CF = +1000 T=1 CF = -1300 T= 2 CF= + 120. If you find IRR of this after tax CF you will

find that IRR = 20% THAT IS NOT EQUAL to Kd(1-T)!!!

This is one of the reasons it is preferable to use Ku - TS/V instead of WACC M&M. It is

preferable because using that expression you can plug in the TS as it happens in reality (say,

taxes paid next year, exchange rate losses, bank commissions, etc.)

[Karnen: though the example above is correct, something still bothers me. TS in my

understanding, doesn't depend on "when" the corporate will pay that tax liability. Accrual

accounting is the standard principle now, and tax authority accepts it. It means that the

company could accrue the interest expense on debt, and still be eligible for the lower tax liability

in that year. In other words, the company has taken "the benefits" of the existence of debt

(assuming of course, EBIT > i). Do I miss out something here?]

IVP:

You have to differentiate between having the "right" to TS and obtaining the TS. You obtain the

earned TS when you PAY taxes. TS are TAX SAVINGS! Those savings will be seen in your

bank account not when you submit the Income Tax report, but when you pay the taxes.

[Karnen: wow, it nailed me down. But wait a minute! the example you gave in that paper, using

the assumption that tax paid in the same year it is accrued, which 100% not realistic....Though I

know you built a case against WACC, however, giving a realistic example, I believe, it is more

important for the practitioners...]


Interest rate on debt is equal to the (market) cost of debt..Is this market at t=0? How about t=1,

t=2, etc.?

IVP: Well, that is something missing there. The assumption is that cost of debt and value of debt

are both market values equal to book values and contractual rates all over the planning horizon.

[Karnen: OK]

Under WACC (FCF), you have Ku(i) - TS(i)/VL (i-1)....Is this formula working under "permanent

debt amount", meaning that D/V could be changing every year, since "Debt amount" stays the

same?

IVP:

, hence

That formula works in any case. The formula is equivalent to the M&M WACC as follows IF

financial expenses are ONLY interest. See

WACC (MM) = Kd(1-T)D% + KeE%

WACC (adjusted) = Ku - TS/V. BUT TS = KdTD_t-1, Hence, Ku -

KdTD_t-1

/V_t-1 = KdD% + KeE% - KdTD% = WACC(MM). Follow?

[Karnen : Follow you]

Debt could and should change every period in order to have D/E constant.

Hopefully, I have clarified and answered your questions. Have I?

Best regards


Karnen:

Hi Ignacio,

I am trying to follow your brain via your file "Constant D% and Non Constant Ke and WACC",

seems to me on the first tab (using Kd), the balance sheet model is built using plug method. Any

gap between assets and liabilities and equity, is "plugged" using "new equity" account, though

your figure for new equity issuance is obtained via cash budget, but still to me, it is a plug

approach.

What do you think?

IVP:

You are right.

I have checked the file and Kd sheet and I don't see any plug there except at t=0. That is a

simple situation that in my model usually is out of the BS. I have an investment and got a debt

from the bank. The difference is what I need to get from equity. It is a shortcut. It should be

(outside the BS): Investment in assets = 4 Debt from bank = 3.14 Equity = 4-3.14= 0.86. And

from there to the BS. Or the contrary, Equity = 0.86 and then Debt = 4- 0.86 = 3.14.

Karnen:

Hi Ignacio,

Upon looking again at your assumption that "Taxes are paid when accrued"...this assumption

doesn't tally with reality. Most of the tax liability or accrual, generally speaking, is always paid in

the following year.

If this is the case, then what is your model for such payment that is not happening in the same

year of that accrual?

I am looking at your file "Constant D%....", tax number in the CB is taken directly from P/L

statement, which meant that "taxes paid when accrued"...


Will the conclusion be different from what you said above, if the tax figure in the CB is calculated

from "tax liability beginning of the year + new accrual - tax liability at year-end +/- deferred tax"?

Karnen

IVP:

Dear Karnen

See below, please.

Hi Ignacio,

Upon looking again at your assumption that "Taxes are paid when accrued"...this assumption

doesn't tally with reality.

Most of the tax liability or accrual, generally speaking, is always paid in the following year.

IVP: YES!!! That is what I am trying to say. Taxes are paid next year hence TS are "received"

next year. To say receive is just a way to say it You don't "receive" a check from the

Government, what you get is a lower tax bill.

If this is the case, then what is your model for such payment that is not happening in the same

year of that accrual?

IVP: NO! You have said it: "Most of the tax liability or accrual, generally speaking, is always

paid in the following year."

I am looking at your file "Constant D%....", tax number in the CB is taken directly from P/L

statement, which meant that "taxes paid when accrued"...

IVP: Yes, in that example, yes. What I say is a caveat. It works IF taxes are paid the same year

as accrued. THAT is another failure of textbook WACC. This WACC assumes that taxes are


paid the same year as accrued and it doesn't happen that way. Imagine a new firm. In year 1 it

files the Income tax report and says it has deduction for interest payments. The firm will pay

taxes next year, HENCE, for year 1, WACC should be KdD%+KeE%. That is not picked by the

standard formula. If you use WACC = Ku TS/V and you have calculated correctly the TS, you

will find that WACC for year 1 is Ku!

Will the conclusion be different from what you said above, if the tax figure in the CB is calculated

from "tax liability beginning of the year + new accrual - tax liability at year-end +/- deferred tax"?

IVP:

Remember, in that example I am assuming taxes are paid the same year. In reality, I would use

something like what you mention. And when calculating TS I have to take that into account.

Agree.

IVP:

Well, well, my dear Karnen

Definitely you have an eagle eye (as we say in Spanish!). May I ask you to read the paper on

OCS with finite cash flows we are submitting to a journal? You see what any other reviewer

sees!

As some of your questions and remarks relate to typos and obvious mistakes I will

answer/comment some of the remarks

See below, please.

Hi Ignacio,

Just finished your spreadsheet and paper "Constant Leverage and....".

Some comments:

1) Page 7: I can't tie up Row 2 of Table 5 that is CFD from the CB to your spreadsheet.


Your table shows 0.72, 0.72, 0,71, and 0.67 vs from what I got in the spreadsheet : 0.71, 1.13,

1.15 and 1.15..

2) Page 10, footnote 6...you said equation (4), but I am too sure as to how to find equation (4) in

that paper?

3) Page 10...paragraph starting with "Observe that the value calculated assuming psi equal to

kd is lower than the value when we assume that psi equal to ku."...from the spreadsheet, the

result is the opposite. With kd, Value = 5.23 and with ku, Value = 3.63. Is the statement correct?

4) Page 11: the paragraph ended with "...all of them (even the APV) require iterations when the

risk of the TS is Kd."... You meant the iteration happens because of D/VL?

IVP:

Yes. D = D%VL, Usually APV is straight forward and doesn't have circularity, but in optimization

for constant D%, there appear a circularity because D = D%V.

5) Page 12: you display the formula Bu_i = BLev_i/(1+ D_i-1/E_i-1)...Is there any reference how

to get this formula? I still owed you on reading chapter 9 and 10 of your book, probably, the

formula derivation for Bu is there?

IVP: see our book.

6) Page 10: If we have pre-determined debt schedule, I guess we can't use constant leverage,

right? this D/V will keep change along with the changes in the VL.

IVP:

Of course you can't. Precisely the idea of the Trade Off "theory" is that you adjust your debt to

get an optimal, but they never say how to reach it.

I could say, overall I could understand your paper and spreadsheet, it is essentially that we

need to use consistent formulas for ke and WACC(FCF or CCF), which formulas should be

aligned with the assumption we are going to use to discount the TS. You proved there in that


paper, that blindly using traditional WACC or just take it for granted what the textbooks told us

that constant leverage will give us constant cost of capital will not necessarily correct. We could

end up with different values under different methods (WACC_FCF, WACC_CCF,

WACC_Ezzel_Miles, Myers_APV) if we are not careful enough to use the correct formula to

derive the ke and WACC.

IVP:

Yes. See our paper on OCS for finite CFs. http://papers.ssrn.com/abstract=1799605. It is not

the actual paper we are submitting (we have made changes, most of them related to formalities

of APA and some extra literature review). If you like the idea of reading carefully it, I could send

the version we submitted to the journal.

Thanks very much for the revelation. The more I read your papers, the more I could see from

which planet you came....a long way to travel..Taggart (1991) to IVP-Joseph Tham (2002)

almost 11 years.

IVP:

Well, knowledge is a long journey. A trip you never know when it ends!!!

Thanks, many thanks for your interest and thoughtful comments.

Karnen:

Hi Ignacio,

Still not clear in my head...back to TS.

TS realized when paid and not when interest expense is accrued (assuming EBIT>i).

Why is so?

In terms of pure cash flows [in/out] : yes, but the concept of Free Cash Flows is not necessarily

pure cash flows. I did remember you touched this in your book Principles of Cash Flows,

reminding the readers that FCF is not identical with cash flowing in and cash flowing out.

http://papers.ssrn.com/abstract=1799605


This bothers me a lot...Seems to me you are coming from "pure blood of cash flowing in and

out"....

IVP:

Well, my dear Karnen,

We have discussed the issue somehow when you defended the idea of opportunity cost.

Remember?

Well, TS is different. TS materialize in cash when you pay LESS tax and that occur next Year!

Best regards

Karnen:

yes, I know...though I still cannot embrace it 100% to accept to live with "pure blood of cash".

Free cash flows somehow are not necessarily cash in the sense that we could see it in the bank

account, flowing in and flowing out.

Discount rate is an opportunity cost concept and to be apple-to-apple, FCF should include

opportunity cost as well.

Having said that I don't say that I don't agree with you.

IVP:

Dear Karnen,

Remember cash flows for valuation are the cash flows in and out from bank and shareholders.

They are from the point of view of investors and debt holders.

Look for what they receive from or "invest" in the firm. When you do that you will see when to

consider TS. If when tax accrued or paid.

Best regards


Karnen:

Hi Ignacio,

Bear with me...am still a bit confusing, what is exactly the big difference between "plug" and "no

plug" method?

As now, I am quite big fan for not using "plug method" anymore. The way you put in your

Principle of Cash Flows book is to start building up the Cash Budget. However, I also suggest

using the predetermined debt schedule instead of D% assumption. I am not too sure whether in

reality, the company will be willing to keep changing its Debt level to keep it up with the D%

assumption. The reality I see, the company has a loan facility with the bank and normally the

credit agreement or in general, we could discuss with the management about the debt

repayment, whether it is bullet/balloon, level or PMT method. I believe that what we need to put

into the valuation spreadsheet.

In your excel file, my point, since you don't use the predetermined debt repayment, instead, you

use the D% assumption, and this has resulted to the use of newly issued equity account to

"plug" any fund deficit between total assets and total liabilities + equity. Am I right in following

your streams of thinking about "plug" and "no plug"?

IVP:

Karnen

The problem of using plugs is that you might have mistaken in modeling and you might not see

them. Using no plugs, while there is a mismatch in the BS you have a mistake somewhere.

Next issue: debt. Of course you start with a given debt schedule and you cannot change that.

With the model (CB) you define when you need new debt and/or equity and you add Those

loans to the loan schedule in your financial statements.

The idea of dynamically defining debt with D% is just for finding the OCS! That works in a

Mickey Mouse example. In reality you should modify the model to be driven by D% and not by

the deficits that arise from the cash flows. Follow?


In summary, if you are not looking for an OCS, forget about a predefined D% and define your

debt schedules as they arise in the CB. If you look for OCS, you have to modify your model and

use Solver to find OCS.

Best regards

2015

Karnen

As we have had discussed it that it is important to know that (1-T) for Kd in WACC will mean

that the tax is paid in the same period it is accrued or the interest in tax deductible in the year it

is paid.

I agree with the above...yet I noted at the same time, that in most cases, like in USA and

Indonesia, the tax authority will require the taxpayers to make monthly installment payments

which will be treated as tax prepayments.

For example, in filing 2014 tax returns, the taxpayer using total corporate income tax in 2014

divided by 12 months (it is apparently, the tax authority assumes that total corporate income tax

will stay the same for 2015 as that of 2014), is the amount to be installed in 2015. This will mean

that the remaining tax liability for 2015 that will be paid in the following year, let's say March

2016, will be total corporate income tax (as per calculation showed in the 2015 tax returns using

the actual taxable income for 2015) minus the tax prepayments or tax installments that have

been made by the tax payer during year of 2015.

It seems to me that including (1-T) for Kd in the WACC will still be a good approximation of the

effective Kd during the year.

What do you think?

IVP

Well, sometimes the firm "prepays" tax or post pays tax. In Colombia (and by sure in other

countries) the Government applies a withholding tax to firms and individuals. The issue here is

to model the way the firm pays taxes (sometimes people and firms "over-pay" taxes because

the withholding tax is more than the proper tax to be paid). For that reason I prefer to model the

WACC as Ku -TS/V and the use of CB. In this way you capture what happens with the tax in the


CB. When you don't use CB and use the WACC with the 1-t factor, you can't see what is going

on. Also that would be crystal clear if you use Ku and CCF!

~~~~~~ ####### ~~~~~~


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