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Valuing bond Fundamentals of corporate finance, BMM Chapter 6 Valuing bond Finansiell ekonomi höst 2012

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Topics Covered Using The Present Value Formula to Value Bonds How Bond Prices Vary With Interest Rates The Term Structure of Interest Rates Real and Nominal Rates of Interest Corporate Bonds and the Risk of Default 2

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Board of Directors Chairman of the Board and members are accountable for the organization Management Chief Executive Officer (CEO) and his team run the company The Corporation (internal) The Marketplace (external) Equity Markets Analysts and other market agents evaluate the performance of the firm on a daily basis Debt Markets Ratings agencies and other analysts review the ability of the firm to service debt Auditors External opinion as to the fairness of presentation and conformity to stds of financial statements Regulators SEC, the OMX, or other regulatory bodies by country Legal Counsel Provides legal opinions and recommendations on legality of corporate activities Entities with capital at risk in the corporation, but can also reap gains or returns from activities with the corporation Entities whose services are purchased by the corporation The Structure of Corporate Governance 3

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Why companies issue bonds? To finance their investment project. Issuing bond does not have the loss of ownership as issuing stocks do, since bond is a debt certificate. Bondholders have a role in monitoring the firm´s activities due to the periodic payment feature of the bond. Bonds provide a fixed rate of return for investors! The required rate of return on bond is lower than the stocks. Since stocks are inherently riskier. 4

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Definitions A bond is a debt security. It is a formal contract promising to repay borrowed money with interest at fixed intervals. (Obligation) Maturity date — the date on which the issuer has to repay the nominal amount. (löptid) Yield to maturity is internal rate of return (IRR, overall interest rate) earned by an investor who buys the bond today at the market price. 5

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Zero Coupon Bond (nollkupongare) A zero coupon bond pay no regular interest. It is issued at a substantial discount to par value (face value). Sensitive to interest rate changes.par value t.ex. SSVX Statsskuldsväxlar är nollkupongare. Current yield: annual coupon payments divided by bond price. 6

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Kopior av aktiebrev och obligation från Bofors- Gullspång Aktiebolag 7

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Premium bond issued by British National savings association 8

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Government bond issued by the State of South Carolina 2011 9

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(SOX) Obligationer Sverige 10

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Exempel: statsobligation 11

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Räkna ut ränta (Yield to maturity) RGKB 1047, säljränta 128,48%, kupong 5kr, slutvärde 100, löptid 8 år + 96/360=8,267 år. Yielden blir 1,338 %. 12

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Exempel (yield to maturity) RGKB 1046, löptid 44 dagar/360 år. Kupong 5,5 säljränta 100,486, slutvärde 100, Yielden blir 1,49%. Du märkte att yielden är lite högre än 8 års yield. 13

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The pricing of bonds Any bond can be valued as an annuity plus a single payment. It is the present value of the interest payments and the principal payment (face value) discounted at the yield to maturity of the bond. Bond dealers earn a spread by selling higher than its bid price. Bid price –ask price= spread 14

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Zero coupon bond (discount bond) Consider a 30-year zero-coupon bond with a face value of $100. If the bond is priced at an annual YTM of 10%, what is the price of the bond today?zero-coupon bond Price = PV (cash flow)=100/(1,1) 30 = 5,73 $ the discount amount is your interest payment. 5,73 $ is the price you pay for the bond. At the maturity date, you will be paid 100 $ face value, the effective annualized return or Yield to Maturity is 10%. 15

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Valuing a Coupon Bond 16

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Valuing a Bond Example If today is October 1, 2010, what is the value of the following bond? An IBM Bond pays $115 every September 30 for 5 years. In September 2015 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%) Cash Flows Sept 1112131415 1151151151151115 17

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Valuing a Bond Example continued If today is October 1, 2010, what is the value of the following bond? An IBM Bond pays $115 every September 30 for 5 years. In September 2015 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%) 18

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Valuing a Bond Example - France In December 2008 you purchase 100 Euros of bonds in France which pay a 8.5% coupon every year. If the bond matures in 2012 and the YTM is 3.0%, what is the value of the bond? 19

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Kalkyler i excel Example - France In December 2008 you purchase 100 Euros of bonds in France which pay a 8.5% coupon every year. If the bond matures in 2012 and the YTM is 3.0%, what is the value of the bond? (obs! På engelska version använder vi NPV I stäälet för Netnuvärde) 20

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Valuing a Bond Another Example - Japan In July 2010 you purchase 200 Yen of bonds in Japan which pay a 8% coupon every year. If the bond matures in 2015 and the YTM is 4.5%, what is the value of the bond? Note the value is 230.73. corrected! 21

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Valuing a Bond Example - USA In February 2009 you purchase a 3 year US Government bond. The bond has an annual coupon rate of 4.875%, paid semi-annually. If investors demand a 0.006003% semiannual return, what is the price of the bond? Present value of c/2 coupon payment over 2 t period. Apply Annuity formula. Halva kupong och dubbel löptid! Samt relevant yielden! 22

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Valuing a Bond Example continued - USA Take the same 3 year US Government bond. If investors demand a 4.0% semiannual return, what is the new price of the bond? 23

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Interest Rate on 10yr Treasuries Year Yield, % 24

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Bond Prices and Yields (inverse relationship) Interest Rates, % Bond Price 25

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Time to Maturity and Prices: increase interest rate, the price of longer term bonds decrease more, all else konstant! Interest Rates, % Bond Price, ($) 30 yr bond 3 yr bond When the interest rate equals the 5% coupon, both bonds sell for face value 26

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Source: Bloomberg.com Figure 1: Yield Curve January 2008: changing term structure 27

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The recent term structure of interest Rate: upward sloping YieldCurve.comYield Curve figures updated weekly since October 2003 To select historical yield curve data use drop-down menu UK Gilt US Treasury 6 Month 3 Month 1 Year 6 Month2 Year5 Year10 Year30 Year August 22, 20110.580.530.611.262.413.78 0.010.020.200.932.123.42 August 15, 20110.620.570.651.302.533.95 0.010.070.190.962.253.73 August 8, 20110.580.470.551.422.693.87 0.010.040.291.252.563.85 August 1, 20110.600.490.631.582.864.02 0.090.150.361.362.80 4.12 28

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UK gilt and US treasury yield vs. Time to maturity (2011 aug 22.) 29

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Interest Rates Short- and long-term interest rates do not always move in parallel. Between September 1992 and April 2000 U.S. short-term rates rose sharply while long term rates declined. A indication of recession in 2000. 30

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Term Structure of Interest Rates The relationship between short term and long term interest rate is called the term structure of interest rate. Spot Rate - The actual interest rate today (t=0) Forward Rate - The interest rate, fixed today, on a loan made in the future at a fixed time. Future Rate - The spot rate that is expected in the future YTM (r) Year 1981 1987 & Normal 1976 1 5 10 20 30 31

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Maturity U.S. Treasury Strip Spot Rates as of February 2009: the yield curve Spot rates (%) 32 The yield curve depicts the term structure of interest rate.

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Yield to Maturity Example A $1000 treasury bond expires in 5 years. It pays a coupon rate of 10.5%. If the market price of this bond is 1078.8, what is the YTM? C0C1C2C3C4C5 -1078.801051051051051105 Calculate IRR = 8.5% Obs: använd Ränta= som argument I excel program svenska version. 33

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Inflation Rates Annual rates of inflation in the United States from 1900–2008. Annual Inflation (%) 35

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Global Inflation Rates Averages from 1900-2006 36

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Debt & Interest Rates Nominal r = Real r + expected inflation (approximation) Actual formula

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UK Bond Yields 10 year nominal interest rate 10 year real interest rate Interest rate (%) 38

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Govt. Bills vs. Inflation (’53-’08) % United Kingdom Inflation T-Bill Returns 39

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Govt. Bills vs. Inflation (’53-’08) % United States Inflation T-Bill Returns 40

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Govt. Bills vs. Inflation (’53-’08) % Germany Inflation T-Bill Returns 41

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Bond Ratings Key to bond ratings. The highest-quality bonds are rated triple A. Bonds rated triple B or above are investment grade. Lower-rated bonds are called high-yield, or junk, bonds. 42 Check the course book BMM for more details.

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Yield Spread: credit risk Yield spread between corporate and government bonds, % Yield spreads between corporate and 10-year Treasury bonds. Obs: the spread indicates the credit risk of Baa related corporate bond over riskfree treasury bond! Years 43

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Prices and Yields Prices and yields of a sample of corporate bonds, December 2008. (jämför yield to maturity! Kapitalkostnad för företag!) Source: Bond transactions reported on FINRA’s TRACE service: http://cxa.marketwatch.com/finra/BondCenter 44

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