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CHAPTER 7 Bonds Valuation

CHAPTER 7 Bonds Valuation. What is bond? Bond Markets Types of Bond Bond Features Bond Valuation Yield to Maturity (YTM) Bonds Rating. What is a bond?. A long-term debt instrument, in which a borrower agrees to make payments of principal & interest,

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CHAPTER 7 Bonds Valuation

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  1. CHAPTER 7Bonds Valuation • What is bond? • Bond Markets • Types of Bond • Bond Features • Bond Valuation • Yield to Maturity (YTM) • Bonds Rating

  2. What is a bond? • A long-term debt instrument, in which a borrower agrees to make payments of principal & interest, on specific dates, to the bondholders. • A legal promissory notes that matures on the last day of its term.

  3. Bond Markets • Primarily traded in the over-the-counter (OTC) market. • Debt financing cost is much cheaper than equity financing. • Coupon payment is tax-deductible. • Most bonds are owned by and traded among large financial institutions.

  4. 4 MAIN TYPES OF BOND 1) Treasury bonds / Treasuries - issued by govt. , no default risk 2) Corporate bonds - issued by corporations, exposed to default risk 3) Municipal bonds / “munis” - issued by state & local govt., exposed to some default risk. 4) Foreign bonds - issued by foreign govt./foreign corp., exposed to default risk & currency/exchange rate risk.

  5. Bond Features • Par value - face value of a bond, paid at maturity (usually $1,000). - represents the amount of money the firm borrows & promises to repay on the maturity date. • Coupon interest rate - stated annual interest rate (generally fixed) paid by the issuer. - Coupon payment = Coupon interest rate X Par value.

  6. Maturity date - years until the bond must be repaid. • Call provision - A provision in a bond contract that gives the issuer the right to redeem the bonds under specified terms prior to the normal maturity date. - Borrowers are willing to pay more & lenders require more, “Callable bonds ”. - mostly for corporate & municipal bonds, not for Treasury bonds.

  7. Issue date - when the bond was issued. • Yield to maturity (YTM) - rate of return earned on a bond held until maturity (also called the “promised yield”). • Term (t) - time period of the bond. • Sinking fund - A provision in a bond contract that requires the issuer to retire a portion of the bond issue each year.

  8. OTHER TYPES OF BOND • Convertible bond - exchangeable for common stock of the firm, at the holder’s option. - usually happens when the stock $ increases enough, therefore the shares of stock will worth more than the bond.

  9. Zero Coupon Bond - pay no interest throughout the term of the bond. • Junk Bond - issued by companies that are not in good financial health. - pay very high interest rates because they are very risky investment.

  10. Warrant - similar to a convertible bond. - gives the holder the right to buy stock at some agreed upon fixed prices within some specified time period in the future. - long-term option to buy a stated number of shares of common stock at a specified price.

  11. Secured bonds - backed by assets of the issuing company. - bonds secured by real estate are called “Mortgage Bonds”. • Debentures - not secured by assets but only by reputation & creditworthiness of the issuing company.

  12. Putable bond – allows holder to sell the bond back to the company prior to maturity at a pre-arranged $. • Income bond – pays interest only when the firm earns enough profits to pay interest. • Indexed bond / Purchasing Power bond – interest rate paid is based upon the rate of inflation.

  13. BOND VALUATION • Bond Value is equal to the PV of a stream of an equal interest payments PLUS the PV of the repayment of the bond’s principal value at maturity.

  14. Formula PV of Bond = PVA of interest payments (PVA x I) + PV of principal repayment (PV x P)

  15. 0 1 2 n r% ... Value CF1 CF2 CFn The value of financial assets

  16. VALUE OF BOND (VB)

  17. 0 1 2 n r ... 100 + 1,000 VB = ? 100 100 What is the value of a 10-year, 10% annual coupon bond, if rd = 10%?

  18. Using a financial calculator to value a bond • This bond has a $1,000 lump sum (the par value) due at maturity (t = 10), and annual $100 coupon payments beginning at t = 1 and continuing through t = 10, the price of the bond can be found by solving for the PV of these cash flows. 10 10 100 1000 INPUTS N I/YR PV PMT FV OUTPUT -1000

  19. The same company also has 10-year bonds outstanding with the same risk but a 13% annual coupon rate • This bond has an annual coupon payment of $130. Since the risk is the same the bond has the same yield to maturity as the previous bond (10%). In this case the bond sells at a premium because the coupon rate exceeds the yield to maturity. 10 10 130 1000 INPUTS N I/YR PV PMT FV OUTPUT -1184.34

  20. The same company also has 10-year bonds outstanding with the same risk but a 7% annual coupon rate • This bond has an annual coupon payment of $70. Since the risk is the same the bond has the same yield to maturity as the previous bonds (10%). In this case, the bond sells at a discount because the coupon rate is less than the yield to maturity. 10 10 70 1000 INPUTS N I/YR PV PMT FV OUTPUT -815.66

  21. Changes in Bond Value over Time • What would happen to the value of these three bonds is bond if its required rate of return remained at 10%: VB 1,184 1,000 816 13% coupon rate 10% coupon rate. 7% coupon rate Years to Maturity 10 5 0

  22. TRADING/SELLING AT……. • PREMIUM (YTM > COUPON RATE) - Bonds selling for more than their face value. • PAR VALUE (YTM = COUPON RATE) - Bonds selling at Par Value ($ 1000) • DISCOUNT (YTM < COUPON RATE) - Bonds selling below their face value

  23. Bond values over time • At maturity, the value of any bond must equal its par value. • If rd remains constant: • The value of a premium bond would decrease over time, until it reached $1,000. • The value of a discount bond would increase over time, until it reached $1,000. • A value of a par bond stays at $1,000.

  24. YIELD TO MATURITY (YTM) • The rate the bondholders would earn if they bought a bond, held until maturity. • The required yield expected by the investors in they invest their money in bond. • Also called as a investors’ required rate of return, internal rate of return, market interest rate or discount rate of return. • YTM = rd

  25. Methods in finding YTM 1) Trial & Error 2) YTM Formula (refer page 149 by Bany Ariffin et.al, 2003). 3) Financial calculator (by using I/YR)

  26. What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887? • Must find the rd that solves this model.

  27. Using a financial calculator to solve for the YTM • Solving for I/YR, the YTM of this bond is 10.91%. This bond sells at a discount, because YTM > coupon rate. 10 - 887 90 1000 INPUTS N I/YR PV PMT FV OUTPUT 10.91

  28. Find YTM, if the bond price is $1,134.20 • Solving for I/YR, the YTM of this bond is 7.08%. This bond sells at a premium, because YTM < coupon rate. 10 -1134.2 90 1000 INPUTS N I/YR PV PMT FV OUTPUT 7.08

  29. Definitions

  30. An example: Current and capital gains yield • Find the current yield and the capital gains yield for a 10-year, 9% annual coupon bond that sells for $887, and has a face value of $1,000. Current yield = $90 / $887 = 0.1015 = 10.15%

  31. Semiannual bonds • Multiply years by 2 : number of periods = 2n. • Divide nominal rate by 2 : periodic rate (I/YR) = rd / 2. • Divide annual coupon by 2 : PMT = ann cpn / 2. 2n rd / 2 OK cpn / 2 OK INPUTS N I/YR PV PMT FV OUTPUT

  32. What is the value of a 10-year, 10% semiannual coupon bond, if rd = 13%? • Multiply years by 2 : N = 2 * 10 = 20. • Divide nominal rate by 2 : I/YR = 13 / 2 = 6.5. • Divide annual coupon by 2 : PMT = 100 / 2 = 50. 20 6.5 50 1000 INPUTS N I/YR PV PMT FV OUTPUT - 834.72

  33. Would you prefer to buy a 10-year, 10% annual coupon bond or a 10-year, 10% semiannual coupon bond, all else equal? The semiannual bond’s effective rate is:

  34. 10.25% > 10% (the annual bond’s effective rate), so you would prefer the semiannual bond.

  35. A 10-year, 10% semiannual coupon bond selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call (YTC)? • Solving for the YTC is identical to solving for YTM, except the time to call is used for N and the call premium is FV. 8 - 1135.90 50 1050 INPUTS N I/YR PV PMT FV OUTPUT 3.568

  36. Yield to call (YTC) • 3.568% represents the periodic semiannual yield to call. • YTCNOM = rNOM = 3.568% x 2 = 7.137% (rate that a broker would quote.)

  37. The effective yield to call can be calculated • YTCEFF = (1.03568)2 – 1 = 7.26%

  38. Default risk • If an issuer defaults, investors receive less than the promised return. • Therefore, the expected return on bonds is less than the promised return. • Influenced by the issuer’s financial strength and the terms of the bond contract.

  39. BOND RATINGS • Bonds are rated by rating agency. • Ex: 1) Moody’s or Standard & Poors OR 2) RAM and MARC (Malaysia).

  40. Evaluating default risk: • Serve as a qualitative guide to the probability of default.

  41. QUIZ????? THAT’S GREAT SIR!!!!

  42. OR MAYBE POP QUIZ? THAT’S BETTER SIR!!!!! GOOD STUDENT……

  43. NEVERMIND, ONLY EXERCISES FOR TODAY….. IS THAT OKAY????

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