Interest Rates and Bond Valuation

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1 and Bond Valuation 1 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. 2 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. Indenture Document which details the legal obligation of the corporation to the bondholders. 3 Bond Ratings 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 Speculative AAA AA+/- system A BBB BB B CCC CC C D Top Quality Lower Ratings are somewhat more susceptible to adverse effects of changes in circumstances and economic conditions than debt in higher rated categories. Low Quality No interest being paid rently in Default 4

2 Bond Ratings 5 Bond Quotes 6 Bond Ratings can change due to many factors. Corporate Bond Ratings McDonalds AA ATT AA- Caterpillar Corp A+ 3 Com BBB Delta Air Lines BBB- AOL BB- Planet Hollywood CCC+ TWA CCC Golden Books Family Entmt D Company Issuing the Bond S&P Research Insight Sept Bond Quotes 7 Bond Quotes 8 Coupon Interest Rate Year of Maturity Determines the Investor s Periodic Cash Flow Cash Flow = Interest Payment = Coupon Rate x Par For IBM: x 1000 = $63.75/Year Determines the Time frame for the Investment IBM Bond: 08 = year 2008, therefore in 2003 this is a 5 year investment

3 Bond Quotes 9 Bond Quotes 10 rent Yield () Daily Trading Volume (,000) Coupon Rate rent Yield = = Market Price =.066 = 6.6 Bond Quotes 11 Bond Quotes 12 Daily Closing Market Price as a of Par Change in from Previous Day s Close IBM Bond $Price = 96 5 /8 x 1000 = $ = 96 5 / 8 x 10 = $966.25

4 Valuation: An Overview 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 Asset characteristics Investor attributes These two areas determine the investor s required rate of return 13 Basic Factors Determining Value Asset Characteristics Expected level of cash flow Timing of cash flow Riskiness of cash flow Investor s required rate of return Investor Attributes Investor s assessment of the riskiness of the asset s cash flows Investor s willingness to bear risk 14 Asset value = Present value of expected cash flows discounted using investor s required rate Bond Valuation Model 15 Bond Valuation Model 16 3 Cash Flows 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) 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) IBM Bond Timeline: Investor that purchases bond today for $ will receive 5 annual interest payments of $63.75 and a $1,000 payment in 5 years

5 Bond Valuation Model 17 Bond Valuation Model 18 Compute Bond s Intrinsic Value Compute Bond s Intrinsic Value $59.03 $54.66 $50.61 $46.86 $43.39 $ $1000 (1.08) 5 $ Compute the Intrinsic Value for the IBM Bond given that you require a 8 return on your investment $63.75 Annuity for 5 years $1000 Lump Sum in 5 years xp/yr NOM EFF P/YR 5 8? xp/yr NOM EFF P/YR 5 8? 1000 Bond Valuation Model 19 Bond Valuation Model 20 Compute Bond s Intrinsic Value $63.75 Annuity for 5 years $1000 Lump Sum in 5 years Compute PV of annuity and PV of Lump Sum in ONE Step xp/yr NOM EFF P/YR 5 8? Bonds that Pay Interest Semi-Annually: Rather than receiving 4 annual payments of $90, the bondholder will receive 4x2 = 8 semiannual payments of 90 2=$45.

6 Bond Valuation Model 21 Bond Valuation Model 22 Bonds that Pay Interest Semi-Annually: Bonds that Pay Interest Semi-Annually: Compute the Intrinsic Value for the Kroger Bond given that you require a 1 return on your investment Compute the Intrinsic Value for the Kroger Bond given that you require a 1 return on your investment. Since interest is received every 6 months, need to use semi-annual compounding Semi-Annual Compounded Rate 1 2 # of Semi-Annual Periods 4 years x 2 xp/yr NOM EFF P/YR 8 5? Yield to Maturity Bondholder s Expected Rate of Return. If an investor purchases bond at today s price and hold it until maturity, what is the annual rate of return that is earned? 23 Yield to Maturity Relationship between YTM and Intrinsic Value Given Required Rate of Return Market Price 24 Compute Intrinsic Value YTM Compare Intrinsic Value to Market Price YTM to Required Rate

7 Yield to Maturity IBM Corporate Bond: < Interest Rate Risk Bond Prices fluctuate over Time 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 > xp/yr NOM EFF P/YR 5? If Price < 1000 bond sells at a Discount (YTM > Coupon Rate) If Price > 1000 bond sells at a Premium (YTM < Coupon Rate) If Price = 1000 bond sells at Par (YTM = Coupon Rate) Interest Rates Interest Rates V b V b Interest Rate Risk Bond Prices fluctuate over Time 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 AAA Bonds are currently yielding 6 Purchase ATT 6s23 Bond for $ xp/yr NOM EFF P/YR 5 6? Interest Rate Risk 2003 AAA Bonds are currently yielding 6 Purchase ATT 6s23 Bond for $ 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) xp/yr NOM EFF P/YR 17 9?

8 Interest Rate Risk 34 Interest Rate Risk AAA Bonds are currently yielding AAA Bonds are currently yielding 6 Purchase ATT 6s23 Bond for $ Purchase ATT 6s23 Bond for $ 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) 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) Market Price for ATT6s23 is now $ Market Price for ATT6s23 is now $ AAA Bonds are currently yielding 5 If you want to sell the the ATT 6s23 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 5) -1, xp/yr NOM EFF P/YR 14 5? AAA Bonds are currently yielding 5 If you want to sell the the ATT 6s22 6s23 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 5) Market Price for ATT6s23 is now $1, Bond Prices fall during periods of rising interest rates and rise during periods of falling interest rates Determined by Real Rate of Interest Expected Inflation Default Risk Interest Rate Risk Liquidity Risk Interest Rates Real Rate of Interest Compensates for the lender s lost opportunity to consume.

9 39 42 Default Risk 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. 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 1. $100 $107 In REAL TERMS, the $107 at the end of the year will only purchase $97.27 worth of constant goods and services = Inflation Rate 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 1. $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. 43 Interest Rate Risk 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. 44

10 Liquidity 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. 45 Determination of Rates k = the nominal, or observed rate on security k* = real, risk free rate of interest IP = Inflation Premium DRP = Default Risk Premium LP = 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 46 Find the Nominal 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.. The Liquidity Premium is for these bonds 47 Real Risk Free Rate = 2.5 Purchase Date 3 Maturity Date 50 1 yr Gov t 2.5 Holding Period

11 53 55 Real Risk Free Rate = yr Gov t 2.5 Real Risk Free Rate = yr BBB Interest Rate Risk Prem.= 0.1 for each year of maturity Default Risk Premium = for Gov t Bonds Interest Rate Risk Prem.= 0.1 for each year of maturity Default Risk Premium = 1. for BBB Rated Bonds Real Risk Free Rate = yr Gov t 2.5 Real Risk Free Rate = yr Gov t Purchase Date Maturity Date IP = Average Inflation Rate over Term Holding Period = years

12 60 62 Real Risk Free Rate = yr Gov t 2.5 Real Risk Free Rate = yr BBB Interest Rate Risk Prem.= 0.1 for each year of maturity 0.4 Default Risk Premium = for Gov t Bonds Interest Rate Risk Prem.= 0.1 for each year of maturity 0.4 Default Risk Premium = 1. for BBB Rated Bonds Term Structure of Relationship between short term rates on a particular security (Typically Treasury Securities) and long term rates Rate () 7.15 Possible YIELD CURVES 63 Yield ve on the Web Maturity

13 Comprehensive Interest Rate Problem Interest Rate Data: Corporate DRP Bond Rating A B IRP 0.2 per year of maturity 0.2 per year of maturity C per year of maturity Expected Annual Inflation Rates for the next 6 years: year C rated corporate bonds currently pay interest annually. What is the real rate of interest for this economy? LP 65

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