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CHAPTER 7

CHAPTER 7. BONDS VALUATION. Financial Market in the Financial System. Financial Market – a market where those who have excess funds and those who are in need of funds will meet to transact the financial assets that include both money and capital market securities.

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CHAPTER 7

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  1. CHAPTER 7 BONDS VALUATION

  2. Financial Market in the Financial System • Financial Market – a market where those who have excess funds and those who are in need of funds will meet to transact the financial assets that include both money and capital market securities. • 4 main parties: households, business firms, foreigners and government. SITI AISHAH BINTI KASSIM (FM2)

  3. Characteristics of a Good Financial Market • Availability of information • Liquidity • Price continuity • Transaction cost • External efficiency or information efficiency SITI AISHAH BINTI KASSIM (FM2)

  4. Types of Securities Market • Money market Short-term securities which have maturity below than one-year. • Capital market Long-term securities which have maturity longer than one-year. SITI AISHAH BINTI KASSIM (FM2)

  5. What is a Bond? • One of a debt financing • A long term debt (fixed income security) in which the issuer (borrower) has agreed to pay fixed income payments for a specified period and to repay a fixed amount of principal at maturity to the bondholder (lender). • Indenture – the contract between the issuer and the bondholder, which sets the obligations of the issuer. SITI AISHAH BINTI KASSIM (FM2)

  6. Key Features of a Bond • Par value – face amount of the bond, which is paid at maturity (assume $1,000). • Coupon interest rate – a rate of interest payment for every bond issued and usually be converted into Ringgit amount by time the rate to the bond par value (CP = PV x CR) • Maturity date – years until the bond must be repaid. • Issue date – when the bond was issued. • Yield to maturity – rate of return earned on a bond held until maturity (also called the “promised yield”). SITI AISHAH BINTI KASSIM (FM2)

  7. Bond Markets • Primarily traded in the over-the-counter (OTC) market. • Most bonds are owned by and traded among large financial institutions. • Full information on bond trades in the OTC market is not published, but a representative group of bonds is listed and traded on the bond division of the NYSE. SITI AISHAH BINTI KASSIM (FM2)

  8. Callable bonds • Allow the issuer to redeem the bond at any time before the maturity date. • The bond will be call at premium price to compensate for the holders. • Issuer will call the bond when market interest rate decline – reduce it interest expenses and take the advantages of lower interest rate in the market. SITI AISHAH BINTI KASSIM (FM2)

  9. Sinking Fund • Provision in the indenture to pay off a loan over its life rather than all at maturity. Failure to meet SF requirement causes bond default, may force firm into bankruptcy. Significant cash drain to firm. • Similar to amortization on a term loan. Reduces amount needed to retire the remaining debt at maturity. • Reduces risk to investor, shortens average maturity. • But not good for investors if rates decline after issuance. SITI AISHAH BINTI KASSIM (FM2)

  10. Types of Bonds • Unsecured Bonds: Bonds that are not backed by an asset or collateral. • Debentures – unsecured long-term bond • Subordinated Debentures – bonds that have a lower claim on assets in the event of liquidation than do other senior debtholders. • Income Bond – issued by firms facing financial difficulties or which are weak financially. • Secured Bonds: Bonds that are backed by an asset or collateral. • Mortgage Bond – secured by real estate or buildings, which are of higher value than the value of the mortgage bond issued. • Collateral Trust Bond – secured by stock and/or bonds owned by the issuer. • Equipment Trust Certificates – used to finance the purchase of ‘rolling stock’ such as trains, ships, boats and trucks. SITI AISHAH BINTI KASSIM (FM2)

  11. Other Types of Bond Issues • Eurobonds – issued by an international borrower and sold to investors in countries with currencies other than currency in which the bond is denominated. • Junk Bonds – also called ‘high-yield securities’ because of the higher risks of default faced by the bondholders. Rated below BBB. • Zero (low) coupon bonds – known as original discount bond is sold at a large discount from par. SITI AISHAH BINTI KASSIM (FM2)

  12. Rating the Bond • To provide the potential investor an objective form of risk analysis and evaluation on the quality of the bond and its issuer. SITI AISHAH BINTI KASSIM (FM2)

  13. Definition of Value • Book Value – the value of an asset shown on a firm’s balance sheet which is determined by its historical cost rather than its current worth. • Liquidation – the amount that could be realized if an asset is sold individually and not as part of a going concern. • Market Value – the observed value of an asset in the marketplace where buyers and sellers negotiate an acceptable price for the asset. • Intrinsic Value – the value based upon the expected cash flows from the investment, the riskiness of the asset, and the investor’s required rate of return. SITI AISHAH BINTI KASSIM (FM2)

  14. Principles of Bond Price Behavior • When the required rate of return (k) differ from the bond’s coupon rate, the market value of the bond will differ from its par: • When required rate of return (k) = coupon interest rate, bond will sell at par. • When required rate of return (k) > coupon interest rate, bond will sell at a discount. • When required rate of return (k) < coupon interest rate, bond will sell at premium. SITI AISHAH BINTI KASSIM (FM2)

  15. The Value of Financial Assets 0 1 2 n k = ?% ... Value CF1 CF2 CFn SITI AISHAH BINTI KASSIM (FM2)

  16. What is the value of a 10-year, 10% annual coupon bond, if kd = 10%? (coupon=10%x$1000=$100/year) 0 1 2 n Kd = 10% ... $100 + $1,000 VB = ? $100 $100 SITI AISHAH BINTI KASSIM (FM2)

  17. Mathematical Calculation Vb = CPN (PVIFA r%,n) + Par Value (PVIF r%,N) = $100 (PVIFA10%,10) + $1000 (PVIF10%,10) = $100(6.1446) + $1000(0.3855) = $614.46 + $385.50 = $1,000 *(If coupon rate = interest/discount rate (k) Vb = Par Value/Maturity Value =$1000) SITI AISHAH BINTI KASSIM (FM2)

  18. Using a financial calculator to value a bond This bond has a $1,000 lump sum due at 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 SITI AISHAH BINTI KASSIM (FM2)

  19. An example:Increasing inflation and kd Suppose inflation rises by 3%, causing kd = 13%. When kd rises above the coupon rate, the bond’s value falls below par, and sells at a discount. 10 13 100 1000 INPUTS N I/YR PV PMT FV OUTPUT -837.21 SITI AISHAH BINTI KASSIM (FM2)

  20. What is the Vb if kd increases from 10% to 13%? Vb = $100 (PVIFA13%,10) + $1000(PVIF13%,10) = $100 (5.4262) + 1000 (0.2946) = $542.62 + $294.60 = $837.22 (bond sells at a discount) SITI AISHAH BINTI KASSIM (FM2)

  21. An example:Decreasing inflation and kd Suppose inflation falls by 3%, causing kd = 7%. When kd falls below the coupon rate, the bond’s value rises above par, and sells at a premium. 10 7 100 1000 INPUTS N I/YR PV PMT FV OUTPUT -1210.71 SITI AISHAH BINTI KASSIM (FM2)

  22. What is the Vb if kd decreases from 10% to 7%? Vb = $100 (PVIFA7%,10) + $1000(PVIF7%,10) = $100 (7.0236) + $1000(0.5083) = $702.36 + $508.30 = $1,210.66 (bond sells at a premium) SITI AISHAH BINTI KASSIM (FM2)

  23. What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887? Must find the kd that solves this model. SITI AISHAH BINTI KASSIM (FM2)

  24. Approximate YTM AYTM (%) = I +(MV-Vb)/N (MV + Vb)/2 ATYM =Approximate yield to maturity I = $Interest or $coupon interest (x% of par value of $1000. Example, if coupon/interest is 9%, paid annually, I = 9% x 1000 = $90) MV = Maturity/Par value = $1000 Vb = Value/Price of bond SITI AISHAH BINTI KASSIM (FM2)

  25. Find the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887 AYTM = I + (MV-Vb)/N (MV +Vb)/2 = $90 + ($1000 - $887)/10 ($1000 + $887)/2 = 11% SITI AISHAH BINTI KASSIM (FM2)

  26. Interpolation (to get exact rate) kdPresent Value 10% $90(PVIFA10%,10) +$1000(PVIF10%,10) = $938.51 X% = $887.00 11% $90(PVIFA11%,10) + $1000(PVIF11%,10) = $883.13 1% Proportion = $938.51 - $887.00 = 0.93% $938.51 – $883.13 Therefore X = 10% + 0.93% = 10.93% SITI AISHAH BINTI KASSIM (FM2)

  27. Current Yield, Capital Gains Yield and Expected Total Return SITI AISHAH BINTI KASSIM (FM2)

  28. 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% SITI AISHAH BINTI KASSIM (FM2)

  29. Calculating Capital Gains Yield YTM = Current yield + Capital gains yield CGY = YTM – CY = 10.91% - 10.15% = 0.76% Could also find the expected price one year from now and divide the change in price by the beginning price, which gives the same answer. SITI AISHAH BINTI KASSIM (FM2)

  30. What is interest rate (or price) risk? Interest rate risk is the concern that rising kdwill cause the value of a bond to fall. SITI AISHAH BINTI KASSIM (FM2)

  31. What is reinvestment rate risk? Reinvestment rate risk is the concern that kd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income. EXAMPLE: Suppose you just won $500,000 playing the lottery. You intend to invest the money and live off the interest. SITI AISHAH BINTI KASSIM (FM2)

  32. Reinvestment rate risk example: You may invest in either a 10-year bond or a series of ten 1-year bonds. Both 10-year and 1-year bonds currently yield 10%. If you choose the 1-year bond strategy: After Year 1, you receive $50,000 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 10% interest rate, and $50,000 annual income. SITI AISHAH BINTI KASSIM (FM2)

  33. Conclusions about interest rate and reinvestment rate risk CONCLUSION: Nothing is riskless! SITI AISHAH BINTI KASSIM (FM2)

  34. Semiannual Bonds Multiply years by 2 : number of periods = 2n. Divide nominal rate by 2 : periodic rate (I/YR) = kd / 2. Divide annual coupon by 2 : PMT = ann cpn / 2. 2n kd / 2 OK cpn / 2 OK INPUTS N I/YR PV PMT FV OUTPUT SITI AISHAH BINTI KASSIM (FM2)

  35. What is the value of a 10-year, 10% semiannual coupon bond, if kd = 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 SITI AISHAH BINTI KASSIM (FM2)

  36. Semiannual Coupons/Interest Vb = I/2(PVIFAr/2%,2N) + MV(PVIFr/2,2N) Example: What is the price of a bond with coupon (interest) of 8.5% paid semi annually, remaining maturity of 12 years, and required rate of return is 10%? I=8.5% x $1000=$85; semi-annually=$42.50 N= 12years x 2 = 24times; r = 10%/2 = 5% Vb = $42.50(PVIFA5%,24) + $1000(PVIF5%,24) = $896.51 SITI AISHAH BINTI KASSIM (FM2)

  37. Semiannual Bonds Vb = PV (Coupon Payments) + PV (Par Value) Vb = CPN PVIFA r/2%, 2N + 1000PVIF r/2%, 2N 2 Vb = CPN(1 + r/2)2N – 1 + 1000 2 (r/2)(1 + r/2)2N (1 + r/2)2N SITI AISHAH BINTI KASSIM (FM2)

  38. 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: 10.25% > 10% (the annual bond’s effective rate), so you would prefer the semiannual bond. SITI AISHAH BINTI KASSIM (FM2)

  39. If the proper price for this semiannual bond is $1,000, what would be the proper price for the annual coupon bond? The semiannual coupon bond has an effective rate of 10.25%, and the annual coupon bond should earn the same EAR. At these prices, the annual and semiannual coupon bonds are in equilibrium, as they earn the same effective return. 10 10.25 100 1000 INPUTS N I/YR PV PMT FV OUTPUT - 984.80 SITI AISHAH BINTI KASSIM (FM2)

  40. Yield to Call Price of Bond: Vb = I (PVIFAr%,N) + Call price(PVIFr%,N) N= the number of years until the company can call the bond. rd= yield to call SITI AISHAH BINTI KASSIM (FM2)

  41. 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)? The bond’s yield to maturity can be determined to be 8%. 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 SITI AISHAH BINTI KASSIM (FM2)

  42. Yield to call 3.568% represents the periodic semiannual yield to call. YTCNOM = kNOM = 3.568% x 2 = 7.137% is the rate that a broker would quote. The effective yield to call can be calculated YTCEFF = (1.03568)2 – 1 = 7.26% SITI AISHAH BINTI KASSIM (FM2)

  43. If you bought these callable bonds, would you be more likely to earn the YTM or YTC? The coupon rate = 10% compared to YTC = 7.137%. The firm could raise money by selling new bonds which pay 7.137%. Could replace bonds paying $100 per year with bonds paying only $71.37 per year. Investors should expect a call, and to earn the YTC of 7.137%, rather than the YTM of 8%. SITI AISHAH BINTI KASSIM (FM2)

  44. When is a call more likely to occur? In general, if a bond sells at a premium, then (1) coupon > kd, so (2) a call is more likely. So, expect to earn: YTC on premium bonds. YTM on par & discount bonds. SITI AISHAH BINTI KASSIM (FM2)

  45. THE END SITI AISHAH BINTI KASSIM (FM2)

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