# LITTLE NOTES ON MODIGLIANI-MILLER WEIGHTED AVERAGE COST OF CAPITAL (WACC)

First, MM WACC is the most used method, we could say 100% being used in valuation reports in Indonesia. I guess, this method becomes so popular because ALL corporate finance textbooks will start teaching the valuation chapters by showing that most well-known MM theory and their formula.

Though I know after many years graduated from corporate finance school, many books, including Berk & DeMarzo (https://www.amazon.com/Corporate-Finance-4th-Pearson-Standalone/dp/013408327X), didn’t tell us, the way MM WACC is shown, is misleading:

Kd(1-Tx) D/V + Ke E/V

By linking (1-Tx) to Kd, though it is simple to tell the story to new babies, this is not right, this tax shield basically will be going to Equity holder. It should be written:

Kd D/V + [ Ke E/V – Kd.Tx.D/V]

Second, MM WACC has a couple of strong assumptions:

1. The Company could exploit 100% tax shield, which we know now, this is not right. OECD and other tax jurisdictions (see the list enclosed) has limited the capability of the company to exploit the tax shield by either using balance sheet approach (DER is limited to certain x, for example, in Indonesia tax jurisdiction, DER for tax calculation is max 4x. Meaning, all tax shields coming from debt above DER 4x, will not be recognized for tax purposes, the Company in calculating the corporate income tax, the interest will not be enjoying the tax deduction]
1. It is “a must” to assume away how much we want to put the ratio of D/V and E/V (one of them will be the residual, depending we start with D/V or E/V first]. This D/V (or E/V) creates circularity, and could only be used in limited cases, so this is not general formula.

D/V in many cases, will depend the company profile itself.

Under project finance financial modeling, D/V seldom to be stabile. We will assess the strength of projected cash flows during the project term (10 – 50 years), and “sculpt” the debt to follow the pattern of the cash flow, and along the way, the debt will be paid down. The Debt amount will be high in the early years of project finance and then down. Theoretically, MM WACC should not be used, Myers- APV is a good one to go. We assess TS separately instead of lumping it into WACC. But of course, this TS discount rate is another big issue to say, how much we want to put there?

For mature company, in many cases, what we see, stabile  book D/E ratio, though this doesn’t automatically we could say, we will have one rate for D/V. For mature company, they will keep debt balance the same, unless, they have new projects. Debt itself may means working capital loan, investment loan, and trade finance loan. So this really depends on the company’s situation. Some could have a stabile debt balance and some couldn’t have. For example, trade finance loan might be up and down dependent upon whether the company has import activities during certain period.

Third, continuously adjusted debt (introduced by Harris-Pringle) or Annually Adjusted Debt (by Miles-Ezzel), though good for academicians, I never it is used in reality. The company could be quite crazy to keep changing their loan balance from year to year.

This book (https://www.amazon.com/Principles-Cash-Flow-Valuation-Market-Based-ebook/dp/B001P81GQS), gave me a couple of fresh things, among others:

Tax Shield (TS) discount rate assumption is so critical if we want to get the consistent results among many approaches (MM-WACC, general WACC, CCF, APV, etc.) But once we talk about TS discount rate, this is never-ending battle, which rate is to use? Myers-APV is also problematic to apply since we do need to decide Ku (cost of unlevered equity), which is not observable in share capital market.

The discount rate being used under “finite” and “perpetual” is different, though in many corporate finance textbooks, probably for the pedagogic purposes, the authors make (try hard) to simplify the chapters and the teaching…just use the perpetual formula to teach (Note: this is not totally wrong, since if you start teaching valuation by using MM theory, then 100% you will get into that very famous formula for perpetual situation. Unfortunately, not many finance authors tell us that this “perpetual” formula is only applicable under very special condition and not a general one. In many cases, they justify their “perpetual” formula by saying that the company lives forever, shares could be exchanged forever, etc…

The book strictly keeps coming back to TS discount that should be explicitly stated. Many corporate finance textbooks, including Berk and DeMarzo, shy away from this. Though in several parts of the book of Berk and DeMarzo, I read, they are in support for the use of Ku or Kd (Under “Leverage and the Cost of Capital” section of Chapter 18, whether the company maintains target leverage ratio, or not).

Joseph Tham to Mattia Landoni (http://www.mattialandoni.com/)

Dear Mattia,

For perpetuity:

Ke = Ku + (Ku – Kd)*(D – Vts)/E for the case Kts = Kd

So one can interpret the term (1 – T) as the adjustment for effective debt.

Due to my ignorance I have never read this interpretation of the term (1 – T)

Interesting and thought provoking.

Mattia:

Yes, but one of the many sources of confusion is that typically people start from a perpetual firm with constant debt, so that

D – Vts = D(1-T)

and the formula for Ke is

Ke = Ku + (Ku – Kd)*D(1-T)/E

But then if you have a different case, e.g., a 1-period firm, the formula becomes

D – Vts = D(1 – T Kd / (1-Kd))

Ke = Ku + (Ku – Kd)*D(1 – T Kd / (1-Kd))/E

Many people do not realize that the formula for Ke should change this way, they use the former version everywhere, and in many cases underestimate Ke significantly. So it is helpful to explain it as D – Vts, even though it’s only for the special case Kts=Kd.

Mattia, could you give me a clue (hint?) on how we develop annual state prices that correspond to the appropriate discount rates? I am lost!!

It’s super simple. One way is that you derive them aprioristically as the prices of Arrow-De breu securities from the utility function of the representative investor in a general equilibrium model.

The second way is, you define a large number of relevant future time-state paths – e.g. a binomial tree with future values of the market portfolio – and for every time-state you derive your best guess of CF from an asset. You do that for many assets whose value is observable. Then, the state prices are the ones that minimize the distance between observed prices and model prices across all assets. Usually people do this using an S&P500 index fund and its option chain, which gives you many assets without having to work a lot to get the cash flows.

Karnen:

Hi Joseph and all,

Many people still saw (1-T) is the favourable adjustment to the effective rate of Kd, since this is shown after Kd in the formula. This sounds logical since there is interest tax shield. Yet, what many don’t tell us, from where this traditional WACC came from. It is in deed “simplified” version. I believe, the finance teacher should write  traditional WACC as :

Kd D/V + (Ke E/V – Kd.T.D/V)

Though mathematically it is simpler, yet this has lead the wrong idea that Ts belongs to debt-holders and not to equity-holders.

Under MM theory, they have no obligation to show the above formula, and instead using the simpler one, since their emphasis of cash flows is Free Cash Flows.

Mattia:

Well put, thanks and nice to meet you all by the way.

Kd D/V + (Ke E/V – Kd.T.D/V)

Also note that, by definition,

Kd D/V + Ke E/V == Ku,

So the above can be written as (and Jonathan Berk and Peter DeMarzo does)

Ku – Kd.T.D/V

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