# FIN 472 Fixed-Income Securities Debt Instruments

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1 FIN 472 Fixed-Income Securities Debt Instruments Professor Robert B.H. Hauswald Kogod School of Business, AU The Most Famous Bond? Bond finance raises the most money fixed income instruments types of bonds and loans Valuation: the two twins price and return: yield-to-maturity pricing Learning objectives: pricing simple bonds and introduction to risk inherent in different bonds FT and bond reporting 1/12/2016 Debt Instruments Robert B.H. Hauswald 2

2 Cash Flow Valuation The building blocks of valuation interest and discount rates future value and present value financial decision making: NET Present Value Valuation formulae: discrete and continuous simple cash flows mind the dates! 1/12/2016 Debt Instruments Robert B.H. Hauswald 3 Valuation Fundamentals Present Value of Future Cash Flows Link Risk & Return Expected Return on Assets Valuation 1/12/2016 Debt Instruments Robert B.H. Hauswald 4

3 The Basic Valuation Insight P 0 = CF (1 + r 1 ) 1 + CF (1 + r 2 ) CF (1 + r n ) n P 0 = Price of asset at time 0 (today) CF t = cash flow expected at time t r = discount rate (reflecting asset s risk) n = number of discounting periods (usually years) This model can express the price of any asset at t mathematically. 1/12/2016 Debt Instruments Robert B.H. Hauswald 5 Valuation of Financial Instruments First Principles: Value of financial securities = PV of expected future cash flows To value bonds and stocks we need to: Estimate future cash flows: Size (how much) and Timing (when) Discount future cash flows at an appropriate rate: The rate should be appropriate to the risk presented by the security. 1/12/2016 Debt Instruments Robert B.H. Hauswald 6

4 Fixed Income Instruments Contractually fixed cash flows at certain (fixed) future dates conceptual: portfolio of cash flows legal: backed by general credit of issuer recovery right in case of missed payment or default examples: CDs, loans, CP, bills, bonds Valuation questions the price is right? what is return and borrowing cost? how to compare returns across instruments? 1/12/2016 Debt Instruments Robert B.H. Hauswald 7 Bond Types Bonds: standardized fixed income security generally tradable, long term (10+ or 15+ years) standardized: same conditions for all owners of security Debenture: Unsecured Bond of 15 years or more backed by general credit of the firm Note: typically 3-10 years unsecured Bill: less than 1 Year duration does not pay coupon: interest at the end types of bills: T-bills, commercial paper 1/12/2016 Debt Instruments Robert B.H. Hauswald 8

5 Loan Types Bank loan: terms are not standardized negotiable, flexible: what does this mean for price? Pure discount loans: corresponds to what FI security? Borrower pays a single lump sum (principal and interest) at maturity Interest only: corporate, sovereign bonds borrower pays interest only (coupon) each period and entire principal at maturity. Amortized loans: consumer (mortgage) loans borrower repays part or all of principal over the life of the loan 1. fixed amount of principal repaid each period: uneven payments 2. fixed payments: uneven principal reduction. 1/12/2016 Debt Instruments Robert B.H. Hauswald 9 Bond Characteristics: Jargon Coupon: Principal: Par (Face) Value: Coupon Rate: Maturity: Price/Proceeds: Current Yield: Yield-to-Maturity: All-in Cost: Interest Payment Amount Borrowed Amount Repaid at End of Loan Coupon / Face Value Years Until Repayment Amount Raised Coupon / Current Price Lifetime return of the bond Lifetime cost of the bond 1/12/2016 Debt Instruments Robert B.H. Hauswald 10

6 Bond Example Consider a U.S. government bond listed as 6 3/8 of December The Par Value of the bond is \$1,000. Coupon payments are made semi-annually (June 30 and December 31 for this particular bond). Since the coupon rate is 6 3/8 the payment is \$ On January 1, 2002 the size and timing of cash flows are: \$ \$ L \$ \$1, /1/ 02 6 / 30 / / 31/ 02 6 / 30 / / 31/ 09 1/12/2016 Debt Instruments Robert B.H. Hauswald 11 Bond or Loan Structure Covenants: legal provisions giving bondholders right to specific actions such as forcing bankruptcy Security: pledged assets committed to paying off debt, Mortgage Bond Seniority: order of payment in bankruptcy 1st Secured debt, Senior Debt, then Subordinated Debentures. Call provision: enables corporation to repay and retire the debt at will before maturity (on coupon dates only) Sinking funds or serial maturities: fund that firm contributes cash to for repayment. investors know in advance when each bond series will be repaid Investment Grade Bonds: Bonds rated Baa or higher by Moody's or BBB or higher by Standard & Poors. 1/12/2016 Debt Instruments Robert B.H. Hauswald 12

7 Pure Discount Bonds Information needed for valuing pure discount bonds: Time to maturity (T) = Maturity date - today s date Face value (F) Discount rate (r): return on bond = yield to maturity \$0 \$0 L \$0 \$F T 1 T Present value of a pure discount bond at time 0: PV F = ( 1+ r) 1/12/2016 Debt Instruments Robert B.H. Hauswald 13 T Pure Discount Bonds: Example Find the value of a 30-year zero-coupon bond with a \$1,000 par value and a YTM of 6%. \$0 \$0 L \$0 \$1, PV F (1 + r) = T = \$1,000 (1.06) 30 = \$ /12/2016 Debt Instruments Robert B.H. Hauswald 14

8 Bond Pricing Information needed to value level-coupon bonds: Coupon payment dates and time to maturity (T) Coupon payment (C) per period and Face value (F) Discount rate: YTM = r \$C \$C \$C \$ C + \$F L 0 1 Value of a Level-coupon bond = PV of coupon payment annuity + PV of face value PV C = r (1 + r) 1/12/2016 Debt Instruments Robert B.H. Hauswald 15 T T 1 F + (1 + r) T T Bond Pricing Illustration Find the present value (as of January 1, 2002), of a 6-3/8 coupon T-bond with semi-annual payments, and a maturity date of December 2009 if the YTM is 5-percent. On January 1, 2002 the size and timing of cash flows are: 1/1/ 02 \$ / 30 / 02 \$ L 12 / 31/ 02 \$ / 30 / 09 \$1, / 31/ 09 \$ PV = (1.025) \$1,000 + (1.025) = \$1, /12/2016 Debt Instruments Robert B.H. Hauswald 16

9 Bond Pricing Exercise Suppose Harley Davidson Co. issued a global bond 20 years to maturity, notional face value \$1,000 Annual coupon is \$110. (11% Coupon Rate) Similar bonds have a yield to maturity of 11%. What is the bond s fair value? Present value of face value = \$1,000/(1.11) 20 = \$ Present value of coupons = \$110 x (1-1/(1.11) 20 )/.11 = \$110 x = \$ Adding the discounted face value and coupons (rounding error): BOND VALUE = \$ \$ = \$1000 NB: if the YTM and coupon rate are the same, the bond must be trading at PAR 1/12/2016 Debt Instruments Robert B.H. Hauswald 17 Bond Values and Yields Yield to Maturity: YTM, the required market discount rate that sets the discounted cash flows = bond s current Market Price calculated as the bond s internal rate of return (IRR) r Bond s typical cash flows: coupons and face value Example 1: Zero - Coupon Bond - Find the Value? Single Payment 10 years from now, \$1,000, Yield to maturity on comparable bonds is 9%. Example 2: Zero - Coupon Bond - Find the YTM Single Payment 10 years from now, \$1,000, Current Bond price: \$400 Given price, how to find the yield-to-maturity (bond return)? 1/12/2016 Debt Instruments Robert B.H. Hauswald 18

10 Interest, Price, Return, Yield Comparing funding costs or investment returns across different maturities, market segments and instruments unified measure required for lifetime borrowing cost: YIELD example: 100, 100, 8% annual coupon, 15Y Borrowing cost/return measured by bond s IRR discount rate equating all cash flows to 0 including issue cost implies: yield-to-maturity (return to investor), all-in cost (borrowing cost to issuer taking into account all fees) Yield-to-maturity: internal rate of return (discount rate) equating all cash flows (proceeds debt service) to 0 formula: y : 1,000 T Ct P + t 1 = t ( 1 + y) ( 1 + y) T 0 = 1/12/2016 Debt Instruments Robert B.H. Hauswald 19 0 Finding the Yield to Maturity It is usually a trial and error process to find the YTM: solving a non-linear equation A financial calculator or tables is the quickest and easiest method Even better: EXCEL Facts of life about bond price and YTM: bond sells at a premium: YTM below coupon rate bond sells at a discount: YTM above coupon rate bond prices and YTM are inversely related! 1/12/2016 Debt Instruments Robert B.H. Hauswald 20

11 Term Structure of Interest Rates Relationship between yield and maturity is called the Term Structure of Interest Rates Graphical depiction is called a Yield Curve: Bloomberg Usually, yields on long-term securities are higher than on short-term securities: premium for uncertainty and inflation Generally look at risk-free Treasury debt securities Yield curves normally upwards-sloping Long yields > short yields Is often flat or inverted prior to recession The Federal Reserve Board sets what interest rate? 1/12/2016 Debt Instruments Robert B.H. Hauswald 21 Discount Bonds/Premium Bonds Discount bond: selling for less than par YTM is greater than the coupon rate. Premium bond: selling for more than par YTM is less than the coupon rate Examples: Discount/Premium bonds Example 1: If the YTM on bonds similar to that of the Harley Davidson Co. (\$1,000 bond, \$110 coupon, 20 years to maturity) were 13% instead of 11% the bonds would trade at? Example 2: If the YTM on bonds similar to that of the Harley Davidson Co. (\$1,000 bond, \$110 coupon, 20 years to maturity) were 9% instead of 11% the bonds would trade at? 1/12/2016 Debt Instruments Robert B.H. Hauswald 22

12 Bond Value \$ YTM and Bond Value When the YTM < coupon, the bond trades at a premium. When the YTM = coupon, the bond trades at par /8 Discount Rate When the YTM > coupon, the bond trades at a discount. 1/12/2016 Debt Instruments Robert B.H. Hauswald 23 Bond 1: Discount Bond Present value of Principal = \$1,000/(1.13) 20 = \$86.78 Annuity present value of coupons = \$110 x (1-1/(1.13) 20 )/.13 = \$110 x = \$ Price = \$ \$ = \$ ==> The difference between this price, \$859.50, and the par price of \$1,000 is \$ This is equal to the present value of the difference between YTM coupons and Harley Davidson's coupons: \$130 - \$110 = \$20 per year for 20 years at 13% = \$20 x PVIFA(13%,20) = \$20 x = \$ /12/2016 Debt Instruments Robert B.H. Hauswald 24

13 Bond 2: Premium Bond Present value of principal = \$1,000/(1.09) 20 = \$ Annuity present value of coupons: = \$110 x (1-1/(1.09) 20 )/.09 = \$110 x = \$1, Adding the discounted face value and coupons together = \$ \$1, = \$1, The difference between this price, \$1, and the par price of \$1,000, \$182.57, = present value of the difference between Harley Davidson's coupons and coupon of bond at PAR: = \$110 - \$90 = \$20 per year for 20 years at 9% = \$20 x PVIFA(9%,20) = \$20 x = \$ /12/2016 Debt Instruments Robert B.H. Hauswald 25 Bonds: Premiums & Discounts What happens to bond values if required return is not equal to the coupon rate? The bond's value will differ from its par value R > Coupon Interest Rate P 0 < par value = DISCOUNT R < Coupon Interest Rate P 0 > par value = PREMIUM 1/12/2016 Debt Instruments Robert B.H. Hauswald 26

14 Rules for Bond Pricing 1. Bond prices and market interest rates move in opposite directions. 2. When coupon rate = YTM, price = par value. When coupon rate > YTM, price > par value (premium bond) When coupon rate < YTM, price < par value (discount bond) 3. A bond with longer maturity has higher relative (%) price change than one with shorter maturity when interest rate (YTM) changes. All other features are identical. 4. A lower coupon bond has a higher relative price change than a higher coupon bond when YTM changes. All other features are identical. 1/12/2016 Debt Instruments Robert B.H. Hauswald 27 Summary Bond valuation: focus on the Cash Flows Split valuation problem into 2 parts the PV of the coupon payments the PV of the final payment: redemption Fair price of bonds = sum of these 2 amounts While cash flows are fixed, market value is not interest rate and yield volatility how to simultaneously find yields and prices? 1/12/2016 Debt Instruments Robert B.H. Hauswald 28

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