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Unformatted text preview: Valuing Bonds
Readings: Text Chapter 10 (up to page 354) OVERVIEW Characteristics/Types of Bonds. Basic Bond Pricing. Yield to Maturity and Associated Pricing Issues.
1 Characteristics of Bonds Bonds (or Fixed Income Securities) promise a stream of fixed cash flows payable at specific dates. Principal, Par Value, Maturity Value Maturity Coupon, Coupon Rate, Interest Rate Covenants Remember bonds have contingent control rights.
2 Customizing a Bond
Covenants refer to special characteristics written into the bond contract to "customize" the bond.
Seniority/Subordination Callable & Sinking Funds Convertible Collateral (Secured) Constraints on further borrowing Constraints on dividends Constraints on asset sales How will various covenants affect price? 3 Major Domestic Issuers
U.S. Federal Government (The Treasury): ~ $5.1 trillion (+ $3.8 tr. is nonmarketable). Federal and Federally sponsored Agencies ~ $3 trillion. Domestic Corporations: ~ $3.5 trillion. State Governments & Municipalities: ~ $2 trillion. Mortgage and asset backed securities: ~ $6 trillion. 4 U.S. Treasury Securities
Treasury Bills (TBills): Treasury Notes (TNotes): Maturity 1 year (13, 26, 52 weeks). Issued as zero coupon (discount) bonds. Issued either weekly or monthly refunding. Maturity: 2 to 10 years. Semiannual coupon payments. Treasury Bonds (TBonds):
Maturity: 10 to 30 years. Semiannual coupon payments. Treasury STRIPS (~25% of long bonds are stripped): 1030 year securities are eligible for stripping. Inflation Indexed Bonds (TIPS)
5 Corporate Bonds
Corporate bonds can be either publicly or privately issued and traded Maturity: overnight (Commercial Paper) to 30+ years. Usually multiple issues per company. Often tailored with covenants. Risky: default risk + liquidity risk. 6 Bond Ratings
Credit rating agencies (Moody's, Standard & Poor's, Fitch) assign ratings to bonds to "quantify" default risk. Description Moody's S&P
Gilt Edge Very High Grade Upper Medium Grade Lower Medium Grade Low Grade/Speculative " " In Default Aaa Aa A Baa Ba B ... D AAA AA A BBB BB B ... D
7 Historical Corporate Default Frequencies
Rating at Issue AAA AA A BBB BB B CCC 1 year 0% 0% 0% 0% .4% 1.5% 2.3% 5 years .1% .7% .2% 1.6% 8.3% 22% 35.4% 10 years .1% .7% .6% 2.8% 16.4% 33% 47.5% 8 Additional Bonds
Municipal Bonds Issued to finance State, County, Town, School Districts Exempt from federal taxes! Issues are small and generally illiquid. Other Types of Bonds Agency Bonds Fannie Mae, Ginnie Mae, etc.. Structured Finance. Collateralized Mortgage Obligations (CMO's) Auto Loans Credit Card Receivables 9 Pricing a Bond
Value Additivity: Bond Price = Present Value of Promised Cash Flows. INT: coupon payment M: par value (maturity payment) N: number of periods to maturity kd: appropriate riskadjusted discount rate (e.g. required rate of return) INT INT M + INT Vd = + + ... + 2 ( 1 + k d ) (1 + k d ) (1 + k d ) n INTn M Vd = + n n (1 + k d ) n =1 (1 + k d ) N 10 Pricing a Bond: Longhand
Example: GE issues a bond: maturity = 3 years, face value = $1,000, coupon rate = 6%, rating = Aa Assume appropriate discount rate for similar bonds rated Aa is 5% and that coupons are annual. 60 60 1,060 Vd = + + 2 3 (1.05) (1.05) (1.05) Vd = 57.14 + 54.42 + 915.67 = 1,027.23
11 Pricing a Bond: Annuity
Example: GE issues a bond: maturity = 3 years, face value = $1,000, coupon rate = 6%, rating = Aa Assume appropriate discount rate for similar bonds rated Aa is 5% and that coupons are annual.
1 1  (1.05) 3 1,000 + Vd = 60 * .05 (1.05) 3 Vd = 60 * 2.723 + 1,000 * .864 Vd = 163.38 + 864 = 1,027.38
12 Pricing a Bond: Calculator
Example: GE issues a bond: maturity = 3 years, face value = $1,000, coupon rate = 6%, rating = Aa Assume appropriate discount rate for similar bonds rated Aa is 5% and that coupons are annual.
3 N 5 I/Y 60 PMT 1,000 FV PV CPT = 1,027.23 13 Yield to Maturity
Yield to Maturity: Average Rate of Return investors will realize if the bond is held to maturity.
Calculated as the single discount rate which makes price = PV of discounted cash flows. Also referred to as the bond's average rate of return or investors required rate of return. $ INT $M Vd = + t n (1 + ytm ) t =1 (1 + ytm )
14 n Calculating YTM: Calculator
Assume IBM has a 10 year, 7 % coupon bond that is priced at 985.33. Assume coupons are annual, what is its ytm? 10 N 985.33 PV 72.5 PMT 1,000 FV I/Y CPT = 7.4634%
15 Approximation for YTM
Assume IBM has a 10 year, 7 % coupon bond that is priced at 985.33. Assume coupons are annual, what is its ytm? M  Vd INT + N ytm 2Vd + M 3 1,000  985.33 72.5 + 10 = .0747 = 2 * 985.33 + 1,000 3 16 Various Domestic Yield Curves 17 Corporate Credit Spreads 18 SemiAnnual Coupons Coupon payments in U.S. are almost always semiannual. Yieldtomaturity is reported as 2*semiannual yield. Example: IBM has a 10 year, 7 % coupon bond that is priced at 985.33. Assume coupons are semiannual, what is its ytm? 20 N 985.33 PV 36.25 PMT 1,000 FV I/Y CPT = 3.7304% YTM = 2 * 3.7304% = 7.4608
19 SemiAnnual Coupons (II)
Assume Ford has a 20 year, 6.5% coupon bond. Your broker indicates that it is priced to yield 6.3%. What is its price (assume semiannual coupons). 40 N 3.15 I/Y 32.5 PMT 1,000 FV PMT CPT = 1,022.56
20 Bond Price Relationships (1)
Interest Rate Price Risk: The value (price) of a bond is inversely related to changes in interest rates (and ytm). ... Price Rates ... Price Rates INT M Vd = + t (1 + k ) (1 + k ) n t =1 n Vd n  tINT  nM = + t 1 n 1 k t =1 ( 1 + k ) (1 + k )
21 Bond Price Relationships (2)
Interest Rate Price Risk and Maturity: Long term bond prices are generally more sensitive to changes in interest rates than are short term bond prices. Example: Assume that kd is 8%.
Bond A Maturity Face Value 15 years $1,000 Bond B 30 years $1,000 8% Coupon Rate 8% What is the current price of each bond? What will be the new price of each bond if kd suddenly increases to 9%?
22 Bond Price Relationships (3)
Price (Vd) will be < par value (M) if the coupon rate (c) is less than the ytm. Conversely, Vd > M if c > ytm. A bond where Vd > M is a premium bond. A bond where Vd < M is a discount bond. A bond where Vd = M is a par bond Heuristic explanation: Coupon payments compensate investors for "giving up" their $. "Low" coupon rate bonds: "High" coupon rate bonds:
23 Bond Price Relationships (4) As maturity date approaches, Vd converges to M. Vd increases with maturity if c < ytm. Vd decreases with maturity if c > ytm. 24 Bond Price Relationships (4)
Example: Calculate the price of the following two bonds assuming 10 years and 9 years to maturity respectively, annual coupons, and kd = 8% Bond A Bond B $1,000 $1,000 6% 10%
25 Par Value (M) Coupon Rate (c) Bond Price Relationships (4) 10 years Bond A 865.80 9 years 875.06 Bond B 1134.20 1124.94 26 Relationship #4 Continued
Assume you purchased bond A and held it for a year. What would be your total return? Initial investment: Gross return after 1 year: 865.80 Coupon Payment: 60 Capital Appreciation: 875.06  865.80 = 9.26 Percentage Return: 60 + 9.26 = .0800 865.80
27 Relationship #4 Continued
What about bond B? Initial investment: Gross return after 1 year: 1134.20 100 Coupon Payment: Capital Appreciation: 1124.94  1134.20 = 9.26
100  9.26 = .0800 1134.20
28 Percentage Return: Corporate Bond Quotes
(WSJ 20 Sep 2006 Most Active)
Bond Nextel Credit Suisse HSBC Holdings Boston Scientific CIT Group Hershey Co Energy East Coupon 5.95 5.85 6.50 6.40 7.375 5.45 6.75 Maturity 3/15/14 8/16/16 5/2/26 6/15/16 4/2/07 9/1/16 7/15/36 Price 97.125 101.481 104.751 100.716 101.065 99.816 102.776 Yield 6.436 5.653 6.149 6.299 5.508 5.474 6.537 Spread 164 84 121 150 n.a. 67 160 Est $ Vol (000's) 165,649 131,160 130,220 83,800 77,914 68,500 67,700
29 Treasury Bond Quotes
Treasury Bonds/Notes (WSJ 19 Sep 2006)
Rate 3.500 6.000 3.375 3.375 3.500 3.500 Maturity Mo/Yr Aug 09n Aug 09n Sep 09n Oct 09n Nov 09n Dec 09n 96:17 103:07 96:03 96:00 96:08 96:06 96:18 103:08 96:04 96:01 96:09 96:07 2 2 2 1 2. 1 4.77 4.79 4.78 4.78 4.78 4.77 Bid Asked Chg. Ask Yld 30 Summary Characteristics of bonds. Overview of bond market Treasury bonds, notes bills, strips Corporate bonds Other bonds Valuing bonds Calculating yieldtomaturity 4 Characteristics of bond prices 31 ...
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 Fall '10
 Masoudie
 Finance

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