Corporate Finance Chapter 3: Debt financing Albert Banal-Estanol
Debt issuing as part of a leverage buyout (LBO) What is an LBO? How to decide among these options?
In this chapter we should talk about Public debt (bonds): The contractual content of a bond issue Bond types and characteristics Private debt: Term loans Revolving credit Private placements Valuing corporate (and government) bonds Relationship between yield and price of zero and non-zero coupon bonds Price dynamics, sensitivity to changes in interest rates and the duration Valuation using arbitrage for safe and risky bonds Provisions and covenants Government bonds
The prospectus p of a bond issue Indenture or trust deed: bond agreement between borrower and a trust company Trust company: a company that represents the bondholders and makes sure that the terms of the indenture are enforced Main elements: Principal or face value and coupon rates (interests), and their dates Principal: nominal amount for calculating interest, typically repaid on due date Coupon: for a given coupon rate (0 for zero-coupon or pure discount bonds): cupon rate x principal CPN number of coupons per year Example: $1000 bond with a 10% coupon rate with semi-annual payments, pay coupons: $1000 x 0.10 / 2 = $50 every 6 months Types of bonds: Registered bond - a bond in which the Company's records show ownership and interest and principal are paid directly to each owner Bearer bonds - the bond holder must send in coupons to claim interest and must send a certificate to claim the final payment of principal
Types of corporate debt Secured debt Specific assets are pledged as collateral that bondholders have a direct claim to in the event of bankruptcy Example1: mortgage bonds (property as collateral) Example 2: Asset-backed bonds (any kind of asset) Unsecured debt: In the event of bankruptcy, bondholders have a claim to only the assets that are not already pledged as collateral on other debt Examples: Notes (maturities<10 years) and debentures (longer) Tranches: Different classes of securities that comprise a single bond issue All classes of securities are paid from the same cash flow source Seniority A bondholder s priority it in claiming i assets not already securing other debt Most debenture issues contain clauses restricting the company from issuing new debt with equal or higher priority than existing debt
International bonds Domestic Bonds Issued by local entity and traded in local market, but purchased by foreigners Foreign Bonds Issued by a foreign company in a local market and intended for local investors They are denominated in the local currency. Yankee bond - a bond sold publicly by a foreign company in the US Samurai - a bond sold by a foreign firm in Japan Bulldogs- foreign bonds in the United Kingdom Eurobonds Not denominated in the local currency of the country in which they are issued Global Bonds Bonds that are offered for sale in several different markets simultaneously
Private Debt (not publicly traded) Term Loans: A bank loan that lasts for a specific term Syndicated: funded by a group of banks rather than just one Revolving Line of Credit: credit commitment for specific period (2,3 years) that can be used as needed Private Placements: Bond issue sold to small group of investors rather than the general public Private as compared to public debt: Less costly to issue (lower registration costs) But also less liquid (but might be traded within financial institutions)
Other types of debt: Sovereign Debt Debt issued by national governments The U.S. treasury issues: Treasury bills: pure discount bonds with maturities up to 26 weeks Treasury Notes : semi-annual coupon bonds with maturities of 2 to 10 years Treasure bonds: semi-annual coupon bonds with maturities > 10 years Long Bonds: those with longest outstanding maturities (currently 30 years) TIPS (Treasury-Inflation-Protected Securities): inflation-indexed bond (the outstanding principal is adjusted for inflation)
Vli Valuing Corporate (and Government) )Bonds
Yield to maturity (cost of debt!) Definition: unique implicit discount rate r that makes the bond cash flows have the value at its current price. Example: for a safe bond P (1 C 1 r ) 1 (1 C 2 r ) 2... FV (1 r C ) N N The IRR of investing in the bond, given its current price Example: Safe bond without coupon with $ 100,000000 of principal has a price of $ 96,618.36. The cash flows and the YTM is: 96,618.36 100,000000 (1 YTM ) 1 The YTM that solves the equation is 3.5%
Zero-coupon bonds Special type of bonds: They don t pay coupons and therefore are always sold at a discount (lower price than the principal), and are also called pure discount bond Treasury Bills: U.S. government bonds with maturities of less than one year The YTM of a zero-coupon bond maturing in n years, can be written as: YTM n FV P 1 n 1 Since a safe bond without coupon maturing in n years gives an interest without risk in that period, YTM must be equal to the risk-free interest rate What if not?
Coupon bonds These bonds: Pay, in addition to the principal, coupons Treasury notes: U.S. government bonds with maturities of one to ten years Treasury bonds: U.S. government bonds with maturities of over ten years YTM of a bond with CPN annual coupons maturing in n years, is y s.t. P 1 1 FV CPN 1 N y (1 y) (1 y ) Similarly, if we know YTM, we can calculate P (We specify P or YTM) The advantage of using YTMi is that titd does not tdepend don the principal i l(to solve this prices are often given in percentage of the principal) N
What is the YTM of the following bond? At treasury bond of $ 1,000 due in 5 years paying a nominal coupon of 10.5% The market price is 1078.80 Cash flows : C0 C1 C2 C3 C4 C5-1078.80 105 105 105 105 1105 IRR of these CF = 8.5%
Relationship between price and YTM Questions: Why bonds traded at a discount have CPN < YTM? Can zero-coupon bonds trade at a premium? Coupon rate often chosen so that trading initially at par, but The price changes later because time to maturity changes And interest rates affect the YTM and the price
Dynamics If the rest does not change, as time passes... The YTM will not change The price (discount or premium) approaches the par Example: Zero coupon bond with a YTM of 5% and FV 100. Value: 100 P( 30 years to maturity) $23.14 30 (1 0.05) 5 years after, the value is 100 P( 25 years to maturity) $29.53 25 (1 0.05) 05) Notice that buying for $ 23.14 and selling to 29.53 after five years, IRR is: 29.53 23.14 1/5 1 5%
Bond prices for a constant YTM Why the changes of non-zero coupon bonds are not smooth?
What happens if the YTM changes? If interest rates change in the economy... Rates that investors demand for investing in bonds also change The price of the asset in the market also changes Example: Zero coupon bond with a YTM of 5% and FV 100. Value: 100 P( 5%YTM) $23.14 30 (1 0.05) If, suddenly, investors s demand d a 6% In general,... 100 P( 6% YTM) $17.41 30 (1 0.06) A higher YTM reduces the present value of remaining cash flows If rates rise, the YTM rise and bond prices fall What types of bonds are more subject to fluctuations in the price?
YTM and price of a 30 year zerocoupon bond
Sensitivity to changes in interest rates 1600 1400 1200 1000 Pr rice 800 600 400 200 0 0 2 4 6 8 10 12 14 5 Year 9% Bond 1 Year 9% Bond Interest rates
Sensitivity and its measurement We have that... Long-term bonds are more sensitive to changes in interest rates than short-term bonds Similarly, bonds with higher coupon rates are less sensitive to changes in interest rates because they pay more upfront Duration of a bond: measures the price sensitivity to changes in interest rates ponders the years for their contribution to total present value average number of years of the discounted cash flows
Computing the duration of a bond 1 PV ( C ) 2 PV ( C2) 3 PV ( C3) Duration Total PV Total PV Total PV 1... Proportion of the total Proportion of the total Year Ct PV(Ct) al 2.75% PV [PV(Ct)/Total PV] PV multiplied by year 1 55 53.53 0.049 0.049 2 55 52.1 0.047 0.094 3 55 50.7 0.046 0.138 4 1055 946.51 0.858 3.433 Total PV = 1102.83 1 Duration= 3.714 years
Valuing safe bonds using arbitrage So far, we focused on the relationship between price and YTM Here, we should look at the price and YTM using similar bonds of known price Price and yield of any safe bond with coupon? By arbitrage, (government) spot interest rates should give same return on cash flows Replicate cash flows of a coupon bond using zero coupon-spot interest rates For example... $ 1,000 bond paying 10% per year is equivalent to a portfolio of 3 zero-coupon bonds Where do we get the spot interest rates from?
The yield curve (US): January 2005/05/06 What does it explain the different shapes of the three curves?
What would happen if the value was not $1153? At the starting point of the project (say, 2012), the yields and price of bonds without coupons (per each $100 of principal are) The actual value depends on the year the project is started. Why?
Instead of prices, we can use YTMs The price should be equal to: P C 1 C 2 (1 1 YTM ) (1 1 YTM 2 ) 2... FV C (1 YTM where YTM n is the YTM of a zero-coupon bond maturing on the same date N N N ) In the example P 100 (1 0.35 ) 100 (1 0.04 ) 1100 (1 0.045 ) 1 2 3 1153 Match the term of the cash flow and the term of the discount rate An increase in interest rates decreases NPVs Notice that the YTM of the bond is a (complexly) weighted average of the YTM of the zero-coupon bond with equal and shorter maturities 100 100 1100 1153 is equal to y 0.44 1 2 3 (1 y) (1 y) (1 y)
Risky bond valuation So far we have valued risk-free bonds (e.g. Treasury bills) Other bonds, like corporate bonds, issuer can default (credit risk): The risk of insolvency changes price of a bond and YTM. How? We should see that Investors pay less for bonds with credit risk than they would for an otherwise identical default-free bond The yield of bonds with credit risk will be higher than that of otherwise identical default-free bonds
Example: two extremes No Default: 1-year year, zero coupon with a YTM of 4%: 1000 1000 P $961.54 1 YTM 1 1.04 Certain Default: issuer will pay 90% of obligation 900 900 P $865.38 1 YTM 104 1 1.04 The yield to maturity in the second case is FV 1000 YTM 1 1 15.56% 56% P 865.38 (we should use promised rather the actual cash flow) YTM higher than the expected return: 900 1 4% 865.38
In reality: risk of default One-year, $1000, zero-coupon bond 50%: repay face value in full /50%: default and receive $900 Because of uncertainty, the discount rate is 5.1% (1.1% premium because default more likely if economy is weak) P 950 $903.90 FV 1000 YTM 1.051 1 1.1063 P 903.90 Investors receive 10.63% at most. In the bad scenario: 900 1 0.43% 903.90 The average return is: 0.5(10.63%) 0.5( 0.43%) 5.1% Notice that lower YTM does not imply lower expected return
Valuing corporate bonds using arbitrage A bond of IBM: pays $ 115 every December for 5 years Suppose that t we are in January 2009 In December 2013 it pays an additional $ 1,000 and bond is canceled. The bond rating is AAA (YTM in the WSJ for AAA bonds is 7.5%) Price P 115 1.075 115 115 115 1,115 2 5 2 3 4 1.075 1.075 1.075 1.075 $1,161.84
Default probabilities and Value-at-Risk (VaR)
Ratings and financial ratios Median of the ratings during three years (1998 2000). Ratio AAA AA A BBB BB B CCC EBITDA / interests 21.4 10.1 6.1 3.7 2.1 0.8 0.1 Return on capital % 34.9 21.7 19.4 13.6 11.6 6.6 1 Gross margin % 27 22.1 18.6 15.4 15.9 11.9 11.9 Total debt / capital % 22.9 37.7 42.5 48.2 62.6 74.8 87.7 Gross margin %= (revenue-cost of goods sold)/revenue Return on capital= net operating profit divided by invested capital (value)
Credit scoring models Companies more likely to go bankrupt, if they have Low return on assets and low interest coverage (EBIT/Interest exp) How can we create a measure (score)? Method 1: Solvency index: Draw straight line separating those who failed and those who do not, so that there are few who default above and many below The solvency ratio (Z) is: Z = return on assets + 5 x coverage of interest Companies with Z> 5 considered "no problem
Method 1: Solvency index 8 7 % 6 Quebraron No quebraron Z=5 Return on assets, 5 4 3 2 D 1 0-0.3 0.2 0.7 1.2 Interest coverage ratio
Method 2: Multiple discriminant analysis No need to be restricted t to only two variables This technique calculates how much weight should be placed on each variable to separate the two groups Altman weights predict 95% of the bankruptcies: Net working capital Retained earnings Z =.72.85 + Total assets Total assets EBIT Equity Sales 3.1 +.42 +1.0 Total assets Total assets Total assets Prediction If Z <1.2 likely l to go bankrupt, If 1.2 <Z <2.9 not clear If Z> 2.9 likely to have no problems
Market-based risk models Estimate t probability bilit of entering bankruptcy in a certain period using: Expected growth in the market value of its assets Variability of future asset values Face value and maturity of the debt Applied to companies, countries, etc.
Example: Worldcom The actual market value of the assets of WorldCom assets, as it approached insolvency 90,000 Val lue million ns $ 80,000 70,000 60,000 50,000 40,000 30,000 Market value of the assets Date of insolvency 20,000 Solvency level 10,000 0 27/09/2001 11/01/2001 12/07/2001 15/01/2002 21/02/2002 28/03/2002 05/03/2002 06/10/2002 19/07/2002
Estimation of the probability of default in next year Moody s estimation of the probability of insolvency of WorldCom (index between 0.02 and 0.20) 25 20 15 10 5 Date of insolvency Probability of default during the next year 0 27/09 /09/2001 11/01 /01/2001 12/07 /07/2001 15/01 /01/2002 21/02 /02/2002 28/03 /03/2002 05/03 /03/2002 06/10 /10/2002 19/07 /07/2002
Value at Risk (VaR) How much can I lose with a given probability and timeframe? Relatively new technique Attempts to be a measure of risk Defines risk as "potential loss Applied to any investment t (stock, bonds, ) Now required by official standards e.g. for banks Factors Value of assets Daily volatility Days of prediction (k) Distribution of returns Likelihood of potential loss
Value at Risk (VaR) Based on a model of evolution of returns & volatility Predicts the evolution of future returns (cumulative k periods) and calculates the expected loss with a given probability VaR of a portfolio/asset on a horizon k for a probability p is: p = Pr [ V (k) VaR] where V (k) is the change in the value of the portfolio / asset
Value at Risk (VaR) of an asset Specify a statistical process for the daily return of the asset Calculate the distribution of future (cumulative) returns: r t N(μ t, σ² t ) Depending on μ t and σ ² t, calculate the (conditional) distribution r[k] = r t+1 + r t+2 +... + r t+k From this, calculate possible losses and their probabilities Example 1: RISKMETRICS (JP Morgan) r t N(0, σ² t ) and σ² t = ασ² t-1 +(1-α)r² t-1 then r[k] N(0,kσ² t+1 ) Example 2: r t N(μ, σ²) ) then r[k] N(kμ,kσ²)
Example You own a portfolio of $ 10 m. in IBM stock. IBM has a daily volatility of 2%. Calculate the VaR for a period of 10 days at 99% (maximum loss at 1% probability) (expressed, typically, positive, even if it is a loss) 10 0.0202 10 6.32% Confidence intervals 2.330.0632 14.74% VaR 0.147410,000,000 $1,473,621
Value at Risk (VaR) of a portfolio What if you also have $ 5 billion of stock of AT & T, with daily volatility of 1%. AT&T and IBM have a correlation of.7. What is the VaR of AT&T and of the combined portfolio? What is the benefit of diversification? (lower expected loss) 2 portfolio 10 2 2 2 2 2 3 + 1 3 + 22 31 3 IBM 10 0.0158 5.01% AT & T Conficence intervals 2.330.05 11.68% VaR _1% 0.1168$15,000,000 $1,751,379 IBM AT & T portfolio 1.58% VaR IBM VR VaR Portfolio $ 1,473,621 y VaR & $368,405 therefore Sum $1,751,379 AT Diversification gains Sum - Var T Portfolio $90,647 $1,842,026
Covenants and Repayment Provisions
Covenants and provisions Restrictive covenants Limitations set by bondholders on the actions of the Corporation For example, covenants may: restrict the ability of management to pay dividends, the level of further indebtedness or specify that the issuer must maintain a minimum amount of working capital Repayment provisions: Issuer can repurchase a fraction of the outstanding bonds in the market or make a tender offer for the entire issue For callable bonds, exercise the call provision Callable bonds: Issuers have the right (but not the obligation) to retire all outstanding bonds on (or after) a specific date (the call date), for the call price Call a bond issue if interest rates lower -> lower price than in market!
Prices of callable (at par) and non-callable bonds on call date If callable and yield<5%, call and refinance at lower rate!
Prices of callable (at par) and non-callable bonds prior to call date
More bond terminology Sinking fund: company makes regular payments into a fund administered i d by a trustee t over the life of the bond These payments are then used to repurchase bonds. Negative Pledge Clause: the processing of giving unsecured debentures equal protection to future debtholders Poison Put: a clause that obliges the borrower to repay the bond if a large quantity of stock is bought by single investor, which causes the firms bonds to be dowgradedd d Pay in kind (PIK): a bond that makes regular interest est payments, but in the early years of the bonds life the issuer can choose to pay interest in cash or more bonds with an equivalent face value
Convertible Provisions Convertible Bond Corporate bond with a provision that gives the bondholder an option to convert it into a fixed number of shares of common stock Conversion Ratio The number of shares received upon conversion of a convertible bond, usually stated per $1000 of face value Conversion Price The face value of a convertible bond divided by the number of shares received if the bond is converted
Example You have a convertible bond with a $1000 face value and a conversion ratio of 15 If you convert bond into stock, you will receive 15 shares If you do not convert, you will receive $1000 By converting you essentially pay $1000 for 15 shares, implying a conversion price per share of $66.67. If the price of the stock exceeds $66.67, you will choose to convert; otherwise, you will take the cash.
Convertible Bond Value
Government bonds
Nominal and real interest rates Nominal interest rate: the one that..... you pay when you borrow money... specified in the contract... is used to discount cash flows Real interest rate: the type...... of growth of your purchasing power, after adjusting for inflation... you are actually paying or obtaining, determined by funds supply/demand It is related to the actual productivity of the economy The relationship between them: 1 r r 1 r 1 i, that is r r r i 1 i r i and, therefore, r r r i
The nominal interest rate and the inflation Return of the US Treasury Bills and the rate of inflation (1953-2003) 16 14 Treasury Bills 12 Inflation 10 % 8 6 4 2 0-2 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Why do they appear to move together?
Determining real interest rates (Fisher 1930) SUPPLY OF FUNDS DEMAND FOR FUNDS Household savings Families investments (e.g. housing) Companies savings (e.g. retained earnings) Public surplus Foreign savings = current account deficit Intermediari es and financial markets Companies investment (e.g. equipment, facilities, inventories) Public deficit Foreign credit = current account surplus Impact of an increase in public deficit? And of an increase in return on investments?
Term structure of interest rates (US): January 2005/05/06 What does it explain the different shapes of the three curves?
What determines the shape of the yield curve? Basically the interest rates expectations: Suppose short-term are equal to long-term rates (curve is flat) If (all) interest rates are expected to rise in the future: invest short-term and reinvest later! Nobody would want to invest long term, so long-term rates should rise (curve increasing) And if they are expected to fall... that would happen? Decreasing ( inverted ) yield curve: It is expected that interest rates fall in future As rates fall as the economy worsens is a negative projection Increasing g( ( steep ) p)yield curve: It is expected that interest rates will rise in future It can be interpreted as a positive economic projection
Graphical analyis Assets with the same liquidity, risk and tax treatment, but different maturities have different yields Interest rate 1 month 3 months 1 year 10 yers Term to maturity
Level Change: Increase in expected inflation or level of activity Higher interest rates!
Change of slope: tighter monetary ypolicy Monetary policy affects short-term rates!
Curve becomes negative: recession coming? Change in interest expectations!
Short, long-term interest rates and spread (US)
Euro zone
The liquidity preference theory The expectations theory leaves out any type of risk Bond prices have some volatility, and this causes some risk, higher for longerterm bonds (creates a liquidity premium!) Uncertainty about inflation is one of those risks (affecting nominal interest rate expectations). Therefore, if there is more uncertainty about inflation (or in times of volatile inflation) liquidity idit premium will be higher h and will be steeper Investors incur extra risk (interest rate, not insolvency) to maintain long-term bonds, so they demand a premium for liquidity. Curve will normally be upward sloping Yield curve & capital budgets Cash flows should be discounted using information from yield curve If you trust in other theories... use arbitration to your advantage
Value at Risk (VaR) Diversification gains 800000 700000 600000 500000 400000 300000 200000 100000 0-1.5-1 -0.5 0 0.5 1 1.5-100000 Correlation between the two bonds