Thoughts on Corporate Valuation : Which One to Use?


Trying to share my thoughts on Corporate Valuation:

The first and foremost equation:

FCF + Tax Shield (TS) = CFD + CFE = CCF (Capital Cash Flows)

FCF = Free Cash Flows (=unlevered cash flows)
CFD = Cash Flows accruing to Debt holders
CFE = Cash Flows accruing to Equity holders

From my experience, tackling the valuation from the CASH FLOWS perspective, is easier to understand. Cash flow is the simple stuff to explain away. How much money will you get at the end of the day…I guess, this is the big concern, before bringing the topic of discount rate, or either the company will finance the project with debt (with its attendant TS) or not (just removed out the TS from the above equation).

Once the equation is brought into the audience, usually, there will be a question about what is Tax Shield cash flows. Then it needs to explain away that the Tax Shield will only show up when the debt is being used to finance a project or a business, and a big note that TS will only have a value if the company’s business has enough EBIT to cover it, or if the fiscal loss could be carried forward (or carried backward like in US tax system).

The next question, who is going to receive the Tax Shield Cash Flow? Equity holders!

Upon discussing the Cash Flow, then it is important to know whether the cash flow is flowing to the FIRM, or the cash flow to the debt holder and/or equityholder. Under the GAAP Statement of Cash Flows, it is cash flows to the Firm, though we could still identify, which cash flows accruing to debtholders and equityholders.

Then, I am always back to the above equation:  FCF   + TS = CFD + CFE

The whole point about the Valuation and Financing is about how the analyst to take account of the tax benefits of the interest deduction from the debt financing. Which we might put under the Cash Flow or we might put under the Discount Rate. I guess, this is what your slide shown on page 11.

I don’t think the FTE (Flow to Equity) method is even comparable to WACC and APV (Adjusted Present Value). FTE is only talking about CFE, however WACC and APV is about FCF + TS or CFD + CFE.

FTE Method is not much used if we are talking about corporate finance, it is mostly spoken in terms of project finance (with or without debt recourse).

WACC and APV is more relevant for corporate finance discussion.

The next question, then what is the difference between WACC and APV.

WACC will treat the tax benefits of interest deduction in the discount rate, by lowering the discount rate, and have higher value, accordingly, as we deal with FCF ONLY = CFD + (CFE – TS)

However, this is easier said than done, since there is a STRONG assumptions by lumping the tax benefits into the WACC formula. First, we assume that the tax benefits will be realized in the year it is incurred (the company has enough EBIT to absorb it or loss carryforward is possible to do and there is enough future EBIT to cover that loss carry forward). Second, the leverage is assumed constant over the life of the cash flow profile, which might be challenging for growth company. Third, classic circularity issue. Fourth, the formula of traditional WACC, though intuitive, but misleading.

Traditional WACC = Kd (1-Tax) Debt/Value + Ke Equity/Value

The correct one:

WACC = Kd Debt/Value + (Ke Equity/Value – Kd x Tax x Debt/Value); or

After_tax WACC = Before_tax WACC – (Kd x Tax x Debt/Value)

The last term in the right hand of equation is the tax benefits from debt financing and this cash flows GOING to the equityholder, and not the debt holder.

APV, as introduced by Steward Myers (1974), then will take care of tax shield separately from WACC, and address it directly as part of the cash flows, which means, then we don’t have stand-alone FCF anymore, but needs to have the Value of the project (FCF) plus the value of TS from the project financing.

The last one, which is most easier one to use is CCF by lumping FCF altogether with TS and discount it with Ku (as suggested by Richard S. Ruback, 1995 and revised in 2000, see, being accessed on 17 August 2020).

With CCF, we don’t have issue with the following:

(i) classic circularity and

(ii) no need to calculate Ke (Cost of levered equity, which I believe nobody could come up with a good guess about Ke) and

(iii) no need to come up with the value of Tax Shield (the big problematic questions that nobody could give satisfying answer up to now, the question that we need to address separately under Adjusted Present Value method).

Showing FCF + TS = CCF = CFD + CFE, in my opinion, is very important to readers.

There is equally important to show (which much not found in many good textbook when they discussed about NPV)

NPV (Owners or Equity holders) = NPV (Project) + NPV (Financing), which is under Perfect Markets assumption => NPV (Financing) = ZERO.

Respondent 1 to Karnen: 

However, since in most cases you assume that the finance institution is sophisticated and that the financial industry is a competitive one (i.e. perfect markets), we usually get that NPV(financing) is zero.

Respondent 2 to Karnen:

When I read the last sentence and earlier thoughts you have, I think at the inside, you respect Miller and nobody else.  I really believe finance is where medicine was before Louis Pasteur or where physics was before Faraday. The establishment believes silly things.  I really like the way you study things — you study the existing theory carefully and now I hope you are seeing that a lot of it is not making sense.  This non-senses comes to some extent from using integral formulas rather than making proofs with simple examples.

Here is the way I think you should think about the debt shield.  Think about it as a government grant.  The interest deduction does not change the cost of funds for the debt holders.  Lets say debt holders get 5% as the interest rate.  They may have different personal tax rates on their funds.  That is the cost of debt.  This is the same for equity.  When you measure the cost of equity (most methods are absurd including the CAPM), you do not think about what kind of tax rate the investor pays; you measure the pre-tax cost of equity for the investors, not their after-tax proceeds.

So if the company gets any kind of gift from the government, customers or anybody else, the traditional thing to do is to use the formula:

EV (from FCF without accounting for tax gift and using cost of funds for debt holders)

Less: Debt
Plus: Cash
Add: Customer contributions
Add: GOVERNMENT GIFT — from tax deduction

Common Equity Value

The government gift occurs on an on-going basis so you cannot just add back the government gift as above.  When you work through the math you can prove what method works best.  I know that changing the amount of debt — including the reduction in debt from the gift — is different from changing the interest rate as in the traditional WACC.  I think it is essential and easily possible to make a proof of what is the correct value.

My suggestion which is different from everything else is:

                    %                                     Cost                           Weighted Average
Debt         Debt x (1-t)/Total             Nominal Cost
Equity          Equity/Total                  Nominal Cost

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