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Chapter 7

Chapter 7. Valuation and Characteristics of Bonds. Chapter 7 Topic Overview. Bond Characteristics Annual and Semi-Annual Bond Valuation Finding Returns on Bonds Reading Bond Quotes Bond Risk and Other Important Bond Valuation Relationships. Bond Characteristics.

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Chapter 7

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  1. Chapter 7 Valuation and Characteristics of Bonds

  2. Chapter 7 Topic Overview • Bond Characteristics • Annual and Semi-Annual Bond Valuation • Finding Returns on Bonds • Reading Bond Quotes • Bond Risk and Other Important Bond Valuation Relationships

  3. Bond Characteristics • Par Value = stated face value that is the amount the issuer must repay. • Coupon Interest Rate • Coupon = Coupon Rate x Par Value • Maturity Date = when the par value is repaid. • This makes a bond’s cash flows look like this:

  4. $I $I $I $I $I $I+$M 0 1 2 . . . n Characteristics of Bonds • Bonds pay fixed coupon (interest) payments at fixed intervals (usually every 6 months) and pay the par value at maturity.

  5. Types of Bonds • Debentures: unsecured debt = bonds. • Subordinated Debentures • Mortgage Bonds • Zero Coupon Bonds: no coupon payments, just par value. • Convertible Bonds: can be converted into shares of stock.

  6. Types of Bonds(cont.) • Indexed Bonds: coupon payments and/or par value indexed to inflation. • TIPs: Indexed US Treasury coupon bond, fixed coupon rate, par value indexed. • I-Bonds: Indexed US Treasury zero coupon bond. • Junk bonds:speculative or below-investment grade bonds; rated BB and below. High-yield bonds.

  7. Types of Bonds(cont.) • Eurobonds - bonds denominated in one currency and sold in another country. (Borrowing overseas). • example - suppose Disney decides to sell $1,000 bonds in France. These are U.S. denominated bonds trading in a foreign country. Why do this? • If borrowing rates are lower in France, • To avoid SEC regulations.

  8. The Bond Indenture • The bond contract between the firm and the trustee representing the bondholders. • Lists all of the bond’s features: coupon, par value, maturity, etc. • Listsrestrictive provisionswhich are designed to protect bondholders. • Describes repayment provisions.

  9. Value • Book Value:value of an asset as shown on a firm’s balance sheet; historical cost. • Liquidation value:amount that could be received if an asset were sold individually. • Market value:observed value of an asset in the marketplace; determined by supply and demand. • Intrinsic value:economic or fair value of an asset; the present value of the asset’s expected future cash flows.

  10. Security Valuation • In general, the intrinsic value of an asset = the present value of the stream of expected cash flows discounted at an appropriate required rate of return. • Can the intrinsic value of an asset differ from its market value?

  11. n $Ct (1 + k)t S V = t = 1 Valuation • Ct = cash flow to be received at time t. • k = the investor’s required rate of return. • V = the intrinsic value of the asset.

  12. $I $I $I $I $I $I+$M 0 1 2 . . . n Bond Valuation • Discount the bond’s cash flows at the investor’s required rate of return. • the coupon payment stream (an annuity). • the par value payment (a single sum).

  13. n t = 1 S $It $M (1 + kb)t (1 + kb)n Vb = + Bond Valuation Vb = $It (PVIFA kb, n) + $M (PVIF kb, n)

  14. Bond Valuation Example #1 • Duff’s Beer has $1,000 par value bonds outstanding that make annual coupon payments. These bonds have an 8% annual coupon rate and 12 years left to maturity. Bonds with similar risk have a required return of 10%, and Moe Szyslak thinks this required return is reasonable. • What’s the most that Moe is willing to pay for a Duff’s Beer bond?

  15. 1000 80 80 80 . . . 80 0 1 2 3 . . . 12 Note:If the coupon rate < discount rate, the bond will sell for less than the par value: a discount. P/Y = 1 12 = N 10 = I/Y 1,000 = FV 80 = PMT CPT PV = -$863.73

  16. Let’s Play with Example #1 • Homer Simpson is interested in buying a Duff Beer bond but demands an 8 percent required return. • What is the most Homer would pay for this bond?

  17. 1000 80 80 80 . . . 80 0 1 2 3 . . . 12 Note:If the coupon rate = discount rate, the bond will sell for its par value. P/Y = 1 12 = N 8 = I/Y 1,000 = FV 80 = PMT CPT PV = -$1,000

  18. Let’s Play with Example #1 some more. • Barney (belch!) Barstool is interested in buying a Duff Beer bond and demands on a 6 percent required return. • What is the most Barney (belch!) would pay for this bond?

  19. 1000 80 80 80 . . . 80 0 1 2 3 . . . 12 Note:If thecoupon rate > discount rate, the bond will sell formore than the par value: a premium. P/Y = 1 12 = N 6 = I/Y 1,000 = FV 80 = PMT CPT PV = -$1,167.68

  20. Bonds with Semiannual Coupons • Double the number of years, and divide required return and annual coupon by 2. VB = I/2(PVIFAkb/2,2N) + M(PVIFkb/2,2N)

  21. Semiannual Example • A $1000 par value bond with an annual coupon rate of 9% pays coupons semiannually with 15 years left to maturity. What is the most you would be willing to pay for this bond if your required return is 8% APR? • Semiannual coupon = 9%/2($1000) = $45 • 15x2 = 30 remaining coupons

  22. 1000 45 45 45 . . . 45 0 1 2 3 . . . 30 P/Y = 1 15x2 =30 = N 8/2 = 4 = I/Y 1,000 = FV 90/2 = 45 = PMT CPT PV = -$1,086.46

  23. Finding a bond’s rate of return? Expected Return • In the marketplace, we know a bond’s current price(PV), but not its return. • Yield to Maturity (YTM) = the rate of return the bond would earn if purchased at today’s price and held until maturity. Annual Actual Return • Current Yield + Capital Gains Yield • I/P0 + (P1 – P0)/P0 = (P1 – P0 + I)/P0

  24. n t = 1 S $It $M (1 + kb)t (1 + kb)n P0 = + Yield To Maturity • The expected rate of return on a bond. • The rate of return investors earn on a bond if they hold it to maturity.

  25. Yield to Maturity Example • $1000 face value bond with a 10% coupon rate paid annually with 20 years left to maturity sells for $1091.29. • What is this bond’s yield to maturity?

  26. 1000 -1091.29 100 100 100 . . . 100 0 1 2 3 . . . 20 P/Y = 1 -1091.29 = PV 20 = N 1,000 = FV 100 = PMT CPT I/Y = 9% = YTM

  27. Let’s try this together. • Imagine a year later, the YTM for the bond on the previous slide fell to 8%. • What is the bond’s expected price? • What is the holding period return, if we sell the bond at this time assuming we bought the bond a year earlier? • PMT =100, FV = 1000

  28. Reading Corporate Bond Quotes Cur Net Bonds Yld Vol. Close Chg. IBM 6 ½28 6.6 14 98 1/4 -2 1/8 • Most info is expressed as % of par value. Par value = 100. • For IBM, 6.5% annual coupon rate, matures in year 2028, Price is 98.25% of par value.

  29. YTM Estimate for IBM Bond • Assuming $1000 Par (or Face) Value and semi-annual coupons • Price = 98.25% (1000) = 982.50, INT/2=1000(6.5%)/2= 32.50, FV = 1000 • Assuming N = 26 (2028-2002): YTM? 982.50 =32.50(PVIFAYTM/2,2N)+1000(PVIFYTM/2,2N) • Calculator Solution: -982.50 = PV,1000 = FV, 32.50 = PMT, 2N = 2(26) = 52 = N, CPT I/Y • I/Y=YTM/2=3.32% YTM(APR) = 2(3.32%)= 6.64%

  30. The Financial Pages: Treasury Bonds Maturity Ask Rate Mo/Yr Bid Asked Chg Yld 6 Feb 26 104:25 104:26 -15 5.63 • What is the yield to maturity for this Treasury bond? (assume (2026-2002) 24x2 = 48 half years) P/Y = 1, N = 48, FV = 1000, PMT = 1000(6%/2) = 30, PV = - 1,048.125 (104.8125% of par) • Solve: I/Y = ytm/2 = 2.816%, YTM = 5.63%

  31. Bond Valuation: What have we learned? 5 Important Relationships • Our Example 1: Duff’s Beer bonds • 12-year bond kb=6%, V = $1,167.68 kb=8%, V = $1,000 kb=10%, V = $863.73 • These values illustrate the First & Second Important Relationships

  32. First Relationship: Bond Prices and Interest Rates have an inverse relationship!

  33. Second Important Relationship From example 1: The coupon rate was 8% kb=6%, V = $1,167.68 kb=8%, V = $1,000 kb=10%, V = $863.73 • When required rate = coupon rate Bond Value = Par Value (M) • When required rate > coupon rate Bond Value < Par Value (M) • When required rate < coupon rate Bond Value > Par Value (M)

  34. Bond Value Changes Over Time • Returning to the original example #1, where k = 10%, N = 12, INT(PMT) = $80, M(FV) = $1000, & V = $863.73. • What is bond value one year later when N = 11 and k is still = 10%? VB = $80(PVIFA10%,11) + $1000(PVIF10%,11) = $870.10

  35. What is the bond’s return over this year? (Proof of YTM = Expected Ret.) • Total Rate of Return = Current Yield + Capital Gains Yield (C.G.Y) • Beg. V = 863.73, End V = 870.10 • Current Yield = Annual Coupon (INT) divided by Beginning Bond Value • Current Yld = $80/863.73 = 9.26% • C.G.Y.=(870.10-863.73)/863.73= 0.74% • Total Return = 9.26% + 0.74% = 10%

  36. Third Relationship: Market Value approaches par value as maturity date approaches.

  37. Fourth Relationship: Interest Rate Risk • Measures Bond Price Sensitivity to changes in interest rates. • Long-term bonds have more interest rate risk than short-term bonds.

  38. Interest Rate Risk Example • Recall from our earlier example (#1), the 12-year, 8% annual coupon bond has the following values at kd = 6%, 8%, & 10%. Let’s compare with a 2-yr, 8% annual coupon bond. • 12-year bond2-year bond kb=6%, V = $1,167.68 V = $1,036.67 kb=8%, V = $1,000 V = $1,000 kb=10%, V = $863.73 V = $965.29

  39. Bond Price Sensitivity Graph

  40. Other Bond Risks • Reinvestment Rate Risk = opposite of interest rate risk, greater for short-term bonds, risk that income from bonds will fall. • Default Risk = measured by bond ratings = ability of issuer to fulfill debt obligations • Aaa, AAA, best rating, lowest default risk

  41. Fifth Relationship • In addition to length of time to maturity, the pattern ( and size) of cash flows affects a bond’s price sensitivity to changes in interest rates. • Duration measures and illustrates this relationship.

  42. Duration • Weighted average time to maturity. • Higher (longer) duration means greater bond price sensitivity to changes in interest rates.

  43. Duration Formula • t = year the cash flow is to be received, • n = the number of years to maturity, • Ct = the cash flow to be received at year t, • kb = the bondholder’s required return, • P0 = the bond’s present value (or today’s price).

  44. Duration Example • Krusty Burger and Burns Power bonds both have 3 years to maturity, $1,000 par value, and a required return of 8 percent. • However, Krusty Burger makes annual coupon payments of 8%, while Burns Power is a zero coupon bond. • What is the duration of each bond?

  45. Suggested Duration Calculation Steps • First, calculate today’s value of the bond. • Second, find the PV today of each time weighted bond CF (CF x time period the CF occurs). • Third, add up all the time weighted PVs Note: The CF and NPV calculator functions can be used to do steps 2 and 3. • Fourth, divide sum of time weighted PVs by today’s bond value = duration.

  46. Krusty Burger Duration • Since Krusty’s required return and coupon rate are equal, today’s value = $1,000. • 80 = PMT, 1000 = FV, 8 = I/Y, 3 = N, CPT PV = $1000 t Ct x CPV(tC) • 80 80 C01 74 • 80 160 C02 137 • 1080 3240 C032572 NPV: I = 8, CPT NPV = 2783 Krusty Burger Duration = 2783/1000 = 2.783

  47. Burns Power Duration • Today’s Burns Power Bond Value: 0 = PMT, 1000 = FV, 8 = I/Y, 3 = N, CPT PV = $793.83 t Ct x CPV(tC) • 0 0 C01 0 • 0 0 C02 0 • 1000 3000 C032381.50 NPV: I = 8, CPT NPV = 2381.50 Burns Power Duration = 2381.50/793.83 = 3.00 NOTE: Duration for zero coupon bond = time to maturity.

  48. Duration Example Conclusion Krusty Burger Duration = 2.783 Burns Power Duration = 3.000 • Burns Power bonds are more sensitive to changes in interest rates. • This is good if interest rates go down, but bad if interest rates go up! • From this example, you can see for bonds with the same time to maturity, lower coupon rate bonds have more interest rate risk.

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