It might be of interest to you in understanding the crucial role of TS (Tax Shield) discount rate in deriving a correct cost of capital formula….


Edward Bodmer

Hello Karnen:


I have become obsessed with you questions and ideas.  I think that the WACC issues can be derived by simple models and clear thinking concepts rather than dense formulas.  I am making simple models to demonstrate various ideas and also videos.  I will be very interested in your thoughts on this.



I have attached a couple of files and articles on tax shields and cost of capital etc.


The first file demonstrates that when the target capital structure does not equal the current capital structure, discounting free cash flows at the WACC (which does not change in theory when the capital structure changes) gives the same answer as computing a new cost of equity with changing capital structure.


The second file is the beginning of work on the tax effects of interest.


The other attachments are articles on WACC and taxes etc that I am reviewing for our analysis.





The (required) return to levered equity will depend as well on the assumption we put on the discount rate for Tax Shield. Some use cost of debt, or return to unlevered equity or between. You could google a whole bunch of finance papers discussing this issue.


WACC is a general formula, the most important what we are going to put into the return to levered equity (Ke). Knowing that TS discount rate assumption is also part of Ke then different assumption for TS discount rate will impact the Ke.


Edward Bodmer


I have been working very hard on your issue and I am attaching the set of videos I have made on this.


Interest Shield Exercise https://www.youtube.com/watch?v=G6BBvAFHJGo
Interest Shield Exercise https://www.youtube.com/watch?v=9LKppeYudVU
Un-lever and Re-lever with Tax Shield https://www.youtube.com/watch?v=jaLOx3RJFkc
Theory of Debt Beta and WACC https://www.youtube.com/watch?v=n_csEtMHveA
Mechanics of Debt Beta and WACC https://www.youtube.com/watch?v=Bvp0ruVYBSw
Unlever and Re-lever with Varying WACC https://www.youtube.com/watch?v=7ny67y-EpR8
Growth Rate, Tax Shields and WACC https://www.youtube.com/watch?v=oKNmQ9fimZc
Circularity, WACC and Ku https://www.youtube.com/watch?v=2EPd8_yi_0M
Growth and WACC Bias
Target Capital Structure without Taxes
Target Capital Structure with Tax Shield


January 2017

Consistent valuation of project Nyborg Discount Rates and Tax Nyborg Nyborg The value of tax shields IS equal to the present value of tax shields Valuing the Debt Tax Shield Cooper Nyborg Tax-Adjusted Discount Rates with Investor Taxes and Risky Debt Consistent methods of valuing companies by DCF


A Light Quiz for Brain: Expected Value


 Note: A light email correspondence with Ignacio Velez-Pareja (IVP) near Christmas holiday 2015.
Karnen to IVP:
Just want to get your insight quick.
An asset offering US$10 (probability 90%, so it is quite big) or US$1,000 (only 10% probable). How much are you going to pay for such asset?
US$10 (since it is highly possible you are going to end up with U$10 on hand)?

US$109 (as a statistician, US$10 x 0.9 + US$1,000 x 0.1)?

Or another number?

The problem with this issue is that here there is involved the risk attitude toward risk you have.
When you say, I am a Statistician, you are saying my attitude towards risk is neutral or if you prefer, risk indifferent. However, you might be a risk averse or risk lover. The problem is that being one of the three (indifferent, lover or averse) might depend on many other variables such as the amount you are dealing with and the size of your own wealth, for instance. Also, as [Daniel] Kahneman & [Amos] Tversky have said, it depends on the context .

Just to give a real example. In my classes I use to illustrate this asking my students if they would accept an investment equal to their full wealth (equity) with probability of 10% of losing that amount. X number of students raise their hand saying YES. I keep going the lecture and later I pose the same situation BUT now I say it is 90% for a positive outcome. Then Y students raise their hands saying YES. However, Y>X. The situation is THE SAME. The difference is in the setting of the problem. 10% of loss is the same as 90% of win! And yet, the answer is different. I have done this MANY times and the pattern of answers has been the same.

In other words, when dealing with risk, logic might not work [very well]. It depends on your inner beliefs and prejudices.

I would say that first, I have to decide if I go into the lottery or not. If as you say, someone selects 10, I would say she is risk averse. If she says 109, I would say she is indifferent towards risk. If she says 5 she is strongly averse to risk; if she says 200 she is strongly risk lover and so on.


Cool answer.

Let’s say you are a risk (read: loss) averse, will you give me the number how much you are going to pay that investment? at the expected value?

I am afraid “expected value” doesn’t exist in the market but why is so important in corporate finance?

I am glad you touched the reference to Daniel Kahneman and Amos Tversky since their significant contribution in decision making with respect to investment is not much mentioned, even in mainstream corporate finance textbooks.

The risk tends to be explained in statistical terms in the book and this makes risk concept a bit misunderstood. It is actually that gain and loss doesn’t weigh equally.

For example, we personally feel more ‘painful’ losing $10 in bad times than gaining $10 the same amount in good times.

Expected value or simple averaging clouds this big difference off to the students.


SURE! That is it.

In any area, the average or expected value doesn’t exist. That is a mathematical construct very good when you don’t know what number to use in an estimation. Please read the paper by Pablo Fernandez on the absurd of CAPM .

If you need a number for your investment I can give you one: 11.7654344. Is that good enough for you?
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