Discount rate for Tax Shield : Unanswered Question?

Readers,

I would like to get your views on my thoughts about the discount rate for Tax Shield (TS). I know this is a classic discussion but important.

According to Taggart, Jr, R. A. (1991): Consistent Valuation Cost of Capital Expressions with Corporate and Personal Taxes. Financial Management, Autumn, pp. 8–20, the CORRECT formula to unlever and lever beta or cost of capital will really depend on the assumption of the Tax Shield discount rate.

I have checked Taggart’s formula being given in that paper, and I found that his paper and understanding is correct.

If that’s the case, then discount rate for Tax Shield is an important topic, though in many finance classes, this topic is not really being emphasized intensely.

Respondent 1 to Karnen:

The behavior of TS depends on EBIT. See (UO = EBIT, OI = Other Income, AI = TS)

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As TS depends on EBIT shall we assume that the discount rate for TS should be Ku (cost of unlevered equity)?

On the other hand, if we see the Cash Flow conservation equation, we have

FCF + TS = CFD + CFE

and

CFE = FCF + TS – CFD

Note :

FCF = Free Cash Flows

TS = Tax Shield (flow)
CFE = Cash Flow to Equityholders
CFD = Cash Flow to Debtholders

Clearly the TS is “owned” by the equity holders. Hence, the Discount Rate for TS should be Ke (cost of levered equity)?

When you assume Ke as a discount rate for TS you might be able to obtain an optimal leverage and optimal VTS (Value of Tax Shield). That doesn’t happen with Kd and Ku as Discount Rate for TS. (see paper written by Felipe Mejia-Pelaez, Ignacio Velez-Pareja and James W. Kolari (2011) : Optimal Capital Structure for Finite Cash Flows, downloadable from https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1799605)

The idea of rebalancing or keeping constant debt is unrealistic. You need debt when you have a deficit. That’s all. Show me any case that tries to keep debt at some level or another one that adjusts debt to keep D% constant… (and don’t forget he should have the value of firm first and apply D%)  etc.

Karnen to Respondent 1:

My current understanding in my financial modelling:

The discount rate for Tax Shield will depend whether in the financial model, we are going to use predetermined debt or debt will keep rebalancing. In other words, the value of the TS will depend how certain they will be in the future and again this will sit on our modelling on debt (predetermined or rebalancing).

If we follow predetermined debt modelling, Kd will – in my opinion – be used to discount the TS. There is no difference with Kd being  used to discount and to get the value of debt. There might be a challenge that even the debt is sure but TS is not sure since the EBIT is not always big enough to absorb all interest burden. To such challenge, I will respond by using banker’s hat: will the bank extend the company with a predetemined debt in the first place if they knew that the project would not have big enough EBIT in the future to ensure interest will be able to be serviced during the debt term? So in this case, there is at least a high probability for that company to have sufficient EBIT in the future during the debt term, otherwise the bank would not give the predetermined loan to that company.

Under the debt rebalancing modelling, the value of TS will logically tie to the project value in the future. Somehow this TS could be certain or not certain hinging upon the success rate of the project…which means tax shields somehow be affected by the business risk. Under this logic, I would say Ku could be used as a discount rate for TS.

However, this logic though sounds good, still not quite satisfactory to me.

Discount rate is all about Opportunity Cost of Capital (OCC), the alternative use of money and ultimately as the required rate of return.

Tax Shield is something previously from the portion that should belong to the government, however, via the tax regime privilege, the tax authority is willing to have the interest expense be deductible on calculating the company’s corporate tax, reducing their tax liability and this government’s portion then goes to shareholders.

So, in other words, Tax Shield, sounds like a “bonus” to the shareholders. The money is not coming from the shareholders, but the shareholders enjoy it.

Then:

How to relate this Tax Shield concept to the OCC, alternative use of money, if the money itself is not coming from the shareholder, but government’s portion? Can we “penalize” this Tax Shield using Kd (cost of debt), Ku (cost of unlevered equity), Ke (cost of levered equity) or in between?

About the debt, I don’t think we could use one model to fit all sizes. It is really dependent on the company, meaning:

1. Permanent debt = this is possible, if the company keeps rolling over the loan. The bank will also enjoy this, as they keep receiving interest. I have seen this practice in some companies. Mutual benefits for both parties.

2. On-off loan depends on the company’s needs for cash. This will refer as working capital loan. this is also I have seen in some companies.

3. Loan taken by linking it to the market value of the project. This one-time loan is taken at certain point of the project finance life, by linking it to the value of the project. It will be locked for example, max 80% to the project value.

Constant D% or target leverage sometimes come up in the Valuation Analysis, but I have no idea whether it is really applied in reality. The analyst might just follow finance textbook approach, that is using constant leverage ratio (called target ratio). Again, this in reality, I don’t think it will be applied in corporate life.

Let me put in the Decision Tree to help a better understandign about what I meant above.

Prof. PDM’s Comments:

It doesn’t matter if it is a bonus, or if it comes from shareholders.  The valuation is the same, and the discount rate should depend on risk.  The two extremes are r_d (no adjustment) and r_u (continuous adjustment) and reality is somewhere between the two.  I prefer to use r_u as the main example pedagogically, since firms that use leverage for the tax shield do tend to adjust it over time.

Tax shields should be discounted at rate r_u if leverage is adjusted continuously to a target level.  (Yes, r_u is presumed stable.)
Karnen’s responses to Prof. PDM:

Once we apply r_u ad the discount rate for tax shield, unlever and relever will be quite simple :

Ke_t = Ku_t + (Ku_t – Kd_t) D_t-1/V_t-1

The same above formula will be used both applied to:

(i) CCF = FCF + TS = CFD  + CFE; and
(i) FCF (without TS)

Combining r_u (or Ku) as discount rate for tax shield and Capital Cash Flows (as suggested by RS Ruback in his paper (2000) : Capital Cash Flows: A Simple Approach to Valuing Risky Cash Flows, downloadable from https://papers.ssrn.com/sol3/papers.cfm?abstract_id=223080, then this is the simplest approach to valuation which the WACC will be compressed to Ku.

Other readings:

  • Valuing the Debt Tax Shield by Ian Cooper and Kjell G. Nyborg (2011), downloadable at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=979910
  • Corporate Income Taxes and the Cost of Capital : Revision by James W. Kolari and Ignacio Velez-Pareja (2013), downloadable from https://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=145648
  • Cost of Capital with Levered Cost of Equity as the Risk of Tax Shields by Joseph Tham, Ignacio Velez-Pareja, and James W. Kolari (2011), downloadable from https://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=145648

Posted in ARTICLES & VIDEOS, COST OF CAPITAL.

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