Bond Prices and Interest Rate Risk - PowerPoint Presentation

1. Bond Prices and Interest Rate RiskChapter 5Kidwell, Blackwell, Whidbee and Sias10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias1

2. The Time Value of MoneyInvesting—in financial assets or in real assets—means giving up consumption until later.Positive time preference for consumption must be offset by adequate return. Opportunity cost of deferring consumption determines minimum rate of return required on a risk-free investment— Present sums are theoretically invested at not less than this rate; Future cash flows are discounted by at least this rate. Time value of money is not really about inflation.Inflation expectations affect discount rate, butDeferred consumption has opportunity cost by definition.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias2

3. Future Value or Compound ValueThe future value (FV) of a sum (PV) is FV = PV (1+i)n where i is the periodic interest rate and n is the number of compounding periods.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias3

4. Present ValueThe value today of a sum expected at a future time is given byPV = FV * (1 / (1+i)^n)With risk present, a premium will be added to the risk-free rate. The higher the discount rate, the lower the present value. 10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias4

5. Bond Pricing: What is a bond?A form of loan—a debt security obligating a borrower to pay a lender principal and interest.Borrower (issuer) promises contractually to make periodic payments to lender (investor or bondholder) over given number of yearsAt maturity, holder receives principal (or face value or par value).Periodically before maturity, holder receives interest (coupon) payments determined by coupon rate. The coupon rate is set as a percentage of par on the face value of the bond10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias5

6. Bond FeaturesThe bond indenture defines the terms of the contract. In general, the issuer promises to repay the principal amount and make coupon payments (most often semi-annually) over the life of the bond.The par or face value of a bond is the amount the borrower owes the lender at maturity. Typically, $1000.The maturity date is the date on which the principal is repaid.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias6

7. How debt differs from equityDebtholders do not have ownership or voting rightsDebt generally has a maturity date at which time the principal is repaid to the lender or owner of the debt.Debt generally has fixed interest payments at specific datesBonds have first claim on the firm’s assets in the event of bankruptcy. Equity holders are “residual” claimants.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias7

8. Types of BondsU.S. government bonds – The U.S. government is the largest individual issuer of bonds in our economy.Used to finance the Federal budgetGenerally considered the highest quality, or risk-free, debtU.S. government has never defaulted and the markets are very liquid.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias8

9. Types of BondsCorporate bondsThe corporate bond market is very large, very active and there are many large volume tradersInstitutional investors, i.e., life insurance companies, pension funds, mutual funds, hold large amounts of the this debtCorporations will have many bond issues trading at any given timeCorporate bond market is much less liquid than equity or U.S. government debt markets Riskiness of corporate bonds varies across firms10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias9

10. Types of BondsMunicipal bonds are issued by local or state governments and agenciesTo fund local projectsThese bonds can be quite risky – depending on the tax revenues of localitiesInternational bonds are issued by foreign governments, or foreign corporations. International bonds also have foreign exchange risk10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias10

11. Bond contractsThe contract for a bond is called its “indenture.” It lays out the financial terms of a bond and defines the contractual obligations between the borrower and the lender.Name of the issuerMaturity date and redemption valueCoupon rate – generally fixed but can be floating (or zero)Dates of scheduled payments10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias11

12. Additional bond features that would be defined in the indentureA call feature allows the firm to redeem or call a debt issue prior to maturity. Bonds are most likely to be called when interest rates have declined.A sinking fund requires the gradual retirement of debt issue through repurchase or deposits to a sinking fund account.Convertible debt is convertible at the option of the holder into common stock.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias12

13. Bond features (continued)Some bonds are sold with warrants which give the holder the option to purchase common stock.Some bonds have “put” features which allow the holder to sell the bond back to the issuer under special circumstances.Coupon rates on new bonds are usually fixed.Coupon rates are generally chosen so that the bond will sell at or near par value when issued.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias13

14. Bond features (continued)Some bonds have coupon rates that float with treasury rates, LIBOR or commodity prices.Original issue discount (OID) bonds are bonds issued with a coupon below prevailing rates. Zero coupon bonds are OID bonds that pay no coupon payments at all.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias14

15. What is a bond? ExamplePar value = $1000Coupon rate = 5%Issued todayMatures 30 years from todayAnnual coupon paymentsSo, the holder receives (the issuer pays) :$50 per year interest for 30 years (coupon rate * par value)$1,000 par value at the end of year 3010/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias15

16. Bond pricing: Bond cash flowsBondholder thus owns the right to a stream of cash flows:Ordinary annuity of interest paymentsFuture lump sum in return of par valueThese cash flows are discounted to their present value to find the bond’s value.The same process can be used at any point during the life of the bond.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias16

17. Bond Pricing: Present ValueThus, the value or price of a bond is the present value of the future cash flows promised, discounted at the market rate of interest consistent with the riskiness of the promised cash flows.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias17

18. PV of Bond Cash FlowsPB = Price of BondCt = coupon at period tFn = Par value due at maturityi = market interest rate (discount rate or market yield); andn = number of periods to maturity10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias18

19. Bond Pricing: PrinciplesCash flows are assumed to flow at end of the period and to be reinvested at i. Bonds typically pay interest semiannually.Increasing i decreases price (PB); decreasing i increases price; thus bond prices and interest rates move inversely.If market rate equals coupon rate, bond trades at par.If coupon rate exceeds market rate, the bond trades above par—at a premium.If market rate exceeds coupon rate, bond trades below par—at a discount.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias19

20. Zero coupon bonds are “pure discount” securitiesNo periodic coupon payments.Issued at discount from par.Single payment of par value at maturity.PB is simply PV of FV represented by par value, discounted at market rate.PB = Fn / (1+i)^n10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias20

21. Risk factors in bondsYield rewards investor for at least 3 risks:Credit or default risk: chance that issuer may be unable or unwilling to pay as agreed.Reinvestment risk: potential effect of variability of market interest rates on return at which payments can be reinvested when received.Price risk: Inverse relationship between bond prices and interest rates.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias21

22. Bond yields: Set by marketDiscount rate at which bond price equals discounted PV of expected payments.Measure of return ideally capturing impact of Coupon payments Income from reinvestment of coupons Any capital gain or loss10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias22

23. Common Yield MeasuresYield to MaturityExpected YieldRealized YieldTotal Return10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias23

24. Yield to MaturityInvestor's expected yield if bond is held to maturity and all payments are reinvested at same yield.Normally determined by iteration—try different discount rates until PB=present value of future payments. Analogous to IRR of a capital project.The longer until maturity, the less valid the reinvestment assumption.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias24

25. Computing Yield to MaturityInvestor buys 5% percent coupon (semiannual payments) bond for $951.90Bond matures in 3 years. Solve the bond pricing equation for the interest rate (i) such that price paid for the bond equals PV of remaining payments due under the bond.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias25

26. Computing Yield to Maturity Solving either by trial and error or with a financial calculator results in yield to maturity of 3.4% semiannually, or 6.8% annually.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias26

27. Expected YieldPredicted yield for a given holding period (same procedure as YTM, but for some holding period shorter than maturity) Must forecast— Expected interest rate(s) Bond price at end of holding period Plug forecast results into bond pricing formula10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias27

28. Realized YieldInvestor’s ex-post or “hindsight” actual rate of return, given the cash flows actually received and their timing. May differ from YTM due to—change in the amount or timing of promised payments (e.g. default).change in market interest rates affecting premium or discount.10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias28

29. Computing Realized YieldInvestor pays $1,000 for 10-year 8% annual coupon bond; sells bond 3 years later for $902.63.Solve for i such that $1,000 (the original investment) equals PV of 2 annual payments of $80 followed by a 3rd annual payment of $982.63 (the actual cash flows this investor received). 10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias29

30. Computing Realized YieldSolve by trial and error or with a financial calculator results in realized yield of 4.91%10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias30

31. Total ReturnYield metric that considers capital gains or losses as well as changes in reinvestment rate. Find interest rate that compounds initial purchase price to sum of terminal value of bond plus future value of all coupon payments received (based on known or assumed reinvestment rate).10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias31

32. Computing Total ReturnTerminal Value of Bond + Future Value of Reinvested Interest Coupons = Total AccumulatedPB = Total Accumulated / (1+i)^nSolve for i10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias32

33. Total Return – Example Expect to hold a bond for four years, 8% annual coupon. Price today is $1000Expect to sell the bond at 1098.35. Thus we expect interest rates to fall What is the total return if we can reinvest the coupons at 7%?10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias33

34. Total ReturnWhat is the future value of the coupon payments at t=4?N=4, I=7, PV=0, PMT=80  FV = 360.49The future sale price is $1098.35. Thus total cash flows at t=4 is equivalent to $1098.35 + $360.49Find the IRR that shows return on:1000 = (1098.35 + 360.49) / (1 + I ) ^ 4  9.9%10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias34

35. Current yieldInvestors may be holding a bond for only a short period of time (~1 year)In this case, they are interested in the “current yield.”The current yield is the amount of the annual coupon divided by the current market price of the bond10/10/17Bonds and Their Valuation35

36. Current yieldA bond trades today at $900 and pays an annual coupon of $90. What is the current yield on the bond if purchased today?Current yield = Annual coupon / current trading price = 90 / 900 = 10%10/10/17Bonds and Their Valuation36

37. Other bond value measuresYield to call – what is the yield of the bond if it is paid off as of its yield date. Note that the corporation may also pay a premium to face value at the call as compensation to investors for early retirement of the debtThis is a bond feature that would have been known in the indenture and would have been priced in the initial issue price.10/10/17Bonds and Their Valuation37

38. 10/10/17Bonds and Their Valuation38Obtaining Bond InformationOn line bond informationListings include coupon rate, maturity year, current yield, trading volume, closing price, and net change in price from previous day.Also, see Moody’s or Standard & Poor’s bond guides. Or, EDGAR (www.sec.gov) for the indentures and information about the bond contract and issuing firm.

39. 10/10/17Bonds and Their Valuation39The Yield Curve is not FlatWhen the yield curve is not flat (I.e., when observed yields are not the same for all maturities), the correct procedure for valuing a bond promising a stream of known cash payments is to discount each of the payments at the rate corresponding to a pure discount bond of its maturity and then add the resulting individual values.The yield to maturity can be found from this calculation.

40. 10/10/17Bonds and Their Valuation40Example: Bond ValuationSuppose you are valuing a bond that pays annual coupons of 10% on the face value of $1000. The bond matures in three years.The cash flows associated with the bond are as follows:CF at t=1  $100CF at t=2  $100CF at t=3  $1100

41. 10/10/17Bonds and Their Valuation41Example: Bond Valuation You know that the yield of a 1-year pure discount bond is 5.5%, of a 2-year pure discount bond is 6.0% and of a 3-year pure discount bond is 6.5%. What is the price you are willing to pay for the bond? What is the yield to maturity of the bond?

42. 10/10/17Bonds and Their Valuation42Example: Bond ValuationValue each of the cash flows at its respective yield.Price = $100 / (1+.055) + $100 / (1.06)^2 + $1100 / (1.065)^3 = $1094.42What is the yield to maturity on this bond:N=3, PV= -$1094.42, PMT=$100, FV=$1000  I= 6.4389

43. 10/10/17Bonds and Their Valuation43Variation in Bond PricesBond prices (and YTMs) will vary with many factors:Creditworthiness of the issuerMaturityCoupon rateTax considerationsBond features – callability, convertibility, etc.Closeness to maturity

44. Bond Price VolatilityNext class!10/10/17Chapter 5 Kidwell, Blackwell, Whidbee & Sias44