1 I. Asset Valuation The value of any asset, whether it is real or financial, is the sum of all expected future earnings produced by the asset. 2 1
II. Bond Features and Prices Definitions Bond: a certificate showing that a borrower owes a specified sum. It obligates the borrower (bond issuer) to make specified payments (interest + principal payments) to the lender (bondholder). Face Value ( Par Value or Maturity Value ): The amount that is paid to the bondholder at the maturity of the bond. Coupon: the stated interest payment on a bond. 3 Face Value & Coupon Rate 2
Bond Coupons Coupon rate: the annual coupon as a percentage of face value. Maturity: the length of time until the debt contract expires. Default: failing to pay a regular coupon or the face value. Bond contracts are contractual obligations. An issuer who default on its bonds is subject to legal actions on behalf of the bondholders. 6 3
The Bond Indenture Contract between the company and the bondholders that includes: The basic terms of the bonds The total amount of bonds issued A description of property used as security, if applicable Descriptions of provisions, if any Details of protective covenants 7 Bond Classification Security Collateral secured by financial securities Mortgage secured by real property, normally land or buildings Debentures unsecured Notes unsecured debt with original maturity less than 10 years Seniority Senior bonds must be repaid before subordinated (junior) bonds 8 4
Bond Example Several years ago, the U.S. Treasury raised money by selling 6.5 percent coupon, 2015 maturity, Treasury bonds ( 6.5s of 2015 ). Each bond has a face value of $1,000. With the coupon rate of 6.5 percent, the government makes coupon payments of 6.5% of $1,000, or $65 each year. When the bond matures in May 2015, the government must pay the $1,000 face value of the bond in addition to the final coupon payment. 9 III. How Bond Value Is Determined A bond pays 8 percent coupons on its face value of $1,000. It makes annual coupon payments and matures in five years. If the appropriate discount rate for the cash flows from this bond is 10%, what is the fair value of this bond? 10 5
$72.73 $66.12 $60.11 $54.64 $670.60 $924.20 11 Bond Valuation Actually, calculating the value of a bond is not different from calculating the present value of a stream of future cash flows. Now, with a couponpaying bond, the stream of future cash flows includes coupon payments and the payment of the face value. 12 6
Bond Value Formula Annuity PV formula FV: Face Value C : Coupon r : Discount Rate T : Time to Maturity 13 Bond Value Formula The value of a bond with coupon C, face value FV, maturity T, and yield, y : 14 7
Most corporate debt securities are coupon-paying bonds. They usually pay semiannual coupons. Also, long-term government securities such as Treasury notes and Treasury bonds make semiannual coupon payments. 15 Bond Valuation Example ABC, Inc. bonds have a $1,000 face value. Its annual coupon is $120 and the bonds mature in 10 years. The market s required return on similar bonds is 11% 1. Use the bond value formula $120 [1 - (1/1.11 )10 ]/0.11 + $1,000/(1.11) 10 = $1,058.89 2. Use the financial calculator PMT = 120; N = 10; I/Y = 11; FV = 1,000; CPT PV = -1,058.89 16 8
Bond Valuation Example Suppose that in January of 2013 a firm raised money by selling 10% coupon, 10-year maturity corporate bonds. The coupons are paid semiannually. Suppose that you decided (in January, 2013) to buy these 10% coupon bonds. What is the fair value of the bond if the market interest rate for this bond is 8%? The par value of this bond is $1,000. 17 Solution Face value = $1,000 Annual Coupon=$1,000 x 0.1 = $100 Semi-annual coupon = $50 Number of coupon payments = 20 Bond annual interest rate = 8% Semi-annual rate = 4% Value of the bond = = 18 9
Zero-Coupon Bonds Some bonds pay no coupons. These securities are called zero-coupon bonds, pure-discount bonds, or deep-discount bonds. The interest income for the investors from these securities is thus realized when the bond matures. Short-term U.S. government debt securities (Treasury bills) and many other money market securities belong to this category. 19 Valuation of Zero Coupon Bonds 20 10
Zero Coupon Bond Example Consider a bond that pays a face value of $10,000 and matures in one year. If the discount rate for this bond is 5 percent, what is the fair value of this bond? V = 21 Quiz What will be the market price of a 8% bond with the face value of $1,000 and 10 years of maturity left. Coupons are paid quarterly. The yield to maturity for the bond is 10% at the market. What will be the market price of the bond five years from now If the yield on the bond does not change? Quarterly coupon rate = 8% 4 = 2% Hence, quarterly coupon = $1,000*0.02 = $20 Quarterly coupon amount = 10% 4 = 2.5% PV = FV (in 5 years) = 22 11
IV. Bond Price and Yield to Maturity The yield to maturity is defined as the discount rate implied by the bond valuation equation, given the market value as the fair bond value. Put different, a bond s yield to maturity is the discount rate that makes the present value of the bond s payments equal to its current market price. Yield to maturity (YTM) can be interpreted as the rate required by investors in the market on a bond. YTM is also called bond s yield for short. 23 Yield to Maturity Market Price where: C = coupon payment FV = face value T = number of periods until the bond matures y = yield to maturity or the market s required return on the bond 24 12
Exercise: Finding the YTM Suppose today is January 2, 2018. ACME bond which matures in 10 years currently sells for $1,154. The $1,000 face-value bond has a coupon rate of 6% with semi-annual coupon payments. What is its yield to maturity? Solution: ytm calculation 25 V. Relationship between Bond Price and YTM Bond price sensitivity to changes in bond yields is an important concern for bond investors. We will learn: How bond price reacts to yield changes. How bond maturity affects the bond price sensitivity to yield changes. The relationship between face value and bond price 26 13
Bond Price Sensitivity to Yield Change $1,000 27 The effect of YTM and Coupon Rate on the Relation between Face Value and Market Value. Suppose a bond has the face value of $1,000, maturity of 5 years, and a coupon rate of 5%, what will happen to the price of the bond if the yield to maturity changes from 8% to 12%? Yield to Maturity 12% 10% Market Value What the bond is called 8% 28 14
Maturity and Bond Price Sensitivity 29 VI. Interest Rate Risk Price Risk Change in price due to changes in interest rates Long-term bonds have more price risk than short-term bonds Low coupon rate bonds have more price risk than high coupon rate bonds Reinvestment Rate Risk Uncertainty concerning rates at which cash flows can be reinvested Short-term bonds have more reinvestment rate risk than long-term bonds High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds 30 15
VII. Determination of Bond Yields The yield to maturity of an individual bond consists of the market s base rate (the default risk-free rate or the pure time value of money) for the specific maturity of the bond and the premium for the risk of default for the bond. Bond default risk is determined by many factors, primarily by default risk. Rating agencies such as Standard & Poors and Moody s periodically evaluate default risks of various bonds and report their ratings. Taxability premium tax payable vs. tax exempt Liquidity premium - bonds that have more frequent trading will generally have lower required returns 31 Inflation and Interest Rates Real rate of interest change in purchasing power Nominal rate of interest quoted rate of interest, change in purchasing power and inflation The ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation. 32 16
The Fisher Effect The Fisher Effect defines the relationship between real rates, nominal rates, and inflation. (1 + R) = (1 + r)(1 + h), where R = nominal rate r = real rate h = expected inflation rate Approximation R = r + h 33 The Fisher Effect: Example If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate? R = (1.1)(1.08) 1 =.188 = 18.8% Approximation: R = 10% + 8% = 18% Because the real return and expected inflation are relatively high, there is a significant difference between the actual Fisher Effect and the approximation. 34 17
U.S. Term Structure as of Oct 5, 2018 U.S. Treasury Yield Curve As of Oct. 5 2018 3.6 3.4 3.2 3 2.8 2.88 2.99 3.07 3.18 3.23 3.34 3.4 2.6 2.64 2.4 2.41 2.2 2 2.15 2.23 36 18
Korea Government Bond Yield Curve (Aug. 28, 2017) Bond Rating Investment-Quality Bond Ratings Low Quality, speculative, and/or Junk High Grade Medium Grade Low Grade Very Low Grade Standard & Poor s AAA AA A BBB BB B CCC CC C D Moody s Aaa Aa A Baa Ba B Caa Ca C C capacity to pay is extremely or very strong capacity to pay is strong or adequate, but more susceptible to changes in circumstances Considered speculative with respect to capacity to pay. Highly uncertain repayment and, in many cases, already in default, with principal and interest in arrears 38 19
Reuters Corporate Spreads Rating 1 yr 2 yr 3 yr 5 yr 7 yr 10 yr 30 yr Aaa/AAA 9 11 22 31 47 59 81 Aa1/AA+ 17 25 26 40 55 68 90 Aa2/AA 19 32 34 45 58 71 94 Aa3/AA- 20 34 35 49 62 72 100 A1/A+ 38 43 47 56 70 84 108 A2/A 41 46 49 58 72 86 112 A3/A- 45 49 52 62 75 89 115 Baa1/BBB+ 57 67 75 83 112 134 161 Baa2/BBB 60 75 83 88 119 142 168 Baa3/BBB- 67 80 85 93 124 149 173 Ba1/BB+ 180 190 200 210 230 250 270 Ba2/BB 190 200 210 220 240 260 280 Ba3/BB- 200 210 220 230 250 270 290 B1/B+ 260 270 280 310 350 390 440 B2/B 270 280 290 320 360 400 450 B3/B- 280 290 300 330 370 410 460 Caa/CCC 445 455 465 490 500 510 540 Note: Reuters Evaluator spreads for bullet bonds 39 VIII. Various Bond Types There are many different types of provisions that can be added to a bond, and many bonds have several provisions it is important to recognize how these provisions affect required returns. Plain vanilla bonds or straight bonds (no special features at all) Income bonds 40 20
Call and Put Options Callable Bond: Bonds are redeemable by bond issuer at a pre-specified price (usually at the face value) from bond holders Puttable Bond: Bondholders hold an option to sell back the bonds at a pre-determined price to the bond issuer. Q. All else being equal, would a bond with call feature be priced higher or lower than a straight bond? What about a put bond (compared with a plain vanilla bond)? 41 Bond price vs. yield of a callable bond (vs. straight bond) 21
Indexed Bonds Coupon rate and face value are linked to a price index Example: TIPS(Treasury Inflated Protected Security) Example: Principal and Interest Payments for a TIPS of 3 year maturity with FV of $1,000 & Coupon Rate of 4% (Annual Payment) $1,000*1.02 $1,020*1.03 $1,020*0.04 Question Two bonds have identical times to maturity and coupon rates. One is callable at 105, the other at 110. Which should have the higher yield to maturity? Why? 22
Question The following two bonds were issued at par. Ignoring credit quality, find three reasons why ABC has a higher coupon rate than XYZ. Bond ABC XYZ Issue Size $1.2 Billion $159 Million Maturity 10 years 20 years Coupon 9% 10% Collateral First Mortgage Debenture Callable Not In 10 years Call Price None 110 23