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.
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.
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)
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 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 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.
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.
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.