“The estimation of credit spreads”

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“The estimation of credit spreads”

University of Groningen

Faculty of Economics and Business Administration

Master Thesis R.T. Slijkoort

(S1601253)

PricewaterhouseCoopers Advisory N.V.

Valuation & Strategy

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Executive summary

This master thesis aims at establishing an approach to calculate the cost of debt for valuation purposes. Besides this, a goal is to determine sovereign spreads for less developed markets by a rather easy to apply method. If we use the term debt we refer only to bonds with fixed coupon payments. Other types of debt are not subject of our research.

The first thing we have to determine is where the company under consideration is located. Is this within the Euro zone, United States or some where else? We started our research with the determination of the risk-free rate. We have reviewed the Svensson model (1994) in order to model term structures. Our conclusion is, however, that the best method to determine the risk-free rate for the Euro zone is to use the yield curve that is modelled by the European Central Bank (“ECB”). This yield curve differs only slightly from the yield curves that we have calculated ourselves for individual benchmark countries (e.g. Germany, Netherlands). The Svensson model can be used to determine the risk-free rate of another country by using its issued government bonds. The sovereign spread that is required by investors based on political, economic and other factors can be derived from the observable government bond prices. Our research has used Euro denominated government bond data of Mexico, Brazil, Croatia and Turkey to determine sovereign spread for these countries.

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The more sand that has escaped from the hourglass of

our life, the clearer we should see through it.

Jean Paul

-Preface

This thesis marks the ending of my MSc BA Finance at the University of Groningen. I was eager to start in practice and have therefore chosen to write my thesis for PricewaterhouseCoopers Advisory N.V. at the Valuation & Strategy department. I have worked here for six months. I wrote my thesis and have worked on several projects to get a feeling of the valuation practice. It was here when I concluded that my career should lie in a different area. The reason for this is that at the end of the day I do not pursue a career in business valuation. However, the acquired knowledge is useful of course for a different job. Within PricewaterhouseCoopers, different people supported me during my study and internship. First of all, I would like to thank my supervisor, drs. M.E. Helmantel, for his help and ideas. Secondly, I also want to thank my colleagues at the Valuation & Strategy department for their help based on their experience and for the nice time I had there. Finally, I would like to thank my girlfriend and my parents and others that I have not mentioned for supporting me during my study and in life in general.

Contents of this thesis shall not be used by any other person than the author without permission in writing from PricewaterhouseCoopers N.V.

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Table of contents

Executive summary………..……2

Preface……….3

Chapter 1 Introduction………...5

Chapter 2 Theoretical background………...7

2.1 Introduction………7

2.2 Interest rates ………..………. ……9

2.3 The influence of default risk...……….. ……15

2.4 Determinants of credit spreads….………. ……23

Chapter 3 Research - Calculating the cost of debt step by step……….25

3.1 Introduction………25

3.2 Methodology of risk-free rates and sovereign spreads……..………26

3.3 Credit spreads for corporate bonds……….. ……….. 30

3.4 Promised and expected yield……..………..35

Chapter 4 Conclusion………..37

References………..…...39

Appendix A Black & Scholes formula………..42

Appendix B Overview rating classes………. … 43

Appendix C Assessment of credit-worthiness of different ratings………...44

Appendix D Factors influencing the credit rating………...45

Appendix E Government bonds data………. …….46

Appendix F Corporate industrial bonds data……….……….. ….48

Appendix G Transition matrices, default probabilities & recovery rates……….. ….52

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1. Introduction

Large firms that are selling their services all over the world need to be an expert in the service they sell. PricewaterhouseCoopers (“PwC”) is one of those large corporations. They are situated in almost 150 countries and are one of the leading companies in corporate valuation. This means that they need to have excellent knowledge about the (financial) markets in those countries. The cost of capital, local risks, country restrictions, etc. are all issues that have to be taken into account.

In corporate valuation the cost of capital is one of the most important factors. If the cost of capital is wrong, the total firm value calculated is off. But how do we determine the cost of capital exactly? There has been a lot of research conducted in this area. However, the emphasis lies on the estimation of the cost of equity and the cost of debt is often left disregarded. A model used to calculate the cost of debt contains adding a risk premium (a measure of systematic risk (beta) to the risk-free rate). Another way to estimate the cost of debt is by calculating the expected yield on a company bond.

An important component in the total cost of debt is the risk-free rate. Historically, the risk-free rate used is often the yield on for example a ten-year government bond. However, recent research (Hull et al. (2004)) has shown that the rate on a five-year interest rate swap might be a better proxy for the risk-free rate. Taking counterparty risk in account, the results show that the five-year risk-free rate lies on average about ten basis points below the five-year swap rate. The results are in line with the prior research conducted by Blanco et al. (2003). Part of this thesis is dedicated to the methodology of the determination of the risk-free rate.

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This means that investors require a higher risk premium (or default spread) because there is more exposure to risk. However, a disadvantage of this method is that the credit ratings are not updated periodically. This results in some cases in outdated ratings and therefore, in biased default probabilities. Subsequently, this can lead to a cost of debt that is too high, because the default spread is too high or vice versa. This is important for the accuracy of the cost of debt over time.

Subtracting the risk-free rate from the yield to maturity on a bond results in the credit spread for that particular bond. To estimate the cost of debt of a company, the credit spread is a crucial factor together with the risk-free rate. There are multiple ways of estimating the credit spread. This will be the main issue in this thesis.

Many theoretical models appoint the spread to the differences in creditworthiness between companies. Others, such as Delianedis and Geske (1999) describe in their paper that the credit spread consists of the default spread and the residual spread. They calculate the residual spread by subtracting the median default spread from the median credit spread. They argue that that the credit spread is determined more or less by the following factors: default risk, liquidity risk, tax factors, jumps and systematic risk.

We try to find an answer to the question what the most accurate method is to calculate the credit spread and furthermore, the cost of debt in general. Therefore, this thesis is a contribution to the existing literature of calculating the cost of capital and more specifically, the cost of debt. The results from our research can be used to fabricate a homogenous approach to determine the cost of debt for the calculation of the weighted average cost of capital of a firm. The research starts with the determination of the risk-free rate and the description of the other components of the cost of debt. The final part of the thesis presents the most important results and gives a general conclusion.

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2. Theoretical Background

2.1 Introduction

Research conducted in the area of the cost of capital widely exists. In this thesis the emphasis lies on the calculation of the cost of debt. The goal in valuation is to estimate the market value of net cash flows. Choosing a discount rate and the distribution of the future cash flows are tasks for asset pricing theory, i.e., models of market equilibrium that explain how uncertain future payoffs are transformed into current market values. The discount factor (or weighted cost of capital) can be split up in two major components:

- Cost of equity.

- Cost of debt (after-tax).

A model used to estimate the cost of equity is by using systematic risk (bèta). A risk premium is added to the risk-free rate in order to come up with a cost of capital (CAPM, one or two factor model). A similar model can be used to estimate the cost of debt. However, because the distribution of debt is not normal, this method is not accurate enough when it is used to calculate the cost of debt. The different types of debt that can be recognised are depicted in figure one.

Short term Long term

Source: PwC presentation on cost of capital.

Figure 1. Types of debt.

Overdraft Loan

Commercial paper Financial lease Fixed coupon

Variable coupon Collateralised Callable Convertible

BANK DEBT BOND MARKET

MONEY MARKET

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The estimation of return on bonds is the main focus of this thesis. However, only bonds that are so-called “plain-vanilla” are subject to our research. The plain-vanilla bonds consist only of bonds with a fixed coupon. The estimation of the cost of debt for the other types of bonds is more difficult and beyond the extent of this thesis. However, this report can be used as a basis for further research in this area.

Ogier et al (2004) describe the key characteristics of debt (bonds). These are firstly, the types of finance are contractually committed to repayment of the original amount (principal) at a certain future date, together with additional payments in the meantime. Secondly, payments have to be made by coupon in order to meet the contractual obligations to the providers of debt. Thirdly, investors who provide these types of debt have no right to any other payments over and above the contractual committed payments.

Providers of debt finance face significantly different (often less) risk than equity investors. Interest costs are paid out of corporate incomes before taxes. The risks associated with cost of debt are interest rate risk and credit risk. Interest rate risk is the risk that can be attributed to changes in the long-term interest rate. All long-term debt, corporate or sovereign, is subject to interest rate changes.

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2.2 Interest rates

This section deals with the methodology of establishing interest rates and modelling term structures. The basis for the interest rate is the risk-free rate. This rate (also known as the default-free rate) is the return investors can obtain with certainty by investing their money in a risk-free asset. The risk-free rate can be calculated in several ways. The first method is to use the yield on n-year government bonds of a particular country (e.g. Netherlands, Germany).

The second method as described in Hull et al (2004) shows that on average the implied risk-free rate lies at 90.4% of the distance from the treasury rate to the swap rate. This implies that the swap rate is a better proxy for the estimation of the risk-free rate. An important factor in the interest rate swap is the counterparty risk. This risk can be defined as the risk that the “insurance party” can not meet its obligations in the case of a credit event. Taking counterparty risk in account, the results show that the five-year risk-free rate lies on average about ten basis points below the five-five-year swap rate. The results are in line with the prior research conducted by Houweling and Vorst (2003) and Blanco et al. (2003).

The third method that some practitioners apply is the use of the London Inter Bank Offered Rate (“LIBOR”) as a proxy for the risk-free rate when valuing derivatives. The problem, however, with the approach of using LIBOR ratings is that direct observations are only possible upon two months of maturity. A way to extend the LIBOR zero curve to two or even five years is to use Eurodollar futures. Traders then use swap rates to extend the LIBOR curve even further. The resulting zero-curve is sometimes referred to as the LIBOR zero curve or the swap zero curve.

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As described in Copeland et al (2005) equilibrium models use assumptions about economic variables in order to specify a process for estimating the short-term interest rates. This results in a mechanical construction of the term structure that does not automatically fit the market data on the term structure of interest rates at a certain point in time. Arbitrage-free models use market data of observable bonds to construct the term structure. By using market data it is ensured that future values of the interest rate are consistent with the term structure of today. The arbitrage-free models are especially useful for determining the price of zero-coupon bonds at a certain point in the future by using today’s observable bond prices.

The models described to model term structures are an extended version of the Nelson-Siegel approach (van Landschoot (2004)) and the Svensson model (1994). The estimation of term structures is a very interesting approach. Jarrow et al (1997) developed a Markov Model for the term structure of credit spreads. The model is based earlier research of Jarrow and Turnbull (1995). The article presents a model for valuing risky debt. The firm’s credit rating is explicitly incorporated in the model and furthermore, the article presents an arbitrage-free model for the term structure of credit risk spreads and the development over time. The model can be used for the valuation of different kinds of debt. (e.g. (foreign) government bonds subject to default risk, credit derivatives and over the counter derivatives with counterparty risk). The credit event is given as an exogenous process. The model can be used to measure the current level of credit exposure and the distribution of credit exposure over the life of the contract.

By using the Svensson model, the risk-free rate of a country and the cost of debt of a corporation can be determined. The model Svensson has developed is a parametric model for estimating and interpreting spot rates. Derivations of the model lead to estimations of instantaneous forward rates. The basis for modelling the term structure based on spot rates is expressed in formula one.

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The European Central Bank (“ECB”) has used this model to construct the term structure. The model uses three beta’s and two tau’s to correspond with the characteristics of the yield curve. The method for estimating the forward rates can be found in formula two.

(2) An example of a term structure based on spot rates composed by the ECB is presented in figure two. The term structure is constructed with observable market data from AAA Government bonds.

Euro area yield curve

2,0% 2,5% 3,0% 3,5% 4,0% 4,5% 5,0% 0 5 10 15 20 25 30 years to maturity in te re s t ra te

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The process described here is suitable for constructing the term structure and deriving the risk-free rate for developed countries. We can imagine that the sovereign rate for Mexico will be higher than the risk-free rate of the Netherlands. The additional risk is a compensation for the country specific risks, such as political and economic risks. The additional premium on top of the risk-free rate is called the sovereign spread. We can use several different methods to determine the risk-free rate of a less developed country.

A often used method is to calculate the yield on government bonds of a specific country. If we compare this to the yields of government bonds of developed countries we can determine a country specific spread or sovereign spread. The process of calculating a term structure for the risk-free rate can also be applied to corporate bonds in order to determine the credit spread for a specific company and/or rating. These issues are described in next section.

In general there are two ways to cope with country risk. The first one adjusts the cash flows and the second one adjusts the discount rate. It is difficult to adjust cash flows for country risk because the probability is very low, but on the other hand, the impact is enormous if a credit event occurs. Besides this, financial analysts are no country experts. Therefore, we will focus on the second method and describe how it can be calculated. The second issue that is relevant is how to determine the level of a company’s exposure (defined by Damodaran (2003) as λ) to country risk and incorporate this in the spread. However, this is beyond the scope of this thesis and can serve as the basis for further research.

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The CRP is added to the risk-free rate of the home country or a developed country. However, there are other methods to determine the risk-free rate of a less developed country. The first model to determine the risk-free interest rate for a specific emerging economy country is by using expected inflation. This is expressed in formula three.

Rfcountry X= Rf€+ (Einf(country X) - Einf(€)) (3)

Where:

Rfcountry X : The risk-free rate for less developed country X Rf€ : The risk-free rate for developed home country Einf(country X) : Expected inflation in less developed country X Einf(€) : Expected inflation in developed home country

Besides using expected inflation we can also use a model that incorporates forward and spot rates of the currency of the country under consideration. This is presented in formula four.

Rfcountry X= Rf€+ ((Fri– Sri)/Sri) (4)

Where Rfcountry X : The risk-free rate for less developed country X Rf€ : The risk-free rate for developed home country Fri : Forward rate of currency x at time i

Sri : Spot rate of currency x at time i

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model: The purchasing power parity (“PPP”) and the interest rate parity. The PPP is used to express the long-term exchange rate equilibrium between two exchange rates in order to equalize their purchasing power. It is an expression of the law of one price. The interest rate parity is the relation between interest rates and exchange rates.

It holds when the ratio of forward and spot rates is equal to the ratio of foreign and domestic nominal interest rates. Interest rate parity is an arbitrage condition which states that the returns from borrowing in one currency, exchanging that currency for another currency and investing it in interest-bearing instruments of the second currency. At the same time purchasing futures contracts in order to convert the currency back at the end of the investment period. This should yield a return equal to the returns from purchasing and holding similar interest-bearing instruments in the first currency. If the returns are different, arbitrage exists and an investor could make risk-free returns. Two versions of the interest rate parity are commonly presented in academic literature - covered interest rate parity and uncovered interest rate parity.

Covered interest parity assumes that the yield of debt in foreign and local currency with comparable risk is traded in an international market without constraints and should be equal when the currency market is used to determine the domestic currency payoff from a foreign bond. This results in an arbitrage-free situation1_.

This paragraph has dealt with the theoretical background of interest rates, term structures and sovereign spreads. This serves as the basis for the next paragraph, where we will describe the influence of default risk in the process of determining the credit spreads and the cost of debt.

1_{Copeland, T.E., Weston, J.F. & Shastri, K. 2005, Financial Theory and Corporate Policy, 4}th_edn,

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2.3 The influence of default risk

As described in paragraph 2.3 we can determine the term structure for interest rates of companies and countries. Subsequently, we can determine a country risk premium for less developed countries. However, we have to bear in mind whether the different yields in the term structure are promised or expected. The promised yield on a bond is also known as the yield to maturity or effective rate of return. It is called promised because investors are only able to earn that rate of return when they hold the bond until maturity. The yield to maturity can be calculated by using formula five.

(5) Where: P: The current bond price.

N: Number of periods C: The cash flow at time t R: The rate of return F: The value at maturity

In fact, the formula is the same as the formula used to calculate the internal rate of return. It is the interest rate that makes the present value of the bond’s cash flows equal to the current price. If the coupon of the bond equals the yield to maturity the bond is sold at par. If the coupon is larger than the current yield and the yield to maturity the bond is sold at a premium and vis-à-vis at a discount.

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Standard methods that are used to calculate the cost of debt assume that the cost of debt equals the promised yield measured by the yield to maturity. However, this yield does not take default in consideration. The expected yield should equal promised yield net of any expected default loss. The expected return on risky debt must lie between the promised yield and the risk-free rate. The difference between the promised yield and the expected yield is expressed formula six.

Promised yield spread = Expected default loss + Expected return premium (6)

However, the expected default loss should not be part of the cost of debt. The reason for this is that the expected default loss is not part of the expected return. Therefore, the expected yield can be calculated as the promised yield and adjust it for expected default loss.

Expected yield = Promised yield – Yield equivalent of expected default loss (7)

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The Markov model is an extension of the model of Jarrow and Turnbull (1997) and treats the bankruptcy process as a finite state Markov process in the credit rating of the firm. This new model has the following characteristics2_:

- A distinction can be made between the different seniority levels of debt of a firm and by way of using different recovery rates it can be incorporated in the model. - The model can be combined with each term-structure model for risk-free debt. - It uses historical transition probabilities for rating classes, i.e. the probability of

shifting to a different rating class over time, to determine the risk-neutral probabilities.

- The model can also be used to price options on risky debt or credit derivatives. The model takes in account: the probability of default, the transition from one rating class to another and the recovery rate. A one-period model is expressed in formula eight.

One-year bond expected return = (E)year-end cash flow / initial bond price,P)-1 (8)

This expected year-end cash flow can be calculated by applying formula nine.

Expected year-end cash flow = π * (1+Q) * F + (1- π ) * λ * F (9)

Where: π: Probability that the bond will not default at the end of year Q: Annual coupon rate

F: Face value of the bond λ: Recovery rate

Excel can be applied in order to model a multiperiod framework. Multiperiod transitions matrices are needed here to determine the default probability in for example a five year time period.

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The average cumulative recovery rates for each rating class are also calculated by rating agencies, such as Moody’s. The recovery rates are averaged over a 24-year period and are used as input for the Markov model. Recovery rates are measured as a ratio of price relative to par value. Although different types of recovery rates exist, Moody’s has chosen to use the issuer weighted mean recovery rates. An overview of the different types of recovery rates is presented in the table below.

Statistic Definition

Issuer-Weighted Mean Recovery Rate

Value-Weighted Mean Recovery Rate

Issuer-Weighted Median Recovery Rate

Issue-Weighted Mean Recovery Rate

Varma, P. (2003) "Recovery Rates on Defaulted Bonds and Preferred Stocks", Moody's Global Credit Research, December

Issue-weighted recovery rates are estimated using recovery rates for each issue and taking the average of all issues. While this measure is widely reported, it is useful only for predicting the average recovery rate on a portfolio of default bonds diversified across issues but without reference to issuer or issue size.

Issuer-weighted mean recovery rates are derived by estimating mean recovery rates for each issuer, then averaging them across issuers. They are useful for predicting recovery rates for portfolios that are well diversified across issuers.

Value-weighted recovery rates represent the average of recovery rates on all defaulted issuers, weighted by the face value of those issues. These estimates are useful for predicting recovery rates on the market portfolio. Issuer-weighted median recovery rates are estimated as median of issuerweighted recovery rates and are used for predicting the most likely recovery rate for a randomly selected issuer.

Table 1 Types of recovery rates used by Moody’s.

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The yield spread can be measured by collecting bond data with the same maturity, liquidity and tax characteristics and compare it to the yield spread on e.g. AAA bonds. This spread is used because it represents non-default components of credit spreads and the default component is very small.

Alternatively, the part of the credit spread that represents expected default loss can be calculated by using the Merton model and applying formula ten.

EDL = –(1/T)ln[e(π-s)T_N(–d

1– πE√T /σE)/ PD+ N (d2+ πE√T /σE)] (10)

This formula is derived from the original Black and Scholes formula3_{. The complete} formula can be found in appendix A. It is logical that the expected default will rise in case of a lower credit rating. This is expressed in the probability of default, which is substantially higher for lower credit ratings.

Cooper and Davydenko (2003) have proposed a simple method of deriving the expected loss from the yield spread of a corporate bond. They describe that the spread on a risky bond consists of three parts: The expected loss caused by default, the risk premium associated with default and a part that has no relation to default. Structural models, like the Merton model, make predictions about the first two components. The non-default spread (they proxy this by a matched AAA-bond spread) is subtracted from the total spread. They use AAA rated bond spreads because research has shown that the spread on these bonds is very small (Elton et al. (2001)) and exists almost entirely out of non-default components. If the bond rating declines, the default spread increases. However, the non-default factors stay the same. Subsequently, they calibrate the Merton model to estimate the expected loss.

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The input of formula eleven consists of, amongst others, the default probability and recovery rate for the bond. These parameters depend on the credit rating of the bond, company or country. These credit ratings are determined by established rating agencies such as Moody’s, Fitch and Standard and Poor’s. Besides credit ratings, several other ratings are constructed. The focus in this report will be on credit ratings. Credit ratings reflect a company’s theoretical ability to meet its financial obligations. The credit ratings are in general determined for a company or country instead of for individual bond series. Therefore, it is rare that different bonds of a company have different ratings. Moody’s has established a rating structure in which rating Aaa represents bonds with no chance of defaulting in the short term. The next best rating is Aa, after that comes A, Baa, Ba, B and Caa. S&P ratings start with AAA, followed by AA, A, BBB, BB, B, CCC respectively.

In order to construct finer rating categories Moody’s divides the Aa category in Aa1, Aa2, Aa3. It divides A into A1, A2, A3 and so on. S&P divides it AA category into AA+, AA and AA-, its A category into A+, A, A- and so on. Moody’s Aaa and S&P AAA are not subdivided. Ratings below Baa3 and BBB- are referred to as “below investment grade”. The rating D (i.e. considered the lowest rating) represents an entity in default or near default. A complete overview of the ratings structures and an assessment of the creditworthiness per rating used by different rating agencies can be found in appendix B and C. But how are the ratings determined and what are the main theoretical advantages and disadvantages of using a rating system? These questions will be dealt with in this section.

Rating agencies use models in which they assess qualitative and quantitative risk factors. The rating agency provides an opinion on the relative ability of an entity (e.g. company or country) to meet financial commitments. These commitments consist of the repayment of the principal, interest, preferred dividends, insurance claims or country obligations.4 _{Often rating agencies divide the companies in subcategories.} They will assess the company’s qualities against many risk factors. Furthermore, they assess the most important factors for the company’s future financial position. Finally, the outcomes of the model are presented to the rating committee of the agency and they determine the final rating.

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Besides this, they calculate (cumulative) default probabilities for different ratings and different subcategories (e.g. corporate bonds, sovereign, financial, bank, insurance and municipal). So the activities are twofold. They determine a credit rating for an individual entity and more in general, they determine default probabilities for each rating for different industries and their complementary bond spreads.

Koller et al. (2005) describe in their book that the rating process is primarily related to two financial indicators. That is, size (in terms of sales or market capitalization) and interest coverage (in terms of EBITA or EBITDA divided by interest expenses). Size is only relevant in extreme situations. Most companies with an AAA rating have a market capitalization higher than $50 billion. An explanation for this can be that large corporations can diversify a lot of risk away. However, only size has no influence on the credit health of a company and another factor that determines credit health is interest coverage. Formula eleven can be used to calculated interest coverage. Interest coverage is defined as a measure of how many times a company can pay its interest obligations out of its EBIT(D)A.

Coverage = EBITA/Interest or EBITDA/Interest

or

Net Debt/EBITDA (11) In the case of convertible debt it can be useful to calculate interest coverage using the last formula. Because the company needs to roll over its convertible debt into normal debt with a higher rate, their interest coverage (by using the first formula) will decrease significantly.

All the criteria rating agencies use in their models are presented in appendix D. Taking into account that this is a non-exhaustive list the factors are subdivided into country & business risk and financial risk. Some of the factors, such as country risk and industry characteristics are harder for the company to influence compared to other factors, such as competitive position and management.

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The advantages of using rating scales in the process of determining the debt margin are that it is relatively easy to apply and the ratings are readily available. However, the most important flaw in using this method is that the ratings and complementary default probabilities are based on historical data and may have little predictive power. The corporate credit ratings are not frequently updated. Therefore, these data might not be an appropriate measure for estimating a credit spread. It is likely that the current credit crunch in the United States has influenced the default probabilities in the entire world. This is not yet expressed in the ratings at this moment. Only large corporations are reviewed periodically and important changes in the default risk of the entity may lead to a rating change. Another disadvantage of credit ratings is that the rating is to some extent rather subjective. Rating agencies assign a rating to a company that reflects their view of the company’s credit risk. Although in most cases the credit ratings of different agencies are the same, in some situations they differ from each other.

Besides this, ratings can be seen as a signalling device. Hand et al (1992) find in their research abnormal returns after a rating change and Wansley et al. (1992) confirm only the abnormal return following a rating upgrade (but not the downgrade). In other words, a rating downgrade signals the market that the probability of a credit event has increased. As a result investors try to dispose their investments. On the other hand, Hite and Warga (1997) find that the strongest bond price reaction is associated with downgrades to and within the non-investment grade class. Their findings are confirmed by Dynkin et al. (2002) who report significant underperformance during the period leading up to a rating downgrade with the largest underperformance being observed before downgrades to below investment grade.

Looking at ratings from a firm perspective we can conclude that ratings largely determine the company’s access to the capital market. If a company is rated below-investment grade (Moody’s Ba1 until C), its debt funding possibilities are substantially smaller than whereas the company was rated investment grade.

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2.4 Determinants of the credit spread

After determining the risk-free rate we can determine the risk premium. This credit spread is the crucial factor in the estimation of the cost of debt. Based on prior research of Delianedis and Geske (1999), Elton et al. (2001) and Chen et al. (2005) the determinants of the credit spread are (some of the factors are firm specific and others are macro-economic): - Default risk - Liquidity risk - Tax factors - Jumps - Systematic risk - Uncertainty of parameters

The difference between the default spread and the credit spread is called the residual spread. Delianedis and Geske (1999) calculate the residual spread by subtracting the median default spread from the median credit spread for a particular rating. Furthermore, they conclude that credit risk and credit spreads are not primarily explained by default, leverage, firm specific risk, and recovery risk, but are mainly attributable to taxes, jumps, liquidity, and market risk factors.

Elton et al. (2001) describe in their paper that the credit spread can be decomposed into three parts.

- The part which is due to expected loss - The part which is due to taxes

- The part which is due to systematic risk

They describe that the largest part of the credit spread can be explained by systematic risk and it is affected by the same influences that affect systematic risk in the stock market.

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Single name credit default swaps are the most liquid of the derivatives that are currently traded for credit risk protection. A single-name CDS is a contract that provides the buyer (company or country) protection in case of a credit event (bankruptcy). There might be an arbitrage opportunity in the bond market when the n-year credit default swap spread does not equal the yield on an n-year par yield bond issued by a company minus the yield on a par default free bond. If the relationship does not hold an arbitrageur can profit from buying a risk-free bond, go short on a corporate bond and sell a credit default swap or vice versa.

The seller of a CDS agrees to provide protection against the risk of a credit event in return for a periodic payment (also known as the insurance premium) until the credit event occurs or until the maturity of the contract. In case of a credit event the buyer receives the difference between the face value of the bonds or loan and the market value after default. The rate of payments made per year is known as the CDS spread.

Credit default swaps are traded on different markets, the so-called CDS-indices. An example is the Dow Jones CDX North America Investment Grade Index. The index is composed of 125 investment grade securities and distributed among six sub-indices. The sub-indices are High Volatility, Consumer, Energy, Financial, Industrial, and Technology, Media & Telecommunications. The composition of the CDX indices is determined by a consortium of thirteen member banks. CDS with a maturity of five years are the most liquid, and are from a liquidity point of view optimal to determine the default spread. The recovery rate is on average set to 40%. This is in line with the average rate from practitioner’s use.

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3. Calculating the cost of debt step by step

3.1 Introduction

In this chapter we will describe the process of calculating the cost of debt by examining the steps in the process. We consider the process described in this chapter the best and most efficient way to assess the credit spread and the cost of debt for a specific company and or country. We have to split up the process into different steps. These steps are considered the following.

- Model the term structure of applicable government bonds - Determine the appropriate risk-free rate

- Calculate the sovereign spread

- Assign a credit rating to the company under consideration

- Model the term structure of bonds with the comparable credit rating - Determine the promised yield and expected yield

- Determine the credit spread

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3.2 Methodology of risk-free rates and sovereign spreads

This paragraph presents the methodology and research results from the process of determining the risk-free rate and the sovereign spread calculated directly from observable bond data. The European Central Bank constructs a term structure daily based on AAA-rated euro area central government bond data. Three yield curves are presented on the website. The yield curve based on:

- Spot rate

- Instantaneous forward rate - Par yield

The forward curve shows the short-term (instantaneous) interest rate for future periods implied in the yield curve. The par yield reflects hypothetical yields, namely the interest rates the bonds should yield to be priced at par. The instantaneous forward rate is the rate that can be used for a very short period in the future starting at time t. The models used to model the term structure of the ECB are the Svensson-model and the continuous compounding method used in the paper of Anderson et al (1996). The data are updated every target business day at noon ECB time. The spot yield curves and their corresponding maturities are calculated using two different datasets reflecting different credit default risks. The first sample contains “AAA-rated” euro central government bonds and the second dataset contains (AAA-rated and other) euro area central government bonds. Eventually, this results in the spot rate yield curve. This model can be used to determine the risk-free rate on a certain date. The method is quite time-consuming and therefore, not efficient to use in practice.

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When the company under consideration is located in the Euro zone it is far more efficient to use the term structure constructed by the ECB in comparison to the collecting data and using the Svensson model ourselves. The term structure AAA-rated euro central government bonds is publicly available and updated every business day at noon and can be found on the website of the European Central Bank (http://www.ecb.int/stats/money/yc/html/index.en.html). For every date in history and different maturities we can determine the appropriate risk-free rate.

But what to do when the company under consideration is not located in the Euro zone? We have to determine the risk-free rate for that particular country. If the country has a less developed financial market and a less stable political regime a country risk premium must be added on top of the risk-free rate of developed country’s. Therefore, the sovereign spread is the spread that is attributed to specific country risks. We can imagine that the risk-free rate for Brazil will be higher than the risk-free rate of the Netherlands. The additional risk is a compensation for the country specific risks, such as political and economic risks. PwC uses two methods to determine country risk – the direct method and the indirect method. The direct method can be used if appropriate bond data are available. The next step is to estimate a yield curve for a government bond denoted in for example Euros. Subsequently, for each maturity the spread can be determined when the yield on a government bond denoted in Euro’s (e.g. sovereign euro benchmark bond) is subtracted.

The indirect method can be used if appropriate bond data are not available. We can use the country’s risk rating from e.g. Moody’s, S&P and Fitch to regress observed spreads against these agency ratings. We can average the risk premiums from the models and use this as a sovereign spread. This method is especially helpful for countries with no sovereign bonds.

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However, the term structure can be modelled at any certain date. The data needed as input is:

- Coupon date - Settlement date

- Coupon in % (annual or semi-annual) - Quoted price

The coupon payments are a promised yield. The expected yield will be lower. The different bonds are used to determine the risk-free rate for different maturities. The output of the model results in the zero curve for a certain country or credit rating. The model of Svensson makes use of four beta’s and two tau’s. Excel is used to solve the function and it is calibrated to minimize the difference between the cash price and the present value of future cash flows.

For the determination of the “risk-free rate” and sovereign spread based on the yield on government bonds we have collected data of Euro denominated government bonds of six countries - Germany, Netherlands, Mexico, Brazil, Croatia and Turkey. The term structures of these countries are presented in figure three. A complete overview of the government bond data can be found in appendix E. The sovereign spread is described further in the upcoming sections.

2,0% 2,5% 3,0% 3,5% 4,0% 4,5% 5,0% 5,5% 6,0% 6,5% 7,0% 7,5% 8,0% 0 2 4 6 8 10 12

time to maturity in years

in te re st ra te Mexico Croatia Turkey Netherlands Germany Brazil

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The reason for the steep incline in the short term maturities can be attributed to the fact that for the short term the Svensson model sometimes is inappropriate to use. However, for longer maturities the model can be used and is accurate in estimating and modelling the term structure. In order to determine the risk-free rate and sovereign spreads we have used the direct method and applied the Svensson model to determine the zero curves for Euro denominated government bonds of the before mentioned six countries. The model is applied to each country separately. All data was found in Bloomberg. The solver function is used to determine the zero rates for the different maturities. If we compare the zero rate of Germany with Brazil or Turkey we can determine a country risk premium. It is important here to compare bonds that are denominated in the same currency. The results for a ten year maturity calculated by this direct method are shown in table two.

Sovereign spreads over risk-free in basis points Time to

maturity

Germany

(Benchmark) in % Netherlands Croatia Mexico Brazil Turkey

10 years 4.58 10 100 121 132 294

Table 2. Sovereign spreads per July 1st_{2008 in Euro.}

The risk-free rate as calculated with the formulas above is used to determine the cost of debt for a particular firm and furthermore, the WACC. On top of the risk-free rate a compensation for additional risk is added, called the credit spread. The determinants of this credit spread are described in paragraph 2.4.

To conclude, the website of the European Central Bank (ECB) provides a good proxy for the estimation of the risk-free rate in the Euro zone. The values found on the website of the ECB show similar results and deviate only several basis points from the yield on the government bonds of Germany and the Netherlands.

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3.3 Credit spreads for corporate bonds

There are several ways to calculate credit spreads. Similar to the construction of yield curves of government bonds we can use the two different methods – the direct and the indirect method. Again, we have applied the direct method. The Svensson model is used. The input of the model consists of Euro denominated corporate bonds of industrial corporations with the same rating but with different maturities. The data is collected from Bloomberg and consists of bonds with fixed coupons and with the same accrued interest method. Only bonds with the following ratings (Moody’s and S&P) are collected and used:

- A+ - A - A-- BBB+ - BBB -

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2,5% 3,0% 3,5% 4,0% 4,5% 5,0% 5,5% 6,0% 6,5% 7,0% 7,5% 8,0% 0 2 4 6 8 10 12 14 16 18 20

time to maturity in years

in te re s t ra te AA AA-A BBB+ BBB BBB-BB

Figure 4. Zero curve for Euro denominated industrial corporate bonds on July 1st2008.

Credit spread in basis points for industrial companies Time to maturity

Germany (Benchmark) in

% AA AA- A BBB+ BBB BBB- BB

9 years 4.55 70 75 102 174 187 249 315

Table 3. Credit spreads per 7-1-2008 in Euro’s

Important here is to determine whether the yield on the bond is promised or expected. This process is described in the next paragraph.

A second method to determine the cost of debt is to split the cost into different items: - Risk-free rate

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The first step in this process is to calculate the default probability. This can be done in two ways. First method (default spread based on historical data): Start with the country rating or bond rating (derived from e.g. Bloomberg, www.fitchratings.com or www.moodys.com) and estimate the default spread for that rating (based upon traded country bonds) over a default free government bond rate (i.e. the risk-free rate) with similar coupon and maturity. This results in the measure of the added default risk premium for that country or company.

The credit ratings for government and corporate bonds have been produced by rating agencies such as Moody’s and Standard & Poor’s (S&P) and Fitch. This is described in section 2.2. After determining the credit rating for an entity and its complementary default probability, the spread can be determined.

Ogier et al. (2004) describe in their book the method that the redemption yield (or yield to maturity) of actively traded bonds of an entity can be observed and this gives a direct measure of the pre-tax cost of debt. In some cases when there is no rating available, a financial ratio can be used to determine it. As described before, interest coverage is an important ratio.

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Subsequently, the credit spread can be observed for comparable companies with the same rating. Taking into account of course that the maturity of the comparable bonds matches the bonds of the company under consideration.

The second method5_{(default spread estimated from bond prices):} The approximate calculation is presented in formula twelve.

h = s / (1-r) (12)

Where: h = default intensity per year

s = spread of the corporate bond yield over the risk-free rate r = expected recovery rate

However, if a more accurate calculation is preferred, the time to maturity and the coupon rate are needed. Subtract the price of the corporate bond from the government bond and the result is the expected loss (EL) for that particular corporate bond with time t to maturity. The expected loss can also be calculated by multiplying the probability of default by the loss given default. The probability of default for each year is set to Q. After this, the total present value of expected loss can be calculated over the time to maturity.

Setting the total expected loss equal to (EL) yields the default probability in %. If you want to estimate a risk premium for bonds, you would need to estimate the expected return based upon expected cash flows. This would result in a much lower default spread and debt risk premium, because the expected yield will always be lower than the promised yield. How to adjust the cash flows for default is described in paragraph 3.4.

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As a practitioner, PwC treated none of the credit spread as systematic risk. This means that the beta of debt (βd) equals zero. This also implies that PwC assumes that all of the firm’s risk is carried by the stockholders. However, it is hard to believe that the return on debt has no risk and has no correlation with the firm’s return on assets. Therefore, this method yields biased calculations of the beta when un-levering and re-levering the beta. The purpose of un-re-levering and re-re-levering beta’s is to show the relationship between the asset beta (or unlevered beta) and its equity beta.

In calculating credit spreads PwC in the Netherlands currently uses a model developed by Aswath Damodaran. This model is especially helpful when no credit rating is available. Another way to determine a rating is based on the leverage structure and interest coverage.

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3.4 Promised and expected yield

If the term cost of debt comes up, usually it is not our first question to ask whether this is a promised or expected return on debt. However, this is important in calculating the weighted average cost of capital. If the promised yield is used then the cost of debt will probably be too high, because default is not taken into account. The question here is thus, “How can we calculate the promised and the expected yield on a bond?” The methodology has been dealt with in paragraph 2.3. This section presents the practical solution.

The outcomes of the formula can also be described as the internal rate of return (“IRR”) or the yield to maturity on a bond. This can be easily calculated. However, default of the bond issuer is not taken into account. The yield to maturity is a good measure of the promised return on a bond investment since it includes all aspects of the investment. It takes capital gains, the face value, time to maturity, coupon and current price in consideration. The problem with quoted yields in for example news papers is that it is unknown whether the yield is promised or expected. This makes it hard to compare yields. Most of the times the quoted yield is the yield to maturity and has to be adjusted for default in order to derive the expected yield. The promised cash flows of a bond can be calculated from observable data. Further, a simple Excel model can be used to solve for the IRR. The promised yield is not an accurate measure to compare credit spreads and the cost of debt in general. The promised yield serves as the basis for calculating the expected yield.

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Considering the two proposed models, the Markov model and the Merton model, we can calculate the “real” cost of debt. We recommend to use the Markov model, because each input variable is available and easy to collect from Bloomberg or for example the Thompson Database. It is less mechanically as the Merton model (that makes use of the Black and Scholes formula) and therefore more efficient to use in practice. To conclude, if data regarding bond series are collected from newspapers for example, one of the few things we have to do is to determine the rating and use the applicable recovery rates and default probabilities to calculate the expected yield. From there, we can compare it to the risk-free rate and the result is the credit spread for that type of bond or rating.

Based on our research there are several steps to take in calculating the cost of debt. These steps are described in this chapter. In chapter 4 we will describe these steps again to conclude, however, in a simplified manner. We hope that this makes clear how to determine the sovereign spread, credit spread and in general, the cost of debt.

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4. Conclusion

In this section we will conclude our research by describing our approach to calculate the cost of debt. Let us start with the risk-free rate. The Svensson model is used to determine the zero rates for government bonds as described in paragraph 3.2. This model is a useful tool to theoretically reproduce the zero curve of government and corporate bonds. However, the procedure is quite time consuming and the outcomes for the risk-free rate in the euro zone differ only slightly from the rates determined by the ECB. Therefore, we recommend that for determining the risk-free rate for the euro zone the spot rate term structure of the ECB is the best method. It is efficient, quick and easy to apply. If we want to model the term structure ourselves, we can apply the aforementioned model and determine the risk-free rate for a specific country.

In order to determine the sovereign spread, we can apply two methods - the direct and the indirect method. If the government of the foreign country has issued bonds we can determine the yield curve for that country. Subsequently, we can determine the sovereign spread with respect to the yield curve of for example Germany (if the foreign bonds are denominated in Euros). It is important to compare government bonds and corporate bonds that are denominated in the same currency. In the case of absence of appropriate data we need to determine the credit rating of the country by using the credit risk rating from acknowledged rating agencies. Hereafter, regress it against available government data from a country with, if available, the same rating. Finally, subtract the determined rate from the benchmark country and the result is the sovereign spread for that country.

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After the yield curve for a specific rating is constructed, we can calculate the credit spread for any maturity by subtracting the yield with respect to the yield on a government bond. Furthermore, the spread can be split up in a default spread and a residual spread. However, we have to bear in mind that collecting the data, plug it into the model and model the term structure is quite time consuming and it might not be convenient to use in practice for efficiency reasons.

The results of our credit spreads assessments are similar to prior research in the area of calculating credit spreads and in general, the cost of debt. If the credit rating declines, the default probability increases and simultaneously, the credit spread increases. The most important reason for this is the rise in the default spread.

The recommendations for further research are based on our findings. The first recommendation is to develop a model that is able to assess a country’s or company’s credit rating at any point in time. The dependence on rating agencies would disappear therefore. The most important reason for developing a model is that ratings change over time and rating agencies update their ratings periodically. The new model should be able to determine a rating at any point in time (e.g. on the valuation date). The second recommendation is to make adjustments in the used models so that is able to determine the credit spread for debt with variable coupon payments, that is collateralised, that is callable and debt that is convertible into equity. This thesis provides the basis for calculating the credit spread only for bonds that have a fixed coupon. The third recommendation is related to the sovereign spread. The level of exposure of a company to country risk can be different, depending on for example market share or international activities. Therefore, the level of exposure to country risk should be used to adjust the sovereign spread for a specific company or government.

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Appendix A Black and Scholes model (1973)

The first part, SN(d1), derives the proportional benefit from acquiring a stock outright. This is found by multiplying stock price [S] by the change in the call premium with respect to a change in the underlying stock price [N(d1)]. The second part of the model, Ke(-rt)N(d2), gives the present value of the expected payment of the exercise price on the expiration day. The fair market value of the call option is then calculated by taking the difference between these two parts6.

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Appendix C Assessment of credit-worthiness of entities with different

ratings

AAA The highest debt rating assigned. The borrowers’ capacity to repay debt is extremely strong

AA Capacity to repay is strong and differs from the highest quality only by a small amount

Investment

grade A Has strong capacity to repay; borrower is susceptible to adverse effects of changes in circumstances and economic conditions

BBB Has adequate capacity to repay, but adverse economic conditions or circumstances are more likely to lead to risk

BB, B Regarded as predominantly speculative, BB being the Sub-investment CCC, CC least speculative and CC the most

grade

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Appendix D Factors influencing the credit rating.

7

Country risk: Macroeconomic Volatility, Legal Issues, Corruption Issues, Government regulations.

Industry characteristics: Industry Prospects for Growth, Cyclicality, Capital Requirements. Competitive position: Price, Quality, Distribution Capabilities, Product Differentiation,

Diversification, Vertical Integration, Size/Market Share/Growth, Geography.

Management: Credit History, Consistency and Credibility, Strategy, Organisation Structure, Number of Changes.

Financial characteristic: Accounting Quality, e.g. depreciation methods, consolidation basis, and off-balance sheet liabilities.

Financial policy: Management discipline to achieve financial goals, Consistent with the needs of the business.

Profitability & coverage: EBIT / Capital Employed, Operating Income / Sales, Earnings on business segment assets, EBIT / Interest.

Capital structure: (Total Debt) / (Total Debt + Equity), Asset Valuation, Off-Balance Sheet Financing, Preferred Stock, Dividend Policy.

Cash flow adequacy: (EBITDA)/ (Interest), (Funds from operations)/ (Total Debt), Debt service coverage, Debt payback period.

Financial flexibility: Insurance coverage, Covenants, legal changes, Access to various capital markets, Ability to sell assets.

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Appendix E Government bond data

Date of this data is July 1st_2008.

Mexico

bond coupon quoted effective

series rate price yield

24-2-2009 8,25% 101,73 5,29% 8-3-2010 7,50% 103,18 5,43% 8-4-2013 7,38% 106,02 5,88% 10-6-2013 5,38% 98,08 5,83% 16-6-2015 4,25% 91,01 5,86% 8-5-2017 11,00% 134,54 5,88% 17-2-2020 5,50% 95,60 6,03% Croatia

24-2-2010 4,63% 98,61 5,51% 14-3-2011 6,75% 102,10 5,87% 23-5-2012 6,88% 102,51 6,23% 10-2-2014 5,50% 98,52 5,90% 15-4-2014 5,00% 96,63 5,70% 14-7-2015 4,25% 91,39 5,84% 29-11-2019 5,38% 96,45 5,89% Germany

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Turkey

21-9-2009 5,50% 99,15 6,22% 18-1-2011 9,50% 105,67 6,96% 6-7-2012 4,75% 91,59 7,24% 10-2-2014 6,50% 96,39 7,29% 1-3-2016 5,00% 85,70 7,52% 16-2-2017 5,50% 87,16 7,57% 2-4-2019 5,88% 87,17 7,66% The Netherlands

31-7-2008 0% 99,68 4,18% 31-10-2008 0% 98,57 4,35% 31-3-2009 0% 96,72 4,50% 15-7-2010 5,50% 101,53 4,69% 15-1-2011 4,00% 98,24 4,74% 15-7-2012 5,00% 100,82 4,77% 15-7-2013 4,25% 98,79 4,75% 15-7-2014 3,75% 94,96 4,73% 15-7-2015 3,25% 91,21 4,75% 15-7-2016 4,00% 95,05 4,76% 15-7-2017 4,50% 98,04 4,77% 15-7-2018 4,00% 93,79 4,79% 15-1-2023 3,75% 87,69 4,96% 15-1-2028 5,50% 106,28 4,99% Brazil

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Appendix F Corporate industrial bond data

Date of this data is July 1st_2008.

AA

13-3-2009 3,25% 98,77 5,05% 30-6-2009 3,50% 99,69 4,88% 11-2-2010 3,75% 97,91 5,12% 15-6-2010 6,00% 101,54 5,14% 6-9-2011 3,88% 96,30 5,16% 26-1-2012 3,25% 94,22 5,06% 31-7-2012 5,38% 100,20 5,32% 16-1-2013 4,13% 96,01 5,13% 28-11-2013 5,13% 99,27 5,28% 8-7-2015 4,25% 94,44 5,22% 23-11-2016 4,25% 91,76 5,50% 22-5-2017 4,63% 95,79 5,23%

AA-bond coupon quoted effective

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A

17-12-2008 3,63% 99,03 5,25% 7-5-2009 5,63% 100,26 5,26% 12-11-2009 6,00% 100,85 5,31% 28-6-2010 3,00% 95,57 5,41% 4-7-2011 5,75% 100,61 5,53% 3-7-2012 5,25% 99,69 5,06% 1-7-2013 5,50% 98,19 5,91% 25-6-2014 4,75% 95,88 5,58% 12-6-2015 5,38% 98,01 5,73% 29-9-2015 3,38% 88,94 5,25% 20-6-2016 4,50% 92,62 5,68% 23-11-2016 4,38% 93,04 5,43% 18-7-2017 5,25% 97,53 5,60% 27-6-2018 4,63% 89,96 5,99% 13-5-2019 5,25% 95,32 5,84% 24-6-2023 5,75% 98,53 5,90% BBB+

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BBB

19-11-2008 4,50% 99,62 5,38% 5-12-2008 6,88% 100,25 6,03% 31-1-2009 6,50% 100,62 5,30% 10-7-2009 5,88% 100,41 5,44% 27-5-2011 5,75% 99,03 6,12% 21-6-2012 4,13% 93,02 6,16% 22-7-2013 5,00% 95,82 5,98% 15-7-2014 5,50% 99,89 5,52% 28-5-2015 4,38% 91,78 5,89% 23-3-2016 4,25% 85,65 6,69% 26-6-2017 5,38% 89,89 6,92% 23-3-2020 4,75% 82,54 6,98% 24-3-2025 4,88% 81,84 6,71%

BBB-bond coupon quoted effective

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BB

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Appendix G Transition matrices, default probabilities and recovery rates

Average One-Year Broad Rating Migration Rates, 1970 -2007

Rating Aaa Aa A Baa Ba B Caa-C Default WR

Aaa 88,647% 7,447% 0,637% 0,000% 0,015% 0,002% 0,000% 0,000% 3,251% Aa 1,075% 87,190% 6,881% 0,254% 0,055% 0,017% 0,000% 0,008% 4,520% A 0,064% 2,724% 87,559% 4,927% 0,493% 0,090% 0,022% 0,020% 4,101% Baa 0,045% 0,193% 4,887% 84,345% 4,309% 0,774% 0,232% 0,169% 5,046% Ba 0,008% 0,055% 0,383% 5,703% 75,649% 7,736% 0,574% 1,097% 8,795% B 0,012% 0,041% 0,157% 0,351% 5,566% 73,440% 5,589% 4,484% 10,361% Caa-C 0,000% 0,028% 0,028% 0,028% 0,168% 9,689% 59,186% 16,597% 13,678%

Average Two-Year Broad Rating Migration Rates, 1970 -2007

Average Three-Year Broad Rating Migration Rates, 1970 -2007

Average Four-Year Broad Rating Migration Rates, 1970 -2007

Average Five-Year Broad Rating Migration Rates, 1970 -2007

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Average Sr. Unsecured Bond Recovery Rates by Year Prior to Default, 1982-2006* Rating 1 2 3 4 5 Aaa 0,0% 0,0% 0,0% 97,0% 74,1% Aa 95,4% 62,1% 30,8% 55,3% 41,6% A 46,4% 54,9% 50,3% 47,7% 48,4% Baa 48,1% 46,4% 47,3% 43,8% 43,9% Ba 42,1% 40,8% 40,6% 44,7% 44,2% B 36,9% 35,9% 37,4% 39,2% 42,3% Caa-C 31,8% 31,2% 34,9% 39,2% 34,7% Investment Grade 48,9% 49,8% 47,9% 46,6% 45,5% Speculative Grade 35,8% 35,6% 37,5% 40,5% 42,3% All Rated 36,9% 37,5% 39,5% 42,0% 43,2% * Issuer-weighted, based on 30-day post-default market prices.

Years prior to default