#StayatHome Financial Modeling : Discount Rate or Opportunity Cost of Capital

Talking about Discount Rate makes me remember the song by Bruce Springsteen…Dancing in the Dark

Even if we’re just dancin’ in the dark
Even if we’re just dancin’ in the dark
Even if we’re just dancin’ in the dark
Even if we’re just dancin’ in the dark

Readers,

Many times, participants asked me about what discount rate that we need to discount the expected cash flows in your financial model? They mostly understand that WACC (Weighted Average Cost of Capital) should be there. But I don’t want to discuss WACC, too boring.

Humming…

I get up in the evenin’
And I ain’t got nothin’ to say
I come home in the mornin’
I go to bed feelin’ the same way
I ain’t nothin’ but tired
Man, I’m just tired and bored with myself
Hey there, baby, I could use just a little help

just a little help, yeah…

Instead of answering, like many finance professors, they will answer back with question..there are no hard and fast rules.

Let’s say, you have a business that runs well. You want to expand this business with another project requiring US$ 1 million, and as usual, you go to your banker. Your banker using 5 Cs’ analysis will look into your business, and come up with the conclusion, this is creditworthy, and the bank will charge with 8% interest per year.

Question: Is the project’s cost of capital 8%?

This might sound quite logical, I got the funding bearing interest of 8% per year, and that money all being used to fund the project’s investment?

“Sound” logical, but is it true? You are in hesitation, and coming to my class asking about this?

The confusion comes from the reality that project’s cost of capital is UNOBSERVABLE. There is no way for us to go to the market and find it or any paper or publication will tell us how much in % the cost of capital for our project will be.

However, interest rate on debt is REAL, and OBSERVABLE. Even your banker could tell you straight how much interest the bank will give you the credit.

Again, you need to put your feet on the ground…time for REALITY CHECK.

The loan interest rate might be related to project cash flows, since the project investment will be financed by the loan and the project cash flows will be used as well to service the debt repayment and the yearly interest rate. Though it is RELATED, but here we are talking about the COST OF CAPITAL to discount the PROJECT’S EXPECTED CASH FLOWS. So in this case, we are talking about the RISK OF THE PROJECT. The loan interest rate then is NOTHING TO DO with the RISK OF THE PROJECT.

When the Banker does the assessment of your business expansion business, and comes up with the annual interest rate, that will say about the soundness of the business, and that includes the already-existing business. Which means that the Bank looks into the current cash flows produced by the already-existing business, plus the new incremental cash flows that will be generated by the business expansion project. If the business expansion project’s cash flows and assets were not sufficient to repay the loan principal and service the interest charge, then the Bank has another door to go, that is the bank could demand repayment from the cash flows generated by already-existing business.

Don’t you think the Banker is the smartest people in the world? Don’t forget to remember: Money attracts Brain! Some people trades products but some people trades money.

Hopefully you are still with me.

The loan then is nothing to do with the project’s risk.

The key words every time we are discussing the cost of capital is THE OPPORTUNITY cost of capital. I guess, we need to keep this OPPORTUNITY word in all textbooks, to remind the readers, and reduce any confusion about the cost of capital. Since it is the opportunity that is the key word, then it will implicate something, we need to compare between two investments, in this instance:

(i) Either the money going to finance the project. Let’s say, the project will only come back with the expected rate of return of 12%; OR

(ii) the money be invested to other investment option, let’s say, other stock in the capital market, with equally risk level, which will return the expected rate of 20%.

So taking the loan or not, IT IS NOT RELEVANT TO THE PROJECT’S DISCOUNT RATE OR COST OF CAPITAL.

I don’t think it will make finance sense at all, if the management decide to:

(i) take the loan with interest rate of 8% per year, and then invest the money to the project with the expected rate of return of 12%, if at the same time…

(ii) the company’s shareholder could pick up the loan with 8% annual interest rate and invest the money to capital market which its expected return of 20%.

I hope Readers will see that when it is the OPPORTUNITY cost of capital, then we need to see everything from the SHAREHOLDERS’ EYES.

Don’t ever forget your SHAREHOLDERS!

Comparing the above two ALTERNATIVES or OPTIONS, then we could say that the Project’s OPPORTUNITY cost of capital should be 20% instead of 8%!!!!!!!!!

You will judge the project’s soundness using the cost of capital of 202% and not 8% (interest rate on loan) or 120% (your expected rate), but 20%, since this is the return that you could get from equally risky investment.

If the money from bank could be used to gain 20% return in the capital market, then it will be easily challenged as to why you put the bank loan money into the project that will give back lower rate, that is 12%.

There is something that I said above that you might not really notice. I refer to the capital or stock market when I said that we need to look to the capital/stock market for finding alternative equally risky investment.

Of course we can’t leave the bonds market away.

To find the OPPORTUNITY COST OF CAPITAL, then we need to look to the Bonds Market and Stock Market. As ever I put before in my another writing “Government Bonds with Negative Yield?”, Bonds Market will always be the anchor for all your investment decisions, either you want to put your money in the bank, real estate, stock, you need to check on the Bonds Market, as interest as the Mother of Economics, is formed through demand and supply forces in that market. Even the expected return rate on common equity will somehow factor into it, the bonds yield. This is why sometimes we find that analysts will use bonds-yield-plus-[subjective]risk-premium approach to estimate a company’s cost of common equity. It is logical to think that companies with risky, low-rated, and consequently high-interest-rate debt (which is readily observable in the market) will also have risky, high-cost equity.

I got a question instantly, then what happens to all those WACC concepts that I got from my finance class?

I don’t say WACC is wrong or correct to be used, yet, probably what we learnt so far is just half the story.

I am trying to depict the WACC discussion into what I call Traditional View and Expanded View.

As you can see, and know very well, under Traditional View, with money flowing from Debt-holders and Equity-holders, WACC to fund a project then will be the weighted average of cost of debt and cost of equity proportional to the market value of each fund.
Well, I guess, nobody from finance schools will challenge the above.

However, I am a bit piqued by knowing that the interest rate on loan/debt (how we get the interest rate, that’s different story, some analysts, just use bonds yield, stated interest rate, etc.) is nothing to do with the project risk. The interest rate being requested by the debt-holder will only reflect the soundness or good health of the Company overall, including its existing business. In the case, the new expansion project can’t repay or service the loan, the bank could come to company to demand repayment from the cash flowing from its existing business.
It will sound a bit non-finance sense to borrow, let’s say 8% and invest the money to the project earning 12% if the shareholders could go the Expanded View, where he/she himself/herself borrow the money at 8% and use the money to fund the project and for that, the shareholders require 20%, the return that he/she could get by putting that money to the stock market (big assumption: the project and the stock market investment has equally risky profile of return and risk).
So under the Expanded view, all projects expected cash flows should be discounted at the equivalent rate of return that the shareholders could earn from alternative equally-risky investments. In this example above, 20% to use to discount the project.

In this case, we don’t even need all those WACC calculation.

In a nutshell, either the project is financed with a mix of debt and equity = since the shareholders could borrow by themselves instead of the company making the borrowing, all projects should be discounted at the rate that the shareholders could earn from other equally-risky investment.

My argument, this Expanded view is very feasible, in United States of America, we know there is pass-through company, called S Corporation. A shell company.

What do you think?

Respondent 1 to Karnen:

In short, I think I agree with everything you say; in particular, ” … all projects expected cash flows should be discounted at the equivalent rate of return that the shareholders could earn from alternative equally-risky investments. In this example above, 15% to use to discount the project.  In this case, we don’t even need all those WACC calculation.”  There is excellent theory (originally developed by Modigliani and Miller) to support this view too and it basically says that except when there is either (1) significant transaction cost differences between enterprise / business sale transactions and debt / equity investment transactions, or (2) information asymmetries between enterprise management and debt / equity investors, the project discount rate (on the assets) would be exactly the same as WACC (see Section 5.3. in the attached).  My personal opinion is that, in most cases, it’s very difficult to determine whether (1) or (2) exists; so I tend to assume the asset project rate = WACC and then just avoid estimating WACC on that basis.

And, yes, I agree with your argument and estimation methods that you suggest as well.

Karnen to Respondent 1:

Could you kindly elaborate further when you said:

so I tend to assume the asset project rate = WACC and then just avoid estimating WACC on that basis. 

Will that mean you don’t use WACC? 

May I know what you are doing when you come to estimate the discount rate?

Seems to me this discount rate is a kind of elusive concept. Different people could have a different way to come up with the discount rate. So meaning there is no single rate or even one range of rates that even two people could agree upon.

I guess the issue is (i) we need to infer Ku (unlevered risk) from Ke or even Kd (and this will lead to a long debatable topic), and second, we don’t have at the moment, the theory to calculate directly the project unlevered risk.

Though there are many books out there showing us to unlever and relever Ke, but all of this will really depend :

whether we assume using fixed book-value leverage ratio

whether we assume using fixed market-value leverage ratio

whether we assume using preset debt

whether we assume periodically adjusted debt

what discount rate assumption we use for TS

etc.

If we read MM 1958 paper, the authors themselves, never figured out how to calculate the cost of capital and they put there that  question must be deferred to a subsequent paper. Though MM gave us a definition of the company’s cost of capital was the opportunity cost of not putting money into the shares of a different firm in the equivalent return class, however, again, they never really defined what that was supposed to mean.

It is interesting to note that you bring up the Certainty Equivalent Method and risk-neutral pricing. However, I am not too often in practice, to see analysts using this kind of method to do their pricing, and this method seems to me has not gone to the mainstream in valuation.

If you could share the way you calculate your discount rate, that will be great.

Respondent 1 to Karnen:

I’ll try to answer in sequence:

(1) “so I tend to assume the asset project rate = WACC and then just avoid estimating WACC on that basis.  Will that mean you don’t use WACC?”

That’s correct: If I can support the assumptions that (i) there are no substantial information asymmetries between an enterprise’s management and the acquirer (e.g., if the acquirer has done adequate due diligence and the target’s management has incentives to properly disclose all significant matters), and (ii) there are likely no substantial differences in transaction costs between an “all equity deal” and a “leveraged deal,” then it follows that Ra = Rl*FV(LIAB) / FV(ASSETS) + Re*FV(EQUITY) / FV(ASSETS) = WACC. So, I just use Ra; the estimated risk-adjusted rate of return on the assets / project. 

And, I agree, MM (1958) just introduced the concepts / ideas without really working out all the theory.  I worked out the modern theory in my book based on the fundamental economic identity for resources and claims against resources (ASSETS := LIABILITIES + EQUITY), and an application of information asymmetry and transaction cost theory under the no-arbitrage principle (following Ross (2004), etc.).

(2) “May I know what you are doing when you come to estimate the discount rate? Seems to me this discount rate is a kind of elusive concept. Different people could have a different way to come up with the discount rate. So meaning there is no single rate or even one range of rates that even two people could agree upon.”

I agree about the wide variation in practice on estimating discount rates, and I think this has mainly to do with the fact that arbitrage pricing theory (APT, Ross 1976) is still rarely taught in university; mainly because people (even professors) think APT is just the same as CAPM but with additional risk factors.  But APT and CAPM are quite different theories: CAPM is based on a priori assumptions like (i) there is such a thing as an observable risk-free asset and rate, and (2) the capital markets are in equilibrium.  If these assumptions don’t hold, then CAPM’s theoretical predictions would not be valid.  In contrast, APT needs neither of these assumptions.

So, I use either an APT-based estimate of risk-adjusted expected rate of return, or I discount estimated certainty-equivalent cash flows using observable risk-free asset yields. 

(3) Regarding levered and unlevered “beta”

If one actually believes CAPM is valid, then using the Hamada equation to work out the relationship between levered and unlevered beta–and, so, estimated discount rates–makes sense.  But I’ve actually tested CAPM many times on equities that *should basically meet the CAPM assumptions* (e.g., Boeing) and the real world data is almost always inconsistent with CAPM theory.  So, I never have used the Hamada equation for anything; basically because it’s based on CAPM being true. 

And, yes, I agree … some of the many assumptions that need to be made along with CAPM and the Hamada equation seem (to me) to be beyond rational belief.

My valuation friends always say to me “But you have to use CAPM because it’s the only accepted theory there is!”  But the actual history is that APT and certainty-equivalent pricing (“risk-neutral pricing”) were developed in the mid- to late-1970s to solve the problems with CAPM.  So, we do have other accepted theories and methods … and the methods are much simpler as well.  It’s just that university professors like to teach CAPM, and hate to teach APT as it was intended.

I’ve attached an redacted example (from an actual, recent valuation report) of using APT to estimate the risk-adjusted discount rate.  I certainly don’t think any theory or estimation method is perfect, but I do think the APT method is more theoretically valid, simpler, and does not require inappropriate assumptions.

Karnen to Respondent 1:

Can you clarify further, how to operationalize this equation? the formula seems to me is not new, this is exactly WACC formula.

Ra = Rl*FV(LIAB) / FV(ASSETS) + Re*FV(EQUITY) / FV(ASSETS) = WACC  

Second, you draw my attention to APT. Yes, APT is a sort of mystery to me even up to now. The corporate finance textbooks give just a glimpse of the APT and its implementation. I believe most of the finance professors just stop after they finished up explaining the CAPM, and shy away from elaborating more on APT. To be honest, I can’t find one good book on putting APT on par with CAPM, meaning the book gives the same proportion as that CAPM. As far as I remember only Financial Theory and Corporate Policy (by Copeland, Weston and Shastri) textbook that is able to explain that to me. Stephen Ross wrote one book : Neoclassical Finance, but it is too technical, I guess, we need one book that could bring this APT concept to more a operational level for valuation analyst to fall in love in using them.

Respondent 1 to Karnen:

On the equation …

Ra = Rl*FV(LIAB) / FV(ASSETS) + Re*FV(EQUITY) / FV(ASSETS) = WACC 

… I was trying to show the following, but wasn’t very clear:

(1)  Ra = is the estimated expected risk-adjusted rate of return on the *assets* (“the project”) … maybe estimated using APT.
(2)  WACC := Rl*FV(LIAB) / FV(ASSETS) + Re*FV(EQUITY) / FV(ASSETS) is the definition of WACC; with each component Rl, Re, FV(L), FV(E), FV(A) being an estimate.
(3)  If there is no significant information asymmetry or transaction cost differential, then Ra = WACC, in which case we only need the estimate of Ra (exactly as you said).

And I agree the difference between APT and CAPM is actually very subtle; I think because if there is, in fact, only one risk factor then CAPM and APT result in the same expected rate of return.  Because of this, most professors I know just say something like “APT is just CAPM with more risk factors” … but then they don’t show that there is a difference between a *risk price* and a *risk factor* (I discuss this problem in Section 2.10 of my book).  The difference between risk price and risk factor can by thinking about the following for asset i:

APT:       Ri = Rf + B1i*RISK PRICE1 + B2i*RISK PRICE2 + B3i*RISK PRICE3 + … 

CAPM:   Ri = Rf + B1i*RISK PRICE1 = Rf + Bi*(ERm – Rf)  where (ERm – Rf) is the “capital market portfolio risk premium”

Because CAPM just assumes there is an equilibrium, (ERm – Rf) is the *risk price* for single aggregated *risk factor*.  But CAPM does not tell us how to find / estimate other risk prices, because in the CAPM equilibrium there is only the one risk price, which equals (ERm – Rf).  In contrast, APT shows how to extract risk prices from market data for any risk based on asset return sensitivities to risk factors.

I also agree with you completely with you on “all asset pricing models are about expectation- ex-ante and not ex-post, and the whole matter then revolves around the future.”  My two favorite financial economists are Fischer Black and Stephen Ross, and in my view Black was essentially a theorist and Ross an empiricist … which I think explains the difference between CAPM (Black) and APT (Ross):  In CAPM, there are unobservable / untestable assumptions; in APT there’s basically just one observable / testable assumption.

In my recent blog article, I show an example in Sections 4 and 5 of CE method valuation, and I also show in Section 5 what is most critical in asset pricing: estimating return sensitivity to risk factors.  If there is a *statistically stable* sensitivity of market returns to a risk factor, then we can reasonably make the argument that ex post risk prices can be used to estimate ex ante expected returns … or at least that’s how I think of it.

Respondent 2 to Karnen:

For myself, I guess, all asset pricing models are about expectation- ex-ante and not ex-post, and the whole matter then revolves around the future. Can use historical data to draw a conclusion or even use it to test the future? I gather, all we need is just to rely on a sense of the prob of the future events. Fisher Black once said that we should put our trust only in logic and theory and forget about statistical empirical results. (quoted from Capital Ideas Evolving by Peter L. Berstein. John Wiley & Sons, Inc.. 2007. Page 94.)

My first understanding and reaction is that if the equity holders do what you say and invest in the firm/project, clearly the wacc reduces to Ke.

Karnen to Respondent 2:

Yes. However, my point, since the shareholder could borrow by him/herself to finance the project (in reality, I have seen this before, where the equity fund is indeed coming from bank loan), then computing WACC for the project is not necessary. All project cash flows could hypothetically be discounted at Ke, even for the case, where the company borrows the money directly from the bank.

Respondent 2 to Karnen:

I don’t see clearly why if the financing with debt is done by the firm, you still say that any project could be discounted with Ke. Explain, please…

Karnen to Respondent 2:

What I would like to say is that:

The forecast cash flows of a project should not be discounted at wacc (debt and equity), but by Ke (cost of equity), the required return that the shareholder could earn from other alternative equally risky investment (in this case, I use return from stock market).

WACC becomes irrelevant since the shareholder could borrow by himself to finance the project and flow the bank loan proceeds in the form of equity.

So whether the company or the shareholders the entity that have the borrowings, it is not relevant, and thus the way discount rate is calculated from WACC.

The value of the company that itself obtains the loan (A) and the value of the company that through its shareholder obtains the bank loan proceeds (in form of equity) B)= both companies A and B should have the same value. In other words, Ke is the appropriate discount rate for both Company A and B. Otherwise Arbitrage will creep into.

Respondent 2 to Karnen:

Not sure.

Just a naive question: how would the firm know if shareholders have financed the investment in the firm?

The firm will not know. The firm will “see” that the project/firm will be financed by equityholders only  if they ask the firm pay all debt, and ok, the firm will know that the firm will be 100% by equity.

If the firm keeps debt it will have to pay interest on debt. And it will earn TS. If this is the situation, it is not clear to me why the firm should discount its projects/investments CFs at Ke and not at WACC or even at Ku in case the firm perceives that equityholders has 100% of capital. In the best case of your proposal, it would be a 100% equity funded firm and in that case the DR would be Ku and not Ke. 

In short, if the firm perceives that it is financed X% by debt and (1-X%) by equity, it might discount any project with WACC etc. If there is no debt, the project/firm CFs should be discounted at Ku.

Karnen to Respondent 2:

Let’s give you one example:

Company A: have 50%:50% mix of debt + equity

Company B: 100% equity but behind that equity, the shareholders have a mix of 50%:50% debt and equity

Do you think the value of Company A the same or not with Company B?

If the same, why, and if not why?

That’s my very basic question about this.

Respondent 3 to Karnen:

Clearly, the value of Company A is not the same as that of Company B (assuming their expected FCFs are identical, EBIT>int, no financial distress costs). 

Va=Vu+VTS > Vb=Vu

If we go to compare the wealth of shareholder in A (Wa) and the wealth of a levered shareholder in B (Wb), then with a simple algebra one can see that the conclusion depends on the income tax rates. If the tax rate for the shareholder in B equals the corporate tax rate, then Wa=Wb, otherwise Wa and Wb will differ with the sign depending on which tax rate is higher.

To avoid confusion, one should not mix the value of a project (firm) and the overall wealth position of an investor in the project (firm).

My humble beliefs

A project’s generic risk is the risk of its FCF with the associated required return Ku equivalent to the expected rate of return from an alternative equally-risky investment. 

Rates to discount the project’s cash flows will depend on a composition of claims on project’s assets (i.e. distribution of the project’s cash flow and risk) 

For all equity capital structure (only equity claim exists) the discount rate for the FCF is Ku, and for a mix of debt and equity it is WACC.

One may prefer to value an equity claim on the project directly, and in this case CFE should be discounted at Ke (with a premium to Ku for the risk of having to serve the debtholder claims on the project’s FCF first). 

Where the shareholder obtained funds to invest in the project is irrelevant, a determinant of the discount rate is the risk of the cash flow being discounted.  

Discounting FCF and Ke is visibly inconsistent and produces senseless result

Judgement by comparing the projects return with the borrowing rate makes no sense.

Karnen to Respondent 3:

Thanks for your generous comments.

You said: Clearly, the value of Company A is not the same as that of Company B (assuming their expected FCFs are identical, EBIT>int, no financial distress costs).

How come the value of Company A is not the same with that of Company B as both they are exactly the same company and produce the same forecasted cash flows)?

Pls remove first all discussions on tax, assuming we are living in a perfect MM world.

I put all these hypothetical example (all else remains the same, only the financial structure is different)

Company A: have 50%:50% mix of debt + equity

Company B: 100% equity but behind that equity, the shareholders have a mix of 50%:50% debt and equity

Other information:

  • Alternative equally risky investment return for that project = 15% (I took from stock market if the shareholder put his/her money in the stock market)
  • Borrowing rate (either going to company A or going to shareholder) = 5%

My questions:

For Company A : how much discount rate will you put there?

For Company B : how much disocunt rate will you put there?

Respondent 3 to Karnen:

Sure, sure… if we alter assumptions to a perfect MM world, then Va=Vb and tax considerations are irrelevant. However, other statements remain valid, just WACC reduces to Ku.

Let’s see how it goes in the hypothetical example suggested

An implicit assumption is “project  firm”. If not, discount rates for the firm and project would differ

It’s not clear what 15% return from an alternative equally risky investment is. Since it is said to be a return a shareholder obtains from the stock market, 15% could be Ke, if return comes from investing in a share of a levered firm, or 15% could be Ku, if the firm is unlevered. 

Let’s assume 15%=Ku (either observed directly or obtained by unlevering Ke)

Since we are in a perfect world, cost of debt capital = borrowing rate

Discount rates are as follows:    

Va = Value(Company A) = PV[ FCF at WACC ] = PV[ FCF at Ku ] = PV[ FCF at 15% ] 

Ea (or Ve(A) depending on a choice for notation) = Value(Equity claim in the Company A) = PV[ CFE at Ke ] = PV[ CFE at 15%+(0.5/0.50)(15%-5%) ] = PV[ CFE at 25% ] = 0,5Va

Vb = Value(Company B) = PV[ FCF at Ku ] = PV[ FCF at 15% ] = Value(Equity claim in the Company B) = Eb 

Obviously, Ea=0,5Eb. However, if we look at a shareholder wealth position, then in full compliance with MM  0,5Va =Ea = Wa = Wb = 0.5Eb = 0.5Vb

Indifference of a shareholder wealth position doesn’t imply that ALL cash flows could be discounted at one and the same rate.

Things become a bit more complicated if we introduce taxes

I suppose comments from Respondent 2 above have an underlying idea similar to comments above.

Karnen to Respondent 3:

Yes, under MM super perfect world, WACC = Ku, this will lead to the same valuation of Company A and Company B.

Stock market return, that I put there, that is not specific industry, we could use a portfolio of shares, since I guess, nowadays, nobody only puts his/her eggs in one company’s shares. I heard many times in the discussion with the investors, they just said that they earned such return rate from putting their money in the stock markets, and use that as the benchmark.

In practice, again, I did remember from my very early email exchanges with Ignacio, bringing Ku to the table of discussion, this is hard, since Ku is not observable. And one question to Ignacio, hopefully he still remembered that, is most of the time, (i) we need to infer Ku from Ke or even Kd (and this will lead to a long debatable topic), and (i) we don’t have at the moment, the theory to calculate directly the Ku.

Though there are many books out there showing us to unlever and relever Ke, but all of this will really depend :

whether we assume using fixed book-value leverage ratio

whether we assume using fixed market-value leverage ratio

whether we assume using preset debt

whether we assume periodically adjusted debt

and Ignacio’s favourite topic, what discount rate assumption we use for TS

etc.

I just sent you a couple of days before, one paper by Clifford S. Ang, CFA and Andrew Lin, CFA, CAIA : The Valuation Impact of Using the Wrong Leverage Ratio to Unlever Betas (http://quickreadbuzz.com/2020/04/29/business-valuation-ang-lin-the-valuation-impact-of-using-the-wrong-leverage-ratio-to-unlever-betas/, accessed on 3 June 2020)  which gives us conclusion that:

The above analysis shows that using the improper leverage ratio to unlever betas can lead to substantial valuation differentials. In a significant percentage of cases, the valuation differentials can exceed 10%. In some cases, the valuation differentials can exceed 50%. The size of the error rate is likely concerning to most valuation analysts.

Nonetheless, the point that you bring something to me is you are talking about the view from total shareholders’ wealth, which sounds interesting to me.

Respondent 3 to Karnen:


I would admit that the extensive argument you provide didn’t persuade me to give up my view: whatever the pass one takes to settle a hurdle rate for an investment decision, it doesn’t make much sense to discount all cash flows of a project (not to say all projects) at this one rate. I see you smoothly move away from your initial question to a related, but different topic, and this is another story.

Karnen to Respondent 3:

However, I came up with this question when in practice, I see even two analysts valuing the same project (part of a company) could come up with two different single rate or two different ranges of rates. When they structure the financing either the loan going direct to the company or thru the shareholders, this has brought up a different way to come up with discount rate. Again, unlever and re-lever is a painful process to explain away, which one to use and again that another debatable topic.

Again, as I put in early email to this discussion, even if we could get 5% loan, but invest in a project returning 12% while the shareholders could earn 15% from the stock market, then that project still is not feasible to go. Put something to discount rate (either WACC, whatever) for the project’s cash flows, in my practice, brings too much complication to the table.

My proposition, if the shareholder “could” borrow the loan to finance the project and flow it to the project, then he/she could increase their expected return (even higher than 15%) and then use that a benchmark to compare against the IRR of the project’s cash flows. This brings discussions becoming lighter to talk and get across. I am trying to avoid as much as possible, about Ku, re-lever & relever beta (or Ke), target leverage ratio, etc.

Respondent 3 to Karnen:

Ok, let me try to explain the point another way. I don’t see much problem, if any, with discounting at Ke (or whatsoever one may call it) regardless of who is levered, a shareholder or a firm. However, If the shareholder takes a levered position (borrows herself and pours money into the project as equity), then it would be inconsistent (in fact, a common mistake) to discount the project’s cash flow (FCF in this case) at that Ke, or compare the project’s IRR to it.

Karnen to Respondent 3:

Under Company B, all FCFs of the projects flow to shareholders, so that FCF Project = FCF Equity = CFE, and we could compare that to Ke. What is the issue with that?

Something that I need to clear off with you, again back to the stock market return. Hypothetically the money from loan creditor and shareholders, could be invested by the company as well into the stock market return, and let’s say it earns the same rate of 15%. Meaning that this investment in the stock market could be made by the shareholders themselves and by the company itself. Leaving with the option for the company, to put the money into the project (IRR 12%) and put the money into the stock market (15%), then it takes no brainer that the company should not take up that project. If you accept with the above notion, then the company doesn’t need WACC or whatever discount rate for the project. All we need to make assessment is only the IRR of the project, and the benchmark other alternative investment (in stock market or other market).

Next discussion will see what is inside the interest, since interest rates are a key factor being included in determining the cost of capital and it provides benchmarks against which to make financial and investment decisions.

Just pick up the interest rate from the market (Note: since it is relatively easier, since the rate is OBSERVABLE and updated INSTANTLY) without really understand what factors are driving the interest rate (or the yields required to induce investments of various types), it might be like a boy with a hammer, which to him, everything looks like a nail.

Question to Respondent 4:

A project will be funded by debt and equity. If the equity holder obtains his/her fund from the bank (somehow bank wants to finance this long-term equity investment in one project, through the shareholder, instead of directly funding the project. The reason might be that the loan thru the shareholder is guaranteed by other shareholder’s assets) with effective annual rate, let’s say 10%. The equity holder have two options hypothetically, invest the proceeds from the bank loan into the project, or put that into the equally risky stock investment in the capital market, yielding expected return of 15%.

My question, for the expected cost of equity for that project (which fund is obtained from loan), do we use 10% or 15%?

Respondent 4 to Karnen:

Hello Sukarnen,

This is a big issue in project finance.  In particular there is something called an Equity Bridge Loan where equity holders borrow their investment and pay it back later.  My opinion about all of the divisions in equity is that first, the overall equity IRR should be evaluated.  In addition you can compute the distribution of equity and investors that have put less risk in the development should accept a lower IRR.


Unlike corporate finance, you can find real data on the cost of capital from transactions where projects are bought and sold and there is a good estimate of the returns investors are willing to accept.



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