A Short Note on Key Drivers behind Price-Earnings (PE) Ratio at Terminal Period

Hi Readers,

PE ratio (or earnings-multiple) is very common being used in the valuation (including in the start-up valuation) regardless many finance scholars will suggest the use of Discounted Cash Flow (DCF) approach, but as you probably already know, that building a full set of projected Financial Statements is easier said than done. Additionally, discounting projected cash flows is about:

discounting EXPECTED CASH FLOWS with EXPECTED [OPPORTUNITY] COST OF CAPITAL

I bet you know as well that EXPECTED is not the same with REALIZED Cash Flows.

For example, if you put the card no. 1, 2, 3, 4 and 5 into a box, and doing thousands of drawings from that box, the EXPECTED card will be :

the Mean = (1+2+3+4+5)/5 = 15/5 = 3

But your reality will be either 1, 2, 3, 4, or 5, so 3 is just of them.

Ok, back to PE ratio.

The hard time for getting the Price of a stock at the end of Terminal period, let’s put it _t (t= terminal).

We could use (i) Direct Comparison or (ii) Direct Capitalization approach.

I guess, the most important is to understand the key drivers or factors that will impact the PE ratio, which I am trying to hand-write it as depicted below.

The conclusion, the P/E at terminal period is other things being equal, the investors should logically pay more for a stock with

  • a higher potential growth (g); and
  • lower required rate of return (r), and
  • lower plowback ratio (b).

The latter is a bit conflicting with getting higher growth rate in Dividends_t+1, which requires the company to plow back more of its earnings to business (as long as the return on new investment is higher than cost of capital, of course!).

From under stable growth scenario of Dividends-Discount Model (DDM), then :

Po = Div_t+1/( r – g)

Po = Today’s stock price

Div_t+1 = next year’s dividends

r = required rate of return

g = growth rate in dividends

From where this “g” comes from?

The source of dividends distribution logically comes from earnings of the business, so the next year’s dividends comes from next year’s earnings x Dividends payout rate.

Div_t+1 = Earnings_t+1  * Dividends payout ratio

Div_t+1 = Earnings_t+1 * (1- b)

b = plowback or retention or reinvestment rate of earnings

So,

Earnings_t+1 = Earnings_t (this year) + Earnings_t * b * return on new investment

then we divide the above equation with Earnings_t, then we will get:

Earnings_t+1 = Earnings_t (this year) + Earnings_t * b * return on new investment

———————————————————————————— / Earnings_t

= Earnings_t+1/Earnings_t = 1 + (1 * b * return on new investment)

= 1+g  = 1 + b * return on new investment

Then

g = b * return on new investment

so to increase the “g”, the company needs to increase the b, that is the plowback ratio.

Is it conflicting? Increase plowback or decrease plowback?

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

Start-up Valuation : Pre-Money and Post-Money Valuation

Readers,

I am quickly jotting down a note on Pre-Money and Post-Money Valuation.

It is defined that

  • The premoney valuation is the value of the existing venture and its business plan without the proceeds from the contemplated new equity issue.
  • The post-money valuation is the pre-money valuation plus the proceeds from the contemplated new equity issue.
One thing that I am trying to understand as to why the Post-Money Valuation is just as simple as adding the new investment Dollar onto the Pre-Money Valuation.

There are two points I would like to note down:

(i) As Pre-Money valuation is the valuation of the assets-in-place, then by injecting the new investment, the business might use that new injection to scale up its existing business even more, higher than the initial projected cash flows. The venture could invest that new injection to buy more stock, hire more qualified engineers and resources, etc. Then where will all this higher positive cash flows be reflected into the Post-Money Valuation?

(ii) if all those higher positive cash flows generated by investment funded by the new injection (assuming the money from the new Venture Capital (VC) flowing into the company or business and not to the existing founders), is not factored into the Post-Money valuation, then there is an assumption that the NPV from the perspective of the Venture Capital from investment in that new venture is ZERO.

NPV (Buy security) = PV (All cash flows paid by the security) – Price (Security) = ZERO.

This assumption that NPV of buying security in the new venture is ZERO might make sense, since if the NPV of buying a security were positive, then this would present an arbitrage opportunity, since positive NPV will mean that the VC is to receive a cash today (at the time of the injection being made to the new venture). Since this arbitrage opportunities theoretically do not exist in the normal markets, then the NPV of buying a security in the new venture is ZERO, meaning the trading securities should not create or destroy the value  (note : financing or financial transactions should be neutral in this case, and its presence is just to adjust the timing and risk of the cash flows to best suit the needs of the firm or investors). The real value should come from the real investment being engaged by the company (Modigliani-Miller proposition, which is pretty much about the conservation of value, or separating investment and funding activities).

If the (ii) sounds OK, then my next question, if the NPV of buying security is ZERO, then why the VC wants to inject the money to the new venture in the first place?

My initial argument is, VC could see that somehow though NPV of buying a security is ZERO, yet, the business might have upside potential in the future that could produce more income (or cash) than initially forecasted. Meaning with VC required rate of return (in the book’s example, using 50%  compound annual rate of return), the actual return could turn out to be much higher rate of return (as a footnote, VC requires really high rate of return as the potential for realizing that expected return from all its portfolio might be only 10% success rate, and the rest is a fall-out).

Prof. PDM to Karnen:

It is just definitional.  Pre-money includes the value generated by the new investments as well, but which goes to the existing investors.

Karnen to Prof. PDM:

I agree with you, the money flowing to the Venture should somehow play a role in having the venture to execute positive NPV projects, otherwise, the VC will not be willing to invest.

Respondent 1 to Karnen:

Note: the respondent’s response is in italics.

Responding to this :  the  definition of:

  • The premoney valuation is the value of the existing venture and its business plan without the proceeds from the contemplated new equity issue.
  • The post-money valuation is the pre-money valuation plus the proceeds from the contemplated new equity issue.

One thing that I am trying to understand as to why the Post-Money Valuation is just as simple as adding the new investment Dollar onto the Pre-Money Valuation.

The main reason that we can usually just add the proceeds to the Pre-Money to get the Post-Money is due to the assumption made regarding the return to new investors. As the deal is “priced” using a required return, providing that return is NPV=0.  Therefore, the equity issue neither adds nor subtracts anything in terms of NPV (dollar value above required return), but adds the proceeds to the total post-offering PV.

There are two points I would like to raise up:

(i) As Pre-Money valuation is the valuation of the assets-in-place, then by injecting the new investment, the business might use that new injection to scale up its existing business even more, higher than the initial projected cash flows. The venture could invest that new injection to buy more stock, hire more qualified engineers and resources, etc. Then where all this higher positive cash flows be reflected into the Post-Money Valuation?

The Pre-Money value is the value of the existing assets/operations in place and the value of all options to expand. New investors are paid required returns (not NPV), leaving any return above the required (any NPV) to the existing Pre-Money owners.  This Pre-Money value of the PV of existing operations and any NPV from intended expansion-option projects (after raising the money and paying a required return (NPV-0 to new investors) includes the NPV of the type of projects you suggest.  Put differently, the “N” part belongs to existing owners; the “PV” part belongs to the investors providing the new capital as their investment is priced at the required rate of return for NPV=0 on their injection.

(ii) if all those higher positive cash flows generated by investment funded by the new injection (assuming the money from the new VC flowing into the company or business and not to the existing founders), is not factored into the Post-Money valuation, then there is an assumption that the NPV from the perspective of the Venture Capital from investment in that new venture is ZERO.

(This is the assumption since we’re using a required return for competing investors considering this type of investment and risk.)

NPV (Buy security) = PV (All cash flows paid by the security) – Price (Security) = ZERO.

This assumption that NPV of buying security in the new venture is ZERO might make sense, since if the NPV of buying a security were positive, then this would present an arbitrage opportunity, since positive NPV will mean that the VC is to receive a cash today (at the time of the injection being made to the new venture). Since this arbitrage opportunities theoretically do not exist in the normal markets, then the NPV of buying a security in the new venture is ZERO, meaning the trading securities should not create or destroy the value  (note : financing or financial transactions should be neutral in this case, and its presence is just to adjust the timing and risk of the cash flows to best suit the needs of the firm or investors). The real value should come from the real investment being engaged by the company (MM proposition, which is pretty much about the conservation of value, or separating investment and funding activities).

If the (ii) sounds OK, then my next question, if the NPV of buying security is ZERO, then why the VC wants to inject the money to the new venture in the first place?

(To make the required return they have calibrated and a competitive market agrees is the “going rate” for that type of investment and risk. The key here is that when we use a discount rate like 50%, we have assumed that such a rate is competitively available to the venture to move money across time. Otherwise the discounting to get value doesn’t make sense. All monies (from existing and new investors) moves across time at that same rate (assuming they have the same claim and risk). This is embedded in the notion that we are allowed to make the time-value adjustments using a single discount rate at each point in time.)

My initial argument is, VC could see that somehow though NPV of buying a security is ZERO, yet, the business might have upside potential in the future that could produce more income (or cash) than initially forecasted. Meaning with VC required rate of return (in the book’s example, using 50%  compound annual rate of return), the actual return could turn out to be much higher rate of return (as a footnote, VC requires really high rate of return as the potential for realizing that expected return from all its portfolio might be only 10% success rate, and the rest is a fall-out).

(It appears that you have worked through the rationale. I think your concern is more fundamental than our textbook application, however.  That is, the concern is not just about discounting in the venture investing context. The same concern would apply to the use of a required discount rate for project financing in a mature company. When we use a required discount rate to impose the new investors’ claims on the cash flow stream (taking the rate to be the competitively offered rate that is appropriate for the investment and risk), we have assumed that all NPV from the funded project goes to existing investors.  This is the same as saying the present value of the new money is equal to the discounted value of future cash flows at the required return. If we have to give some NPV to the new investors, then the “required” return is higher than the return we’re asserting is the “required” return.  Again, this is a fundamental assumption involved in discounting using “required” returns – there is a competitive fringe of investors that can only successfully demand the market-determined required rate of return. You don’t have to pay them above that amount. You cannot get their money for less. This means that the NPV goes to existing owners of the right to take the new capital and create something beyond the required return on that new capital. Existing investors get the NPV in such a context. Perhaps it would help to think of the expansion rights as something like a patent that can only be used by its owners.)

Karnen to Respondent 1:

From reading your comments, it sounds to me that the first investor and second investor will be compensated with MAX the required rate of return. If this is the case, then the investor’s money in nature is similar to DEBT, which means they will only get what is PROMISED to them from investing their money into the venture. Then all NPV, or any ACTUAL return from the venture above the required rate of return, then this will go to the founder(s). If this is correct, then the first and second round will only have downside risk, but can’t enjoy the upside potential of the venture.

The reference to the Exit Value at Period_t-1 (fifth year in the case being shown). This “Exit value” could mean anything, I gather, not necessarily, the venture will really free-flow the money to the investors and founders.

Yes, the exit value is just an imposed horizon value that could be from a conjectured IPO, acquisition or private equity buyout of one’s investment.  For example, if one considers the IPO the event for that horizon, it is not (in the U.S.) typically a liquidity event given that insiders typically are locked up for 6 more months. Nonetheless, we can think of the IPO price as some type of valuation to “mark to market” the locked-up investors’ investments. Their eventual realized proceeds could be more or less than the IPO price.

In many books I read about the Silicon Valley success stories, the Exit here will mean the successful IPO, for example, eBay, Netscape, Google, Facebook, Twitter, etc. So in the case of IPO, since there is no money free-flowing to the investors (both first round and second round) from the venture, but the 1st and 2nd investors if they want, they could sell their shares to the public as well (or offer their shares to other private investors), then the ACTUAL rate of return to the 1st and 2nd round investor, will not be limited to the required rate of return they put in the first place. If this is correct, then this is not in line with what I understand from the one I explained above which 1st and 2nd round investor return profile will be similar to DEBT, in other words, their return will be MAX to the required rate of return..

When we use a discount rate on expected cash flows to get a value today that is paid by an investor that investor owns a security with those expected cash flows. When actual cash flows are realized, then the rules of the security (the security’s position in the waterfall) determines the actual/realized cash flows which can be more or less than those that were “expected” when the security was purchased. It is true that some securities will have levels where additional cash flows “knock in” or “knock out.” That is, the security’s legal structure can allow for acceleration or deceleration of participation in cash flows at various levels.  Whether the participation level starts, stops, accelerates or decelerates is part of the negotiation when the security is created/purchased. Traditional debt knocks out its participation in cash flow above the level of its principal and accrued interest. Traditional equity knocks in when debt claims have been serviced. Hybrid securities can have both debt-like and equity-like claims. If those are to have max and min characteristics (usually referred to as “participation” in VC investments) they should be specified in the legal documents defining the securities at the time of purchase. 

The valuation approaches treat the securities as they would produce flows in “upside scenarios,”  i.e., as if converted to equity.  If one wanted to base the valuation on a larger (broader than the three we consider) scenarios where detailed treatment of “downside scenarios” and liquidation preferencing, etc. is taken into account, then one would need to have a mathematical description of the waterfall specification and then proceed to consider more scenarios and their likelihoods.  Our observation of much of the early-stage venture financing is that such detailed inclusion is seldom considered to be a significant component of the price to which venture investors agree.  More often, the value appears to be based on some “upside scenario” and the associated realized returns in those scenarios (X% per year or 3X, 5X or 10X on investment, etc.). Perhaps this is a concession to the large amount of complete write-offs for failed ventures (where even the debt-like preferencing doesn’t provide much in the way of cash flow). Of course, 50-100% is clearly not an “expected” return. It is a “utopian” return targeted for successful investments so that overall portfolio returns will be reasonable (given that many of the investments are 100% losses).

Debt Cost of Capital : Which to Use?

Readers,

Another question that is frequently being asked is about Debt Cost of Capital.

Though in practice, analysts and finance books and papers spend more time in discussing the EQUITY cost of capital, yet most of the corporation issues more DEBT than EQUITY.

Looking into the size of the world’s capital markets, both in total or for each country, the size of the debt markets in 2011 was much higher compared to equity market.

IMF 2011 the size of the World’s Capital Markets

source:
https://www.imf.org/external/pubs/ft/gfsr/2012/02/sa/satable1.pdf (accessed on 20 June 2020)

If we look the Capital Markets size in year 2018, Bonds Market capitalization still surpassed the capitalization value in the Equity Market, as displayed below.

Source:
https://www.sifma.org/wp-content/uploads/2019/09/2019-Capital-Markets-Fact-Book-SIFMA.pdf (accessed on 20 June 2020)

When it comes to determine Debt Cost of Capital, using the survey shows the following findings (see the answer to Point No. 5, which gave us that in estimating the before-tax cost of debt:

(i) the surveyed corporations 26% uses U.S. Treasury Yield + Spread, 21% marginal YTM outstanding debt and 21% weighted average outstanding issues

(ii) the surveyed financial advisors: 55% current yield to maturity and 45% new debt yield to maturity

(iii) the surveyed textbook or trade books : 83% yield to maturity and 17% marginal cost of new debt


Source: “Best Practices” in Estimating the Cost of Capital: An Update by W. Todd Brotherson, Kenneth M. Eades, Robert S. Harris, and Robert C. Higgins (2011). Accessed from
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2686738 on 20 June 2020).

While in 2011 Survey conducted by the AFP Association for Financial Professionals, in its report : 2011 AFP Current Trends in Estimating and Applying the Cost of Capital Report of Survey Results, reported that

(i) Thirty-seven percent of organizations simply use the current rate on the debt that they have outstanding, while a third forecast the rate for new debt issuance.
(ii) Twenty-two percent use the average rate on outstanding debt over a defined period of time, and

(iii) seven percent consider the historical rate on outstanding debt.

(iv) A plurality of smaller organizations use the current rate on outstanding debt while the most widely cited method for large organizations and publicly traded organizations is the forecasted rate for newly issued debt.

AFP 2011 report were accessed from
http://business.baylor.edu/don_cunningham/How_Firms_Estimate_Cost_of_Capital_(2011).pdf on 20 June 2020.

We could see from the above that there were no consistency among corporations and finance advisors, with what is suggested to be used by many finance textbooks.

There are two points I would like to discuss related to cost of debt:

(i) Knowing the difference between PROMISED RETURN vs EXPECTED RETURN with regards to the interest rates on corporate debt or bonds

(ii) Using DEBT YIELD TO MATURITY as the Debt Cost of Capital and the mistake that we could fall into.

Let’s start this fun journey!

A. PROMISED RETURN vs EXPECTED RETURN OF CORPORATE DEBT RETURN

I gather, we are all clear that in doing the corporate valuation, we need to DISCOUNT:

(i) PROMISED [forecasted] CASH FLOWS with the PROMISED rate of return; or

(ii) EXPECTED [forecasted] CASH FLOWS with the EXPECTED rate of return.

However, when we are talking about Net Present Value, this will be about discounting the EXPECTED CASH FLOWS with the EXPECTED rate of return.

Now we have PROMISED vs EXPECTED rate of return, and what makes them different?

I am tying to sketch quickly the components of the corporate bonds interest as displayed below:

Expected rate of return is distinguished from promised rate of return for corporate bond, since unlike that of government bonds, for corporate bonds, there is a probability (read: risk) that the promised principal and coupon will not be repaid or serviced.

So, return on default-free [government] bonds + RISK premium = this will be EXPECTED RETURN. Adding the [expected] default risk premium onto EXPECTED RETURN, then it is PROMISED RETURN.

When I put here PROMISED, it means that the company put its promise to the lender that it will pay FIXED future payments. However, bear in mind that though the company promised to pay the lender FIXED future payments, yet it doesn’t mean that there is a guarantee a FIXED RATE OF RETURN over horizons shorter than the bonds’ maturities, and the longer the bonds will mature, generally speaking, it will be riskier investments compared to shorter maturities. This will be applicable even for the government-issued bonds.

Remember : FIXED INCOME is not the same with FIXED RATE OF RETURN!

Something that I would like you to bring home that, except for 100% default free bonds, the PROMISED rate of return will be HIGHER than the EXPECTED rate of return. If you’ve ever found the Rate of Return published in the financial information, then that is QUOTED rate of return and QUOTED rate of return = PROMISED rate of return.

I need to go back a bit. Above I am saying that the EXPECTED rate of return will consist of :

(i) Default risk-free rate of return

(ii) PLUS RISK PREMIUM. This risk premium could include, among others, the liquidity premium, maturity risk premium, and tax premium, foreign exchange rate risk premium and other risk to compensate the lender for his/her willingness to take on risk, which risk is systematic and non-diversifiable.

Tax premium is present since the interest from the government bonds might be taxed at rate lower than that of corporate bonds.

Liquidity risk premium is present coming from the fact that there may not be always a ready buyer for the corporate bonds. Generally speaking, there will be always buyers for government-issued bonds or treasury bills or notes.

Maturity risk premium is added since there is a chance that the default risk-free rate will change over time. The longer the maturity will come, the higher the maturity risk premium will be added on. However, this maturity risk premium will be applicable not only for corporate bonds, but also for government bonds. Since government bonds/bills/notes have zero default risk premium and zero liquidity premium then, we could say, that the difference of rate of return of shorter government bills and longer government bonds or notes, should come largely from the maturity risk premium, which will factor into it, the risk of future inflation.

So to recap the components of the required rate of return being asked by the investors for any debt instrument or bond will include the following elements as depicted below.

In calculating the cost of debt, Prof. Aswath Damodaran put that :

In general terms, it is determined by the following variables:

  • The riskless rate. As the riskless rate increases, the cost of debt for firms will also increase.
  • The default risk (and associated default spread) of the company. As the default risk of a firm increases, the cost of borrowing money will also increase.
  • The tax advantage associated with debt. Since interest is tax deductible, the after-tax cost of debt is a function of the tax rate. The tax benefit that accrues from paying interest makes the after-tax cost of debt lower than the pretax cost. Furthermore, this benefit increases as the tax rate increases.

Source: Aswath Damodaran. Investment Valuation : Tools and Techniques for Determining the Value of any Asset. Third Edition. 2012. John Wiley & Sons, Inc., Hoboken, New Jersey. Page 211.

So we see that at least in the general terms, in determining the cost of debt, there are two elements, (i) the risk-less rate and (ii) the default risk. Any investment instrument that is to be considered purely risk-free will require two basic conditions to be satisfied:

  • no default risk. This element will make the debt instrument issued by private sector not considered, since it might have some measures of default risk, even for those debt instruments falling under AAA (or Aaa) rating.
  • no reinvestment risk. This has a painful implication to the valuation since essentially, we need to use the different risk-free rates for each period, and different expected returns in determining the cost of debt. For example,
    • the risk-free rate for a one-year time horizon has to be the expected return on a default-free government one-year zero coupon bond,
    • the risk-free rate for a two-year time horizon is the expected return on a default-free government two-year zero coupon bond, and so on.

To be said that a debt is RISK-FREE, then the the actual returns on debt (or any investment) should be equal to its expected returns. And as far as it relates to debt, again this is only possible if there is no default risk and no reinvestment risk.

In similar vein of discussion, then there are two sources of risk:

  • interest rate risk, which is about the general changes in the long-term rates (this is somehow also about the expected inflation and expected LONG-TERM real growth rate)
  • credit or default risk

Here, then we have long-term vs short-term debt. In general,

  • When interest rates go up, bond prices fall (and vice-versa), with longer-maturity bonds will be more sensitive to long-term rate changes. This is because longer-term bonds have a greater duration than near-term bonds that are closer to maturity and have less coupon payments remaining, which means that longer-term bonds are also exposed to a greater probability that interest rates will change (up or down) over its remaining duration.
  • The above fact lies in the very nature of the fixed-income (periodic fixed coupon payment) nature of bonds, meaning when the investor purchases a bonds, then the investor will be stuck to that PROMISED fixed coupon payment. Whatever happens to the market interest rate, the investor can’t not ask the issuer to change its coupon payment.

So first, there is an Inverse relationship between bonds yield (or market interest rate) and bonds price.

Second, we need to differentiate short-term and long-term debt. Longer-term is more exposed to the changes in the interest rate, and this relationship between price and interest will be INVERSE. This inverse relationship will exist even if the debt is default-risk free.

Third, long-term debt then tends to have a beta higher than 0, or positive beta, though the figure might be small, 0.2. However, with short-term default-free debt, then the beta tends to have a near-zero beta, as its value will not be altered by changes in the expected long-term interest rate. This will bring us that when we refer to risk-free debt (no reinvestment risk and no default rate risk), this should necessarily be short-term. This is why we found the finance textbooks or any finance websites suggested that risk-free rate of return can be estimated by using the interest rate on a short-term government-issued debt instrument, such as one-year US Treasury bill.

From the above, we could then need to be able to distinguish now the RISK-FREE DEBT from DEFAULT-RISK DEBT. RISK-FREE DEBT will include the DEFAULT-FREE DEBT, but DEFAULT-FREE DEBT is NOT necessarily RISK-FREE DEBT.

Then how to reconcile the whole discussion above?

  • First, I need to bring you to EXPECTED and PROMISED rate of return again. EXPECTED Rate of Return will include the risk-free rate (this will again necessarily mean SHORT-TERM) plus all kinds of RISK PREMIUM mentioned above, including the Maturity risk premium, with longer-term debt. We could use the government zero-coupon bonds with matching duration, to take out the reinvestment rate risk, which will give us the risk-free debt with longer period.
  • ADDING ON the EXPECTED rate with the DEFAULT RISK premium, then we will have PROMISED rate of return.

Before we move to next discussion, there are one point worthy noting that we don’t need to use the year-to-year specific risk-free rates, as a practical compromise, the present value effect of using year-specific risk-free rates tends to be small for most well-behaved term structures. Well-behaved term structures would include a upward-sloping yield curve, where long-term rates are at most 2 to 3 percent higher than short-term rates (as said by Prof. Damodaran, page 155 of the same source textbook above.)

First we will see how the bank or lender viewed this

Second, the components of the expected rate of return, time premium etc (continued)

Discussion

Cost of debt should always refer to the current and expected market rate, meaning that historical rate is supposed to not be used. Some I noted, the analysts will use the expected incremental borrowing rate and YTM (with or without default be factored into).


When we value existing business or value new business (or expansion of the existing business), using market rate of debt will be more relevant as the discount rate instead of going back to calculate the Interest paid_t/D_t-1.

Respondent 1 to Discussion:

Strictly the cost of debt is what the market says. That’s ok.

However, if you look around, MOST (MOST is most!) firms don’t have traded debt. Not even all the firms in the stock market have public debt (say publicly traded bonds).

In our real life, in everyday life, what we find is non-traded debt and its cost is just KdD_t-1 where Kd is the contractual or stipulated value of Kd.

Let’s see some statistics:

In the US you have this number of traded firms, according to Damodaran website.

Total Market7053
Total Market (without financials)5878

These firms are traded, agree? According to 2015 Statistics of U.S. Businesses, of the 5.9M firms in the U.S., 3,643,737 have fewer than 5 employees. Their total employment is 5,877,075. Let’s say, 6 millions and 94 industries. From these industries, Damodaran shows industries with 94 to 611 firms. Adding ALL emerging markets together he adds to

Total Market22402
Total Market (without financials)20162

These numbers of firms include firms from China and India. Just imagine the hodgepodge of data we have. Well, you could say, don’t use Damodaran’s data. OK.

Where do we have a slightly better idea of what beta for a given firm should be? Where do we get a better estimate of Kd the firm pays and TS that the firm gets for those items? Perhaps we should develop an idea about a subjective estimate of Ke done by the owner. (Remember that the great idea of CAPM is to be able to estimate the Ke for an unknown inaccessible owner).

From these industries, Damodaran shows industries with 9 to 907 firms.

From Damodaran tables you can “obtain” the betas (levered and unlevered) for each industry.

Now you can tell yourself how good are our estimates of betas and hence our Ku and Ke. 

Going back to Kd, who has a better estimate of Kd for most firms in our countries? In the same US for the enormous number of firms that don’t trade? What I am trying to call your attention is that recognizing that Kd SHOULD be the market Kd rate and not the contractual cost of debt is irrelevant. YES! In the VERY FEW cases we deal with large firms and not all of them issue public bonds.

In short, if we become very picky, we will conclude we can’t make a reasonable estimate of cost of capital for firms and owners!

Karnen’s comments to Respondent 1:

I guess, differentiating whether the debt is publicly traded or not, is not a crucial point to me. Debt is debt….meaning that it will be foolish for lenders to extend their money to the company without really looking into the market (or at least what the market is expecting).

Kd and Ke (or Ku) is different stuff, and Kd should be relatively much easier (I don’t say it is easy) to calculate.

I always remember that that it is necessary to “asking the people that give you the money, how much return they want it back”. Again this philosophy could go to Kd. Debt is different from Ke, since we don’t need to estimate it, we just have to look at the going market rate for debt, or asking the lenders (or banker, bonds trader, etc.). Even if the debt is not publicly traded, however, plenty of information is up there in the market. Big banks usually post their prime lending rate. or we have LIBOR (which many banks are still anchoring their ask rate started from LIBOR), etc. The interesting part of Kd, the historical cost of debt is not relevant anymore. So in my personal opinion, estimating Kd is not like taking something from the thin air.

Other point about Kd is most of it is about PROMISED rate of return (though if the default rate is high, we need to factor it to get the EXPECTED rate of return, the one that we will use into the Cost of Capital). Since it is a PROMISED coupon rate, then we could see into the market, how much big COUPON RATE that have been published in the market.

Prof. Damodaran in many of his valuation textbooks suggested to calculate Kd by using Risk-free rate + default spread to come up with the [promised] cost of debt (see page 211 of 3rd Edition of Investment Valuation, which uses synthetic rating). I don’t say that I totally agree with Prof. Damodaran’s approach, yet, it means we could use the information from the market for the Kd.

For Ke (or Ku), using data from market is a lot problematic, we could either go straight to estimate the expected returns (i) directly from the historical average return (with its all troubling big standard error of expected return) or (ii) infer beta from historical data, and use CAPM. But this is a whole different discussion.

I go even further, stating that even that the debt is whether publicly or not publicly traded is irrelevant at all.

Just to put the debt on the public exchange or not, this will not change the nature of the expected return on debt. Other than transparency (institutional issue) and liquidity that the exchange could provide in order to match the consumption-savings profile of the investors, then expected returns on a debt should likely reflect the company-specific DEFAULT risk of the debt issuer. This should not come as a surprise in view of its very nature of the debt instrument, promising the FIXED rate of return (=coupon rate being fixed during the term of the debt) to the lenders.

Accordingly, we see that the debt beta is mostly approaching to zero, meaning that its expected return could be said uncorrelated with the market volatility. In other words, the famous mean-variance rationale cannot be applied to debt instruments that have limited upside gain and much greater downside potential coming from the company-specific events.

Karnen:

Now we moved to why it is important to know the difference between PROMISED Yield-to-Maturity (YTM) and EXPECTED YTM.

Quoted BONDS YTM is a promised YTM, since the repayment of bonds principal and the service of bonds interest are as promised by the bonds issuer to the bondsholder.

If the default rate is relatively small, then we could use the quoted YTM as the reasonable proxy for the expected Cost of Debt.

Let’s check using Moody’s data.

Source: Moody’s Investors Service. Annual Default Study: Corporate Default and Recovery Rates, 1920 – 2017. Data Report 15 February 2018

Note: IG = Investment Grade; SG = Speculative Grade

From the above Exhibit, we could see that there is a huge gap for the default rate between those bonds in the Investment Grade vs Speculative Grade.

For Investment-grade bonds, with 20 years of data, the default rate maxed at 5.33%. However, for those Speculative-grade bonds, the second year has reached 8.51% default rate and peaked at 40.75% at 20th year.

With such high default rate for speculative grade bonds, then quoted YTM which calculation is based on PROMISED cash flows, then if we use that quoted YTM as the expected cost of debt, then we have overstated the expected YTM.

So for the speculative-grade bonds, we need use the following formula:

Kd is the Expected YTM.

Alternatively,

Expected YTM = Kd = (1 – pb) [Interest + Principal] + pb ( [Interest + Principal] – Expected Loss), or
= promised Yield to Maturity – Prob(default) * Expected Loss Rate

Pb here is the probability of default.

Prof. Sheridan Titman and Prof. John D. Martin gave a good illustration using Moody’s data on default and recovery rate about how to come up with promised YTM and expected YTM, as illustrated in their well-written Valuation book.

Source : Valuation, The Art and Science of Corporate Investment Decisions. Third Edition. Page 149. Pearson Education, Inc.

Upon factoring the default and recovery rate, we could see that there is a meaningful gap between promised YTM vs expected YTM, in this example, 17.76% vs 11.87%, or 589 basis point difference.

So, using promised YTM instead of expected YTM, we have over-estimate the cost of debt, resulting in overstated cost of capital. However, this is not necessarily bringing the valuation being overstated or understated, since it will depend whether this overstated cost of debt (and cost of capital) be offset partially by the overstated/over-optimistic scenario being built into the expected future cash flows, the ones that are being discounted. It means that it is common to see that the analysts inadvertently introduce too-hope-for (technically speaking, forecasting errors) into the estimates of the cash flows.

Personally, my suggestion, is reality check is critical in the cost of debt and valuation, and in this case, the selection of peers becomes parallel-wise important to do.

Financial Model + RISK

Readers,

It is said that “the search for value” is what drives a huge amount of efforts over a long period of time in the financial markets and among finance scholars.

However, this is not wholly correct or half the story. The other half story and more imposing is “the search for [understanding] the risk”.

A bit historical background on this:

  • Markowitz Modern Portfolio Theory is about giving equal weight to RISK as well as return (1952).
  • Sharpe CAPM shows us that the expected return on risky assets is a function of its RISK (1964).
  • 2M’s (Modigliani-Miller) 2 propositions (1958) said that the value of a company is a function of its business’s RISK and changing the capital structure or its financing side just will change how that risk is parceled up among the debt and share-holders.
  • Fama’s Efficient Market Hypothesis explains the market that gave the mantle to CAPM, that is there is no free lunch as far as it relates to RISK (1970)
  • Black-Scholes-Merton (1976)’s option pricing is coming from the needs to hedge the RISK.

So it all those 5 monumental points in finance history..all is about the RISK.

So, when we are building the financial models, the model should center on the risk. The models built are not about just looking at the resulting parameters, such as ROI, IRR, NPV, Equity Value, EPS, etc. but the risk measurement should be there and shown. A good financial model is providing us the insight into the risk.

Some models has managed to incorporate some modeling methods to deal with the uncertainty in the modelling, such as factoring the probability, sensitivity analysis, scenario analysis, simulation, break-event point analysis, stress-testing, VAR, Monte Carlo analysis, etc.

However, the risk should be understood not just as the NUMBER as there is no simple mechanical way to depict this. Logic and theory should be the foundation to grasp the RISK.

The complication with RISK is the inter [cross]-interaction among so many factors and elements of responses from the decisions being made in the financial markets, including factors that are coming from non-financial markets, such as politics, consumers behaviour and demand, technology, production and supply chain, innovation — in other words – EVERYTHING that HUMAN could make the decisions [betting and responding to] over it.

(continued)