3 -1 Bond Valuation n. Application of present value techniques to bonds and stocks n. Pricing and Valuation are the core issues in finance
3 -2 Some standard forms of Bonds n C=coupon, F=face value, T=maturity date n Pure Discount or Zero-coupon bonds l PV=FV/(1+r)T n Level-coupon bonds l PV=C/1+r + C/(1+r)2 + • • • + C/(1+r)T + F/(1+r)T n Consols l PV=C/r n Floaters n Convertibles
3 -3 Bond Features n Coupon Payments: Regular interest payments l Semi annual for most US corporate bonds l Types of Coupon payments • Fixed Rate: 8% per year • Floating Rate: 6 -month Treasury bill rate + 100 basis points.
3 -4 Bond Features n Face or Par Value: amount of money to be repaid at end of loan l $1, 000/bond n Maturity: number of years from issue date until principal is paid n Coupon Rate: annual coupon / face value
Features of a May Department Stores Bond 3 -5 Terms Amount of issue $200 million Date of issue 8/4/94 Explanations The company will issue $200 million worth of bonds. The bonds were sold on 8/4/94. Maturity 8/1/24 The principal will be paid in 30 years. Face Value $1, 000 Denomination of the bond is in $1, 000 Annual coupon 8. 375 Each bondholder will receive $83. 75 per bond per year (8. 375% of the face value). Offer price 100 The offer price will be 100% of the $1, 000 face value per bond. Coupon dates 2/1, 8/1 $41. 875 will be paid on these dates Security None Sinking Fund Annual from 8/1/05 Annual payments to this fund starting from the indicated date Call Provision not callable before 8/1/04 Deferred call feature Call Price 104. 188 initially declining to 100 Buy back price is $1041. 88, declining to $1, 000 on 8/1/1 Rating Moody’s A 2 This is one of Moody’s higher ratings. The bonds have a low probability of default.
3 -6 Bond Valuation (Assuming Level Coupon Payments) n Discounted Cash Flow Valuation l Bond Value = PV (Promised Cash Flows) l Bond Value = PV (Coupon Payments) + PV (Face Value) l Bond Value = PV (Annuity) + PV (Lump sum)
Yield-to-Maturity (YTM) n Required market interest rate that makes the discounted cash flows of the bond equal to its price n Interest rate that we will use in the bond valuation equation n Does not always equal the bond’s coupon rate 3 -7
3 -8 IPC issues 5 -year $1, 000 face value bonds with an annual coupon of 100. What is the coupon rate and what is the price of the bonds if the YTM on similar bonds is 10%?
3 -9 General Expression for the Value of a Bond Annuity Formula
3 -10 Example 2: Pricing of a regular bond n IPS issues a 10 -year bond l l l YTM = 24% Coupon Rate = 8% Face value = $1, 000 n What is the price of the bond at the issue date? n What is your minimum selling price if you sell this bond one year before its maturity?
3 -11 Notes on the Bond Pricing Formula n Semi annual coupons: 10 -year bond with 12% coupon rate paid semi annually l Halve the coupon rate and quoted YTM l Double the number of periods l YTM=APR! n Risk-free market interest rate versus YTM l YTM takes into consideration the risk of the cash flows n Finding YTM: trial and error, EXCEL, financial calculator.
3 -12 Semi-annual coupons: What is the price of a $1000 bond maturing in ten years with a 12% coupon that is paid semiannually if the YTM is 10%
3 -13 Discount bond example: Suppose a year has gone by and the IPC 10% annual coupon bond has 4 years to maturity. What is the price (present value) of the bonds if the YTM on similar bonds is 11%?
3 -14 Premium Bond Example: Suppose in the second year the yield-to-maturity for similar bonds decreases to 9% instead of increasing to 11%. What is the price of the 4 -year IPC $1000 par value 10% annual coupon bond?
Par, Discount and Premium Bonds The relation of YTM and the coupon rate n Par Bonds: l Price = Face Value l YTM = Coupon Rate n Discount Bonds: l Price < Face Value l YTM > Coupon Rate n Premium Bonds: l Price > Face Value l YTM < Coupon Rate 3 -15
3 -16 Interest Rate Risk of Bonds n Risk that the bond you own will change in value because interest rates (e. g. YTM) have changed n Review: l As interest rates rise, PV decreases all else equal l As interest rates fall, PV increases all else equal n Interest rate sensitivity depends on time to maturity and coupon rate
3 -17 Determinants of the Interest Rate Risk of Bonds: Part I n Time to Maturity: l The longer the time to maturity, the greater the interest rate risk, all else equal • Higher t in formula => greater compounding effect => small changes in r, big changes in price l 10% 2 -year and 15 -year bonds • 15 year bond’s price will change more with a change in the YTM.
Interest Rate Changes and Bond Values: Both bonds are par bonds originally Suppose YTM decreases to 8%: Suppose YTM increases to 12%: 3 -18
3 -19 Interest Rate Risk and Time to Maturity (Figure 7. 2) Bond values ($) 2000 $1, 768. 62 30 -year bond Time to maturity 1500 Interest rate 1 year 5% 30 years 1000 $916. 67 $1, 047. 62 $1, 768. 62 10 1, 000. 00 15 956. 52 671. 70 20 1 -year bond $1, 047. 62 916. 67 502. 11 $502. 11 500 5 10 15 20 Interest rates (%) Value of a Bond with a 10% Coupon Rate for Different Interest Rates and Maturities
3 -20 Determinants of the Interest Rate Risk of Bonds: Part II n Coupon Rate: l The lower the coupon rate, the greater the interest rate risk, all else equal • Low coupon => more of the bond’s value comes from the face amount l 0% (pure discount) and 10% 8 -year bonds • 100% of the 0% coupon bond’s price comes from face amount • 10% bond’s price depends on eight $100 annual coupons plus face value
3 -21 Which Bond has a higher interest rate risk? n A: 30 -year, 10% coupon or B: 15 -year, 10% coupon? n A: 30 -year, 10% coupon with face value of $1, 000 or B: 25 year, 10% coupon, with face value of $10, 000? n A: 30 -year, 11% coupon or B: 30 -year, 9% coupon? n A: 30 -year, zero-coupon with face value of $1, 000 or B: 30 year, 10% coupon, with face value of $10, 000? n A: 30 -year, 10% coupon or B: 25 -year, 15% coupon? n A: 30 -year, 10% coupon or B: 20 -year, 8% coupon?
3 -22 The Interest Rate Risk of Bonds n Duration l A measure of the interest rate risk of a bond l average maturity of a bond’s cash flows l The higher the duration measure, the greater the interest rate risk
Bond pricing Theorems 3 -23 n The following statements about bond pricing are always true. l Bond prices and market interest rates move in opposite directions. l When a bond’s coupon rate is (greater than / equal to / less than) the market’s required return (YTM), the bond’s market value will be (greater than / equal to / less than) its par value. l Given two bonds identical except for maturity, the price of the longer-term bond will change more than that of the shorter-term bond, for a given change in market interest rates. l Given two bonds identical but for coupon, the price of the lower-coupon bond will change more than that of the higher-coupon bond, for a given change in market interest rates.
3 -24 Implicit Interest on a Zero-coupon n Suppose EIN company issues a $1, 000, 5 -year zero-coupon bond. n Calculate the price if the YTM-15% n What is the total amount of implicit interest on this bond? n What is the yearly implicit interest using amortization (required by law)?
3 -25 Solution n PV = 1, 000 / 1. 155 = $497 n Total Implicit Interest = $1, 000 - $497 = $502 n Using straight-line interest expense, we have $502/5 = $102. 60 per year. n Using amortization, we have for the first year: l l l Beginning value = $497 Ending value = $1, 000 / 1. 154 = $572 Implicit interest in year 1 = $572 - $497 = $75 Implicit interest in year 2 = ($1, 000 / 1. 153) - $572 = $86 et cetera n What would be preferred by the corporation?
3 -26 Inflation and Returns n Key issues: l What is the difference between a real and a nominal return? l How can we convert from one to the other? n Example: Suppose we have $1, 000, and Diet Coke costs $2. 00 per six pack. We could buy 500 six packs. Now suppose the rate of inflation is 5%, so that the price rises to $2. 10 in one year. When we invest the $1, 000 it grows to $1, 100 in one year. n What’s the return in dollars? n What’s the return in six packs?
3 -27 Reading the Wall Street Journal n Majority of bonds is traded OTC n Bonds are quoted as a % of the face value n Bonds are quoted as ATT 7 s 05 l AT&T issue, maturing in 2005, 7% coupon n Close = last available price on close previous business day (% of F) n Net Change n Current Yield = coupon / closing quote n Volume
3 -28 Treasury Bonds n Always semi-annually n Quoted in 32 nds (smallest ‘tick’ size) l Bid price = 132: 20 means 132 + 20/32 percent of the face value = $1, 329. 375 l Change: -46 means the price (bid or ask) fell by 46/32%, or 1. 4375%. l YTM is based on ask price l Bid-ask spread l “n” indicates notes, rather than bonds
3 -29 Inflation and Returns n A. Dollars. Our return is ($1100 - $1000)/$1000 = $100/$1000 = ____. The percentage increase in the amount of green stuff is 10%; our dollar return is 10%. n B. Six packs. We can buy $1100/$2. 10 = ____ six packs, so our return is (523. 81 - 500)/500 = 23. 81/500 = 4. 76% The percentage increase in the amount of brown stuff is 4. 76%; our six-pack return is 4. 76%.
3 -30 Inflation and Returns, concluded n The relationship between real and nominal returns is described by the Fisher Effect. Let: R = the nominal return r = the real return h = the inflation rate n According to the Fisher Effect: 1 + R = (1 + r) x (1 + h) n From the example, the real return is 4. 76%; the nominal return is 10%, and the inflation rate is 5%: (1 + R) = 1. 10 (1 + r) x (1 + h) = 1. 0476 x 1. 05 = 1. 10
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