Chapter 7 Bond Valuation May 04 Bonds
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Chapter 7 Bond Valuation May 04 1 2 Bonds Debt Instrument Bondholders are lending the corporation money for some stated period of time. Liquid Asset Corporate Bonds can be traded in the secondary market. Price at which a given bond trades is determined by market conditions and terms of the bond. Interest Rates and Bond Valuation Bond Terminology Par Value Usually $1,000 also called Face Value Coupon Interest Rate Borrowers (firms) typically make periodic interest payments to the bondholders. Maturity Time at which the original principal (Par Value) is repaid to the bondholder. 3 Moody’s and Standard & Poors regularly monitor corporate financial statements and assign a rating to the corporation’s debt similar to a personal credit report Investment Grade Indenture Document which details the legal obligation of the corporation to the bondholders. 4 Bond Ratings Speculative AAA Top Quality AA+/- system Lower Ratings are somewhat more A susceptible to adverse effects of BBB changes in circumstances and conditions than debt in BB economic higher rated categories. B CCC CC Low Quality C No interest being paid D Currently in Default Chapter 7 Bond Valuation May 04 5 Bond Ratings 6 Bond Quotes Bond Ratings can change due to many factors. Cur Yld Bonds AMR6¼27 ATT 8.35s28 IBM 63/8 08 Kroger 9s07 Corporate Bond Ratings McDonalds AA ATT AACaterpillar Corp A+ 3 Com BBB Delta Air Lines BBBAOL BBPlanet Hollywood CCC+ TWA CCC Golden Books Family Entmt D Vol cv 6 8.3 110 6.6 228 8.8 74 Close Net Chg 91¼ 102¾ 965/8 1017/8 -1½ +¼ -1/8 -¼ Source: Wall Street Journal Company Issuing the Bond S&P Research Insight Sept. 2000 7 Bond Quotes Bonds AMR6¼27 ATT 8.35s28 IBM 63/8 08 Kroger 9s07 Cur Yld Vol cv 6 8.3 110 6.6 228 8.8 74 Close Net Chg 91¼ 102¾ 965/8 1017/8 -1½ +¼ -1/8 -¼ Source: Wall Street Journal Coupon Interest Rate Determines the Investor’s Periodic Cash Flow Cash Flow = Interest Payment = Coupon Rate x Par For IBM: .06375 x 1000 = $63.75/Year 8 Bond Quotes Cur Yld Bonds AMR6¼27 ATT 8.35s28 IBM 63/8 08 Kroger 9s07 Vol cv 6 8.3 110 6.6 228 8.8 74 Close Net Chg 91¼ 102¾ 965/8 1017/8 -1½ +¼ -1/8 -¼ Source: Wall Street Journal Year of Maturity Determines the Time frame for the Investment IBM Bond: 08 = year 2008, therefore in 2003 this is a 5 year investment Chapter 7 Bond Valuation May 04 9 Bond Quotes Bonds AMR6¼27 ATT 8.35s28 IBM 63/8 08 Kroger 9s07 Cur Yld Vol cv 6 8.3 110 6.6 228 8.8 74 Close Net Chg 91¼ 102¾ 965/8 1017/8 -1½ +¼ -1/8 -¼ 10 Bond Quotes Bonds AMR6¼27 ATT 8.35s28 IBM 63/8 08 Kroger 9s07 Cur Yld Source: Wall Street Journal -1½ +¼ -1/8 -¼ Coupon Rate = 6.375 = .066 = 6.6% Market Price 96.625 11 AMR6¼27 ATT 8.35s28 IBM 63/8 08 Kroger 9s07 Net Chg 91¼ 102¾ 965/8 1017/8 Daily Trading Volume (,000) Bond Quotes Bonds Close Source: Wall Street Journal Current Yield (%) Current Yield = Vol cv 6 8.3 110 6.6 228 8.8 74 Cur Yld Vol cv 6 8.3 110 6.6 228 8.8 74 Close Net Chg 91¼ 102¾ 965/8 1017/8 -1½ +¼ -1/8 -¼ Source: Wall Street Journal Daily Closing Market Price as a % of Par IBM Bond $Price = 965/8 % x 1000 = $966.25 = $966.25 = 965/8 x 10 12 Bond Quotes Bonds AMR6¼27 ATT 8.35s28 IBM 63/8 08 Kroger 9s07 Cur Yld Vol cv 6 8.3 110 6.6 228 8.8 74 Close Net Chg 91¼ 102¾ 965/8 1017/8 -1½ +¼ -1/8 -¼ Source: Wall Street Journal Change in from Previous Day’s Close Chapter 7 Bond Valuation Valuation: An Overview May 04 13 14 Basic Factors Determining Value Investor Attributes Asset Characteristics Investor’s assessment of the riskiness of the asset’s cash flows Expected level of cash flow The value of an asset is its intrinsic value or the present value of its expected future cash flows, where these cash flows are discounted back to the present using the investor’s required rate of return. Value is impacted by Timing of cash flow Investor’s willingness to bear risk Riskiness of cash flow Asset characteristics Investor attributes These two areas determine the investor’s required rate of return Investor’s required rate of return Asset value = Present value of expected cash flows discounted using investor’s required rate Bond Valuation Model 15 3 Cash Flows IBM Bond Timeline: Amount that is paid to purchase the bond (PV) Periodic Interest Payments made to the bondholders (PMT) Repayment of Par value at end of Bond’s life (FV) Cur Yld Bonds AMR6¼27 ATT 8.35s28 IBM 63/8 08 Kroger 9s07 Other Terminology Time frame for cash flows (N) = Bond’s Maturity Interest Rate for Time Value is the rate at which future cash flows are being discounted to present. (I/YR) 16 Bond Valuation Model Vol cv 6 8.3 110 6.6 228 8.8 74 Close Net Chg 91¼ 102¾ 965/8 1017/8 -1½ +¼ -1/8 -¼ Source: Wall Street Journal Investor that purchases bond today for $966.25 will receive 5 annual interest payments of $63.75 and a $1,000 payment in 5 years. 2003 0 2004 1 63.75 2005 2006 2 3 63.75 63.75 2007 4 63.75 2008 5 63.75 1000.00 Chapter 7 Bond Valuation May 04 17 Bond Valuation Model Compute Bond’s Intrinsic Value 18 Bond Valuation Model Compute Bond’s Intrinsic Value 2003 2004 2005 2006 2007 2008 2003 2004 2005 2006 2007 2008 0 1 2 3 4 5 0 1 2 3 4 5 63.75 63.75 63.75 63.75 $59.03 $54.66 $50.61 $46.86 $43.39 63.75 1000.00 63.75 63.75 63.75 $63.75 Annuity for 5 years -254.54 $1000 (1.08) 5 $680.58 $935.12 N I/YR 5 8 xP/YR Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment. 19 Bond Valuation Model Compute Bond’s Intrinsic Value 2004 2005 2006 2007 2008 0 1 2 3 4 5 63.75 63.75 $63.75 Annuity for 5 years 63.75 ? P/YR FV 254.54 +680.58 935.12 63.75 Cur Yld Bonds AMR6¼27 ATT 8.35s28 IBM 63/8 08 Kroger 9s07 63.75 1000.00 N I/YR 5 8 NOM % PV EFF% ? 1 45 P/YR N I/YR 5 8 xP/YR NOM % PV EFF% PMT FV P/YR ? 1000 FV 63.75 1000 Vol Close Net Chg 91¼ 102¾ 965/8 1017/8 -1½ +¼ -1/8 -¼ Source: Wall Street Journal 2004 0 PMT -680.58 20 cv 6 8.3 110 6.6 228 8.8 74 $1000 Lump Sum in 5 years -935.12 xP/YR PMT $1000 Lump Sum in 5 years Bond Valuation Model 2003 Compute PV of annuity and PV of Lump Sum in ONE Step PV EFF% 63.75 1000.00 Bonds that Pay Interest Semi-Annually: 2003 63.75 NOM % 63.75 45 45 2005 2006 2007 2008 2 3 4 5 45 45 45 45 45.00 1000.00 Rather than receiving 4 annual payments of $90, the bondholder will receive 4x2 = 8 semiannual payments of 90÷2=$45. Chapter 7 Bond Valuation May 04 21 Bond Valuation Model Bonds that Pay Interest Semi-Annually: 2003 2004 0 45 45 Bonds that Pay Interest Semi-Annually: 2005 2006 2007 2008 2003 2 3 4 5 0 1 45 45 45 45 45 45.00 1000.00 2004 45 2007 2008 3 4 5 45 45 45 45 45 45.00 1000.00 -967.68 # of Semi-Annual Periods 4 years x 2 Bondholder’s Expected Rate of Return. 2006 2 Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment. Since interest is received every 6 months, need to use semi-annual compounding Yield to Maturity 2005 1 45 Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment. Semi-Annual 10% Compounded Rate 2 22 Bond Valuation Model N I/YR 8 5 xP/YR 23 NOM % PV EFF% ? PMT FV 45 1000 P/YR 24 Yield to Maturity Relationship between YTM and Intrinsic Value If an investor purchases bond at today’s price and hold it until maturity, what is the annual rate of return that is earned? Given Required Rate of Return Market Price Compute Intrinsic Value YTM Compare Intrinsic Value to Market Price YTM to Required Rate Chapter 7 Bond Valuation May 04 29 Yield to Maturity Bond Prices fluctuate over Time IBM Corporate Bond: 2003 2004 0 2005 2006 2007 2008 2 3 4 5 63.75 63.75 63.75 1 -966.25 63.75 966.25 < 1000 7.2% > 6.375% 7.203% N xP/YR 5 I/YR NOM % PV EFF% PMT P/YR FV ? -966.25 63.75 1000 As interest rates in the economy change, required rates on bonds will also change resulting in investor’s intrinsic values changing and market prices changing. 63.75 1000.00 Interest Rates • If Price < 1000 bond sells at a Discount (YTM > Coupon Rate) • If Price > 1000 bond sells at a Premium (YTM < Coupon Rate) Vb Vb Interest Rates • If Price = 1000 bond sells at Par (YTM = Coupon Rate) 32 Interest Rate Risk When bonds are originally issued, the coupon rate is set to match current prevailing rates. Over time, the prevailing rates may change, but the coupon rate is fixed. Results in the market price of the bond changing. 33 Interest Rate Risk 2003 Bond Prices fluctuate over Time 2003 31 Interest Rate Risk AAA Bonds are currently yielding 6% Purchase ATT 6s23 Bond for $1000.00 2006 AAA Bonds are currently yielding 9% If you want to sell the the ATT 6s23 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 9%) AAA Bonds are currently yielding 6% Purchase ATT 6s23 Bond for $1000.00 -743.69 -1000 N I/YR 5 6 xP/YR NOM % N I/YR 17 9 xP/YR PV PMT FV ? 60 1000 EFF% P/YR NOM % PV PMT FV ? 60 1000 EFF% P/YR Chapter 7 Bond Valuation May 04 34 Interest Rate Risk 2003 2003 AAA Bonds are currently yielding 6% Purchase ATT 6s23 Bond for $1000.00 2006 2006 AAA Bonds are currently yielding 9% Market Price for ATT6s23 is now $743.69 2008 2009 AAA Bonds are currently yielding 5% -1,098.99 N I/YR 14 5 xP/YR NOM % PV PMT FV ? 60 1000 EFF% P/YR AAA Bonds are currently yielding 5% If you want to sell the the ATT 6s23 6s22 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 5%) 36 Interest Rates AAA Bonds are currently yielding 9% If you want to sell the the ATT 6s23 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 9%) Market Price for ATT6s23 is now $743.69 If you want to sell the the ATT 6s23 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 5%) AAA Bonds are currently yielding 6% Purchase ATT 6s23 Bond for $1000.00 If you want to sell the the ATT 6s23 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 9%) 2009 35 Interest Rate Risk Market Price for ATT6s23 is now $1,098.99 Bond Prices fall during periods of rising interest rates and rise during periods of falling interest rates. Interest Rates Interest Rates Determined by Real Rate of Interest Expected Inflation Default Risk Interest Rate Risk Interest Liquidity Risk Rates Real Rate of Interest Compensates for the lender’s lost opportunity to consume. 37 Chapter 7 Bond Valuation May 04 39 Interest Rates Default Risk 42 Interest Rates Expected Inflation For most securities, there is some risk that the borrower will not repay the interest and/or principal on time, or at all. The greater the chance of default, the greater the interest rate the investor demands and the issuer must pay. Savers are hurt by inflation since the money that is saved will purchase fewer good and services Example: Joe saves $100 for one year in an account earning 7% interest. During the year prices go up by 10%. $100 $107 In REAL TERMS, the $107 at the end of the year will only purchase $97.27 worth of constant goods and services. 107 = 97.27 1.10 1+ Inflation Rate 43 Interest Rates Interest Rates 44 Interest Rate Risk Expected Inflation Savers are hurt by inflation since the money that is saved will purchase fewer good and services Example: Joe saves $100 for one year in an account earning 7% interest. During the year prices go up by 10%. $100 $107 In REAL TERMS, the $107 at the end of the year will only purchase $97.27 worth of constant goods and services. Conclusion: Savers will demand to be compensated for expected inflation so as not to be hurt by the effects of inflation. If interest rates rise, lenders may find that their loans are earning rates that are lower than what they could get on new loans. The risk of this occurring is higher for longer maturity loans. Lenders will adjust the premium they charge for this risk depending on whether they believe rates will go up or down. Chapter 7 Bond Valuation Interest Rates May 04 45 46 Interest Rates Determination of Rates Liquidity k = k* + IP + DRP + IRP + LP Investments that are easy to sell without losing value are more liquid. Illiquid securities have a higher interest rate to compensate the lender for the inconvenience of being “stuck.” k = k* = IP = DRP = LP = the nominal, or observed rate on security real, risk free rate of interest Inflation Premium Default Risk Premium Liquidity Premium - Reflects the ability to sell security easily. IRP = Interest Rate Risk Premium - Reflects interest rate risk long term securities are more sensitive to changes in interest rates Interest Rates Determination of Rates EXAMPLE Find the Nominal Interest Rates for 1 year and 4 year Government Bonds and 1 and 4 year BBB Corporate Bonds using the following information: • The Real risk-free is currently 2.5%; • Inflation is expected to be 3% in the next year, 4% in the year after that, and 5% for each year thereafter • All bonds currently include a 0.1% Interest Rate Risk Premium for each year remaining to maturity • The Default Risk Premium for BBB rated bonds is currently 1.0%. • The Liquidity Premium is 0% for these bonds 47 50 Interest Rates Determination of Rates EXAMPLE 0% k = k* + IP + DRP + IRP + LP Real Risk Free Rate = 2.5% Expected Inflation Rates 1 2 3 3% Purchase Date Maturity Date Holding Period 1 yr Gov’t 2.5% 4 ∞ Chapter 7 Bond Valuation May 04 53 Interest Rates Determination of Rates EXAMPLE Determination of Rates EXAMPLE 0% k = k* + IP + DRP + IRP + LP 4 ∞ 3.0% 3% Interest Rate Risk Prem.= 0.10% for each year of maturity 0.1% 0.0% 5.6% Default Risk Premium = 0% for Gov’t Bonds 57 Interest Rates Determination of Rates EXAMPLE 0% 3% 4% 5% Purchase Date 5% Maturity Date ∞ ∞ 3.0% 3% Interest Rate Risk Prem.= 0.10% for each year of maturity 0.1% 1.0% 6.6% Default Risk Premium = 1.0% for BBB Rated Bonds 58 Interest Rates Determination of Rates EXAMPLE 0% 4 yr Gov’t 2.5% Real Risk Free Rate = 2.5% Expected Inflation Rates 1 2 3 3% 4% 5% 4 5% IP = Average Inflation Rate over Term = Holding Period 4 k = k* + IP + DRP + IRP + LP 4 yr Gov’t 2.5% 4 1 yr BBB 2.5% Real Risk Free Rate = 2.5% Expected Inflation Rates 1 2 3 k = k* + IP + DRP + IRP + LP Real Risk Free Rate = 2.5% Expected Inflation Rates 1 2 3 0% k = k* + IP + DRP + IRP + LP 1 yr Gov’t 2.5% Real Risk Free Rate = 2.5% Expected Inflation Rates 1 2 3 55 Interest Rates 3%+ 4%+ 5%+ 5% 4 years ∞ 4.25% Chapter 7 Bond Valuation May 04 60 Interest Rates Determination of Rates EXAMPLE Determination of Rates EXAMPLE 0% k = k* + IP + DRP + IRP + LP 3% 4% 5% ∞ 4 4.25% 5% 0% k = k* + IP + DRP + IRP + LP 4 yr Gov’t 2.5% Real Risk Free Rate = 2.5% Expected Inflation Rates 1 2 3 62 Interest Rates Interest Rate Risk Prem.= 0.10% for each year of maturity 0.4% 0.0% 7.15% Default Risk Premium = 0% for Gov’t Bonds 63 Term Structure of Interest Rates Relationship between short term rates on a particular security (Typically Treasury Securities) and long term rates 4 yr BBB 2.5% Real Risk Free Rate = 2.5% Expected Inflation Rates 1 2 3 3% 4% 5% 4 ∞ 5% Interest Rate Risk Prem.= 0.10% for each year of maturity 0.4% 1.0% 8.15% Default Risk Premium = 1.0% for BBB Rated Bonds Interest Rates Yield Curve on the Web Rate (%) Possible YIELD CURVES 7.15 http://stockcharts.com/charts/YieldCurve.html 5.6 1 4 Maturity 4.25% http://www.smartmoney.com/onebond/index.cfm?story=yieldcurve 64 Chapter 7 Bond Valuation May 04 65 Comprehensive Interest Rate Problem Interest Rate Data: Corporate DRP Bond Rating A 1.2% IRP LP 0.2% per year of maturity 0% B 1.8% 0.2% per year of maturity 0% C 2.9% 0.2% per year of maturity 0% Expected Annual Inflation Rates for the next 6 years: 0 1 6% 2 5% 3 4% 4 2% 5 3% 6 4% 3 year C rated corporate bonds currently pay 10.25% interest annually. What is the real rate of interest for this economy?
