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2. 2 Bonds are simply long-term IOUs that represent claims against a firm’s assets. Bonds are a form of debt Bonds are often referred to as fixed-income investments. Bond Basics

3. 3 Key Features of a Bond Debt instrument issued by a corp. or government.

4. 4 Key Features of a Bond Par value = face amount of the bond, which is paid at maturity (assume $1,000). =

5. 5 Key Features of a Bond Coupon rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest.

6. 6 Key Features of a Bond Maturity date – when the bond must be repaid. Yield to maturity - rate of return earned on a bond held until maturity.

7. 7 What is interest rate risk? Interest rate risk is the concern that interest rates will change, and therefore, a reduction in the value/price of a security.

8. 8 Suppose you just inherited $500,000. You intend to invest the money and live off the interest. Interest rate risk example

9. 9 You may invest in either a: 10-year bond series of ten 1-year bonds Both bonds currently yield 5%.

10. 10 If you choose the 1-year bond strategy: After year 1, you receive $25,000 in income and have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000. If you choose the 10-year bond strategy: You can lock in a 5% interest rate, and $25,000 annual income.

11. 11 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

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13. 13 Bond Value Bond Value = PV(coupons) + PV(par) Bond Value = PV(annuity) + PV(lump sum) Remember: As interest rates increase present values decrease ( r  → PV  ) As interest rates increase, bond prices decrease and vice versa

14. 14 Bond Valuation Compute the value for an IBM Bond with a 6.375% coupon that will mature in 5 years given that you require an 8% return on your investment. What are the annual interest payments ($)? Compute the value for an IBM Bond with a 6.375% coupon that will mature in 5 years given that you require an 8% return on your investment. What are the annual interest payments ($)?

15. 15 0 1 2 3 4 5 2009 2010 2011 2012 2013 63.75 1,000.00 IBM Bond Timeline:

16. 16 $63.75 Annuity for 5 years $1000 Lump Sum in 5 years 0 1 2 3 4 5 2009 2010 2011 2012 2013 63.75 1000.00 IBM Bond Timeline:

17. 17 = 63.75 PMT 1000 FV 8% I 5 N = PV = 935.12 $63.75 Annuity for 5 years $1000 Lump Sum in 5 years 0 1 2 3 4 5 2009 2010 2011 2012 2013 63.75 1000.00 IBM Bond Timeline:

18. 18 Most Bonds Pay Interest Semi-Annually: What is the value of a bond with a semi-annual coupon with 5 years to maturity, 9% (nominal) coupon rate if an investor desires a 10% (nominal) return?

19. 19 Most Bonds Pay Interest Semi-Annually: e.g. semiannual coupon bond with 5 years to maturity, 9% annual coupon rate. Instead of 5 annual payments of $90, the bondholder receives 10 semiannual payments of $45. 0 1 2 3 4 5 2013 2014 2015 2016 2017 45 45.00 1000.00 45

20. 20 Compute the value of the bond given that you require a 10% s-a. return on your investment. Compute the value of the bond given that you require a 10% s-a. return on your investment. Since interest is received every 6 months, we need to use semiannual compounding V B = 45 - PMT 1000 - FV 5% - I 10 - N Most Bonds Pay Interest Semi-Annually: 0 1 2 3 4 5 2013 2014 2015 2016 2017 45 45.00 1000.00 45

21. 21 Most Bonds Pay Interest Semi-Annually: = PV = 961.39 Compute the value of the bond given that you require a 10% s-a. return on your investment. Compute the value of the bond given that you require a 10% s-a. return on your investment. Since interest is received every 6 months, we need to use semiannual compounding 0 1 2 3 4 5 2013 2014 2015 2016 2017 45 1,000 45

22. 22 Semiannual Bonds Coupon rate = 14% - Semiannual YTM = 16% (APR) Maturity = 7 years Value of bond? Number of coupon payments? (2t or N) 14 = 2 x 7 years Semiannual coupon payment? (C/2 or PMT) $70 = (14% x Face Value)/2 Semiannual yield? (YTM/2 or I/Y) 8% = 16%/2

23. 23 Semiannual Bonds Semiannual coupon = $70 Semiannual yield = 8% Periods to maturity = 14 Bond value = 70[1 – 1/(1.08) 14 ] /.08 + 1000 / (1.08) 14 = 917.56 Using the calculator: 14 N 8 I/Y 70 PMT 1000 FV CPT PV = -917.56 Using Excel: =PV(0.08, 14, 70, 1000, 0)

24. 24  If bond Sells at a DISCOUNT (less than $1,000) then YTM > Coupon Rate  If bond Sells at a PREMIUM (more than $1,000) then YTM < Coupon Rate Yield to Maturity -1,000 0 1 2 3 4 5 2013 2014 2015 2016 2017 80 1,000

25. 25 Valuing a Discount Bond with Annual Coupons Coupon rate = 10% Annual coupons Par = $1,000 Maturity = 5 years YTM = 11% Price= ?

26. 26 Valuing a Discount Bond with Annual Coupons Coupon rate = 10% Annual coupons Par = $1,000 Maturity = 5 years YTM = 11% Using the formula: B = PV(annuity) + PV(lump sum) B = 369.59 + 593.45 = 963.04 Using the calculator: 5N 11I/Y 100PMT 1000FV CPT PV = -963.04 Note: When YTM > Coupon rate  Price < Par = “Discount Bond” Using Excel: =PV(0.11, 5, 100, 1000, 0)

27. 27 Valuing a Premium Bond with Annual Coupons Coupon rate = 10% Annual coupons Par = $1,000 Maturity = 20 years YTM = 8% Price = ?

28. 28 Valuing a Premium Bond with Annual Coupons Coupon rate = 10% Annual coupons Par = $1,000 Maturity = 20 years YTM = 8% Using the formula: B = PV(annuity) + PV(lump sum) B = 981.81 + 214.55 = 1196.36 Note: When YTM Par = “Premium Bond” Using the calculator: 20N 8I/Y 100PMT 1000FV CPT PV = -1196.36 Using Excel: =PV(0.08, 20, 100, 1000, 0)

29. 29 Yield to Maturity If an investor purchases a 6.375% annual coupon bond today for $900 and holds it until maturity (5 years), what is the expected annual rate of return (YTM)? -900 ?? 0 1 2 3 4 5 2013 2014 2015 2016 2017 63.75 1000.00 + ?? 900

30. 30 Yield to Maturity YTM B = 63.75 PMT 1000 FV 5 N -900 PV I = ? If an investor purchases a 6.375% annual coupon bond today for $900 and holds it until maturity (5 years), what is the expected annual rate of return ? Will it be >< than 6.375%? -900 ?? 0 1 2 3 4 5 2013 2014 2015 2016 2017 63.75 1000.00 + ?? 900

31. 31 What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887? 90 01910 r d =? 1,000 PV 1. PV 10 PV M 887 Find r d that “works”!...

32. 32 10 -887 90 1000 NI/YR PV PMTFV 10.91 INPUTS OUTPUT

33. 33 Types of Bonds Vanilla – fixed coupons, repaid at maturity Zero Coupon – pay no explicit interest but instead, sell at a deep discount Convertible – can be converted into to stock

34. 34 Types of Bonds Junk Bonds – below investment grade

35. 35 Government Bonds Treasury Securities = Federal government debt Treasury Bills (T-bills) Pure discount bonds Original maturity of one year or less Treasury notes (T-notes) Coupon debt Original maturity between one and ten years Treasury bonds (T-bonds) Coupon debt Original maturity greater than ten years

36. 36 Tax Consequences A taxable bond has a yield of 8% and a municipal bond has a yield of 6% If you are in a 40% tax bracket, which bond do you prefer? 8%(1 -.4) = 4.8% The after-tax return on the corporate bond is 4.8%, compared to a 6% return on the municipal At what tax rate would you be indifferent between the two bonds? 8%(1 – T) = 6% T = 25%

37. 37 Bond Ratings Moody’s, Standard & Poor’s and Fitch regularly monitor issuer’s financial condition and assign a rating to the debt Investment Grade Below Investment Grade (Junk) AAABest Quality AAHigh Quality AUpper Medium Grade BBBMedium Grade BBSpeculative BVery Speculative CCCVery Very Speculative CC CNo Interest Being Paid DCurrently in Default

38. 38 Bond Ratings – Investment Quality High Grade Moody’s Aaa and S&P AAA – capacity to pay is extremely strong Moody’s Aa and S&P AA – capacity to pay is very strong Medium Grade Moody’s A and S&P A – capacity to pay is strong, but more susceptible to changes in circumstances Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay

39. 39 Bond Ratings - Speculative Low Grade Moody’s Ba, B, Caa and Ca S&P BB, B, CCC, CC Considered speculative with respect to capacity to pay. The “B” ratings are the lowest degree of speculation. Very Low Grade Moody’s C and S&P C – income bonds with no interest being paid Moody’s D and S&P D – in default with principal and interest in arrears

40. 40 What affects Bond prices? Risk Interest rates

41. 41 What is the “term structure of interest rates”? What is a “yield curve”? Term structure: the relationship between interest rates (or yields) and maturities. A graph of the term structure is called the yield curve.

42. 42 Draw a normal yield curve

43. 43 Hypothetical Treasury Yield Curve 0 5 10 15 1 10 20 Years to Maturity Interest Rate (%) 1 yr 8.0% 10 yr 11.4% 20 yr 12.65% Real risk-free rate Inflation premium Maturity risk premium

44. 44 What factors can explain the shape of this yield curve? This constructed yield curve is upward sloping. This is due to increasing expected inflation and an increasing maturity risk premium.

45. 45 Current Yield Curve Bloomberg

46. 46 Default risk If an issuer defaults, investors receive less than the promised return. Influenced by the issuer’s financial strength and the terms of the bond contract.