Interest Rates and Bond Valuation

1. Interest Rates and Bond Valuation Chapter 6

2. Key Concepts and Skills • Know the important bond features and bond types • Understand bond values and why they fluctuate • Understand bond ratings and what they mean • Understand the impact of inflation on interest rates • Understand the term structure of interest rates and the determinants of bond yields

3. Chapter Outline • Bonds and Bond Valuation • More on Bond Features • Bond Ratings • Some Different Types of Bonds • Bond Markets • Inflation and Interest Rates • Determinants of Bond Yields

4. Issuer (Seller) of Bonds (Borrower) = “Bond Issuer” • Bonds = Debt = Liability = Long-term debt • 1 Bond usually means the corporation borrows $1000 (face value) • Corporations usually issue many Bonds • Bond Issue: • The total number of bonds that a corporation issues at the same time, in denominations of $1,000 or $5,000 each • Like any contractual debt: • Bond issuer pays periodic interest to the bondholder • Bond issuer pays the face value back at the end of the bond term

5. Issuer (Seller) of Bonds (Borrower) = “Bond Issuer” • When you issue a bond, you borrow the money, then use the money to buy assets that earn more cash than the cash you have to pay out to the bondholder • Leverage • Example: • Borrow money at 8% interest and buy a machine that earns the corporation 13% • The difference between 13% and 8%, or 5%, is left for the stockholders

6. Buyer of Bonds (Lender) = “Bondholder” • Bonds = Asset • 1 Bond usually means the borrow lends money to the corporation or government • Like any contractual debt: • Bondholders are paid periodic interest for loaning money to the corporation and are paid back the face value at the end of the bond term • When you buy a bond you are paying for a future steam of cash flow

7. Bond Vocabulary: • Face value = par value = loan repayment at maturity = FV • Annual interest payments = “annual coupon” • Coupon is from the days when you presented coupon to get paid interest • Annual interest rate (not discount rate) = coupon rate = annual interest rate for calculating interest payments = annual coupon/face value • Number of interest payments per year = n • Periodic rate (not discount rate) = periodic coupon rate = (annual coupon rate)/n • The book is inconsistent with the use of “coupon” (sometimes annual, sometimes semi-annual) • Periodic interest payment = periodic rate*face = PMT • Years until maturity = term of bond = years until paying back face value and last periodic interest payment = x • Maturity = specified date on which principal is repaid

8. Bond Vocabulary: • Yield To Maturity (YTM) = discount rate used to value bond = i = YTM • YTM = Bond Yield = Required Return = Market Rate = Rate required in the market on a bond • YTMs are quoted like APRs • YTM = (Period Discount Rate) * n • Example: YTM = 10% and bond pays semiannual interest payments, then period discount rate = YTM/n = .10/2 =.05 • Effective Annual Yield on the Bond = (1+.10/2)2 = .1025

9. Bonds • Bonds are interest only loans • Corporations/Governments borrow money, pay interest each period, then pay back face amount at end of bond term • Corporations/Governments plan to issue bonds and then set the coupon rate, but by the time they actually issue the bond the financial markets have already calculated a discount rate for the future values that is often different than the coupon rate • Corporations/Governments issue bonds and get the “cash in” (Bonds sold in primary market) • Many Bonds from Corporations/Governments can be traded in the financial markets (Bonds sold in the secondary market)

10. Bonds • Each bond has a price expressed as a percentage of the face value: • For example, 103 means 1.03 times the face value of the bond • When the corporation issues the $1,000 face-value bond, it receives $1,030 • At maturity, the corporation pays back only the face value of $1,000 • 103 and 103% and 1.03 all convey the same meaning  The bond is selling for 3% above the face value

11. Example 1 • On January 1, Cox Construction Corp. issues 750 10-year bonds with a face of $1000 with a coupon rate of 9% at 103, with interest payable semiannually, on June 30 and December 31

12. This Bond with its 9% coupon, is priced to yield 8.74% at $1,030

13. But If The Loan Has A Face Value Of $750,000, Why Did The Bondholder Pay $772,500?

14. If a corporation offers a rate of interest that is higher than the market rate for similar securities, investors may be willing to pay a premium for the bond • If a corporation offers a rate of interest that is lower than the market rate for similar securities, investors will demand a discount on the bond

15. What Are Similar Securities? • Similar securities are bonds or other investment vehicles issue by other corporations (different than the one being considered) that have similar business and financial risks • The similarities could be: • Similar credit ratings • Similar business activities • Similar capital structure

16. Bond Prices YTM > Coupon Rate YTM < Coupon Rate

17. Definitions • Premium • The excess of the price received over the face value of a bond • YTM < Coupon Rate • “Bond sold at a premium” • Discount • The amount by which the issue price is less than the face value of a bond • YTM > Coupon Rate • “Bond sold at a discount”

18. The Issuance of Bonds at a Discount: Example 2 • On January 1, Muller, Inc., issues 700 6%, 20-year bonds with a face value of $1,000, at 96, with interest to be paid semiannually, on June 30 and December 31

19. This Bond with its 6% coupon, is priced to yield 6.25% at $960

20. Bond Price (Valuation) from Cash Flow Perspective

21. Excel • Bond Valuation from Bondholder’s Point of View: • =PV(rate,nper,pmt,fv,type) • =PV(YTM/n,n*x,PMT,FV,0) • Bond Valuation from Bond Issuer’s Point of View: • =PV(rate,nper,pmt,fv,type) • =PV(YTM/n,n*x,-PMT,-FV,0) • Finding YTM rate from Bondholder’s Point of View: • =RATE(nper,pmt,pv,fv,type,guess) • =RATE(n*x,PMT,-PV,FV,0)

22. Example 3

23. Example 3

24. Example 3 CF Is From Point Of View Of Issuer

25. Bond Values And Why They Fluctuate • Bond Valuation: • As time passes, interest rates change in the market place • As new information about the company, the industry, the economy comes out, interest rates change • As time passes the amount of cash paid out to the bondholder does not change • Because of this the value of the bond will fluctuate • Rates , Bond Value  • Rates , Bond Value 

26. Graphical Relationship Between Price and YTM

27. Valuing a Discount Bond with Annual Coupons Payments (Example 4) • Consider a bond with a coupon rate of 10% and coupons paid annually. The par value is $1000 and the bond has 5 years left until maturity. The yield to maturity is 11%. What is the value of the bond  What is the price to you, buying in the secondary market? • Using the formula: • B = PV of annuity + PV of lump sum • B = 100[1 – 1/(1.11)5] / .11 + 1000 / (1.11)5 • B = 369.59 + 593.45 = 963.04 • Answer: “You would be willing to pay $963.04 cash out (negative) for the future cash flows.” or said this way: “The bond with a 10% coupon is priced to yield 11% at $963.04.”

28. Valuing a Premium Bond with Annual Coupons Payments (Example 5) • Suppose you are looking at a bond that has a 10% annual coupon rate and a face value of $1000. There are 20 years to maturity and the yield to maturity is 8%. What is the value of the bond  what is the price to you? • Using the formula: • B = PV of annuity + PV of lump sum • B = 100[1 – 1/(1.08)20] / .08 + 1000 / (1.08)20 • B = 981.81 + 214.55 = 1196.36 • Answer: “You would be willing to pay $1196.36 cash out (negative) for the future cash flows.” or said this way: “The bond with a 10% coupon is priced to yield 8% at $1196.36.”

29. Interest Rate Risk • The risk that arises for bond owners from fluctuating interest rates • How much interest rate risk a bond has depends on: • How sensitive its price is to interest rate change • The sensitivity depends on two things: • All things being equal, the longer the time to maturity, the greater the interest rate risk • All things being equal, the lower the coupon rate, the greater the interest rate risk

30. Interest Rate Risk And Time To Maturity

31. Interest Rate Risk To Loss Of Principal (current price) • Longer time to maturity • Small changes in market rate have substantial affect on bond value • Face value is discounted over many periods and thus compounding magnifies small interest rate changes • Lower Coupon rate • Bond with lower coupon rate is proportionally more dependent on the face value • (Bond with larger coupon rate has a larger cash flow early in life, so value less sensitive to discount rate)

32. Interest Rate Risk Increases At A Decreasing Rate

33. Computing YTM • Yield-to-maturity is the rate implied by the current bond price • Finding the YTM requires trial and error (iteration) if you do not have a financial calculator and is similar to the process for finding i with an annuity • If you have a financial calculator, enter N, PV, PMT and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign)

34. YTM with Annual Coupons (Example 6) Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928.09 Will the yield be more or less than 10%?

35. YTM with Semiannual Coupons (Example 7) Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1197.93 Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there?

36. Use One Bond YTM To Find Price Of Another Bond: Example 8 Below Market rate = discount Above = premium

37. Bonds and Stocks: • Like stock, bonds bring capital (money) into the corporation so that it can invest in profitable projects • Bondholders are creditors • They have a fixed claim to cash flow • Stockholders are owners • They have a residual claim to cash flow

38. Bonds and Stocks • Debt is not an ownership interest in the firm • Creditors do not have voting rights • Interest is tax deductible • Dividends are not tax deductible • Unpaid debt is a liability • Legal claim against assets • If debt is not paid creditors have the legal claim to assets before shareholders • One of the costs of issuing debt is the possibility that you will not be able to make interest payments  creditors force firm into bankruptcy  firm is terminated • This does not arise when equity is issued • Corporations try to create hybrid financial instruments that are Debt/Equity in order to have: • Tax benefits of debt • Bankruptcy benefits of equity

39. Debt Not an ownership interest Creditors do not have voting rights Interest is considered a cost of doing business and is tax deductible Creditors have legal recourse if interest or principal payments are missed Excess debt can lead to financial distress and bankruptcy Equity Ownership interest Common stockholders vote for the board of directors and other issues Dividends are not considered a cost of doing business and are not tax deductible Dividends are not a liability of the firm and stockholders have no legal recourse if dividends are not paid An all equity firm can not go bankrupt Differences Between Debt and Equity

40. Bond Terms and Types • Bonds = Long-term debt • Privately placed • Directly placed with the lender • Public-issue bonds • Offered to the public • Finance jargon” • Long-term debt = funded debt • Short-term debt = unfunded debt • Example: “A firm planning to fund its debt requirements may be replacing short-term debt with long-tern debt”

41. Bond Terms and Types • Trustee (Investment Bank, other…) • Appointed by the corporation to represent bondholders • Must make sure terms are obeyed • Must manage sinking fund • Must represent bondholders in default • Indenture • “The written agreement between the corporation and the lender detailing the terms of the debt issue”

42. Bond Types • Registered Form • The form of bond issue in which the registrar of the company records ownership of each bond • Payment is made directly to the owner of the bond • Bearer Form • The form of bond issue in which the bond is issued without record of the owner’s name • Payment is made to whoever holds the bond • Uncommon in the USA

43. Bond Types • Security: • Generic term that means Stocks or Bonds or other investment vehicles that are backed by an asset • A document indicating ownership or creditorship; a stock certificate or bond • Dictionary definition of Security: • Something deposited or given as assurance of the fulfillment of an obligation; a pledge; collateral

44. Bond Types • Debt securities are classified according to the collateral and mortgages used to protect the bondholder • Securities Backed By Collateral • Collateral = any asset pledged on the debt (often means assets such as stocks or bonds – financial assets) • If the borrower does not pay the interest and principal to the bondholder, the bondholder can take the collateral • Mortgage Securities • Debt secured by a mortgage on real assets (property, but not cash or inventory) of the borrower • Called: • Mortgage Trust Indenture, or Trust Deed • Most utility and railroad bonds are secured by a pledge of assets

45. Bond Types • Unsecured Debt • These creditors have a claim on property not otherwise pledged • Debenture • Unsecured debt (maturity >= 10 years) • Most financial and industrial companies’ public bonds are debentures • Note • Unsecured debt (maturity < 10 years) • Subordinate Debt • Must give preference to superior debt • Debt is not subordinate to equity

46. Bond Types • Sinking Fund • An account managed by the trustee for the purposed of repaying the bonds, or early bond redemption • Bond Issuer must put away some money each period to save up in order to pay off the bond • Protective Covenant • A part of the indenture limiting certain actions that might be taken in order to protect the lender • Negative (thou shalt not): • Example: Limit the amount of dividends paid • Positive (thou shalt): • Example: CA/CL must be greater than 1.5

47. Bond Types • Call Provision • An agreement giving the corporation the option to repurchase the bond at a specific price prior to maturity • Call Premium (Pay for the Option) • The amount by which the call price > par value • Example: Bond face = $1,000, Call Price = $1,100 • Call Price goes down over time • Deferred Call Provision • Can call only after a certain date • Call Protected Bond • Can’t be redeemed by issuer • Make-Whole Call • When bond called, bondholder gets PV of future cash flows at a reasonable rate • Derivative security jargon: • Call = Buy • Put = Sell

48. Financial Markets • Primary Markets • Original sale of equity or debt • Corporation issues security • Secondary Markets • After original sale of equity or debt • You sell/buy security • Dealer Markets (Over-the-counter markets (OTC)) • Dealers buy and sell for themselves • Most debt is sold this way • Example: NASDAQ • Auction Markets (Exchanges) • Brokers and agents match buyers and sellers • Most of the large firms’ equity is sold this way • Example: NYSE

49. Bond Characteristics and Required Returns • The coupon rate depends on the risk characteristics of the bond when issued • Which bonds will have the higher coupon, all else equal? • Secured debt versus a debenture • Subordinated debenture versus senior debt • A bond with a sinking fund versus one without • A callable bond versus a non-callable bond

50. Bond Ratings And What They Mean • Bond Rating firms: • Moody’s • Standard and Poor’s (S&P) • They rate: • The likelihood of default • The probability that creditors are protected • They ask they question: What is the risk associated with the firm issuing the debt? • They do not rate the probability of bond value change due to interest rate risk • The Debt Crisis of 2007 shows that Ratings can be less than accurate: • How do they take risky loans and repackage them to get a AAA “Super Senior” rating? (That’s what they did!)