Valuation and Characteristics of Bonds

1
Chapter 7

• Valuation and Characteristics of Bonds

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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 bonds cash flows look like this

4
Characteristics of Bonds

• Bonds pay fixed coupon (interest) payments at
  fixed intervals (usually every 6 months) and pay
  the par value at maturity.

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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.

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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.

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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.

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The Bond Indenture

• The bond contract between the firm and the
  trustee representing the bondholders.
• Lists all of the bonds features
• coupon, par value, maturity, etc.
• Lists restrictive provisions which are designed
  to protect bondholders.
• Describes repayment provisions.

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Value

• Book Value value of an asset as shown on a
  firms 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 assets expected
  future cash flows.

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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?

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Valuation

• Ct cash flow to be received at time t.
• k the investors required rate of return.
• V the intrinsic value of the asset.

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Bond Valuation

• Discount the bonds cash flows at the investors
  required rate of return.
• the coupon payment stream (an annuity).
• the par value payment (a single sum).

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Bond Valuation
Vb It (PVIFA kb, n) M (PVIF kb, n)
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Bond Valuation Example 1

• Duffs 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.
• Whats the most that Moe is willing to pay for a
  Duffs Beer bond?

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P/Y 1 12 N 10 I/Y
1,000 FV 80 PMT CPT PV
-863.73

• Note If the coupon rate lt discount rate, the
  bond will sell for less than the par value a
  discount.

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Lets 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?

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P/Y 1 12 N 8 I/Y
1,000 FV 80 PMT CPT PV
-1,000

• Note If the coupon rate discount rate, the
  bond will sell for its par value.

18
Lets 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?

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P/Y 1 12 N 6 I/Y
1,000 FV 80 PMT CPT PV
-1,167.68

• Note If the coupon rate gt discount rate, the
  bond will sell for more than the par value a
  premium.

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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)
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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

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P/Y 1 15x2 30 N 8/2
4 I/Y 1,000 FV 90/2 45
PMT CPT PV -1,086.46
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Finding a bonds rate of return?

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

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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.

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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 bonds yield to maturity?

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P/Y 1 -1091.29 PV 20
N 1,000 FV 100 PMT CPT I/Y 9 YTM

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Lets try this together.

• Imagine a year later, the YTM for the bond on the
  previous slide fell to 8.
• What is the bonds 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

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Reading Corporate Bond Quotes

• Cur Net
• Bonds Yld Vol. Close Chg.
• IBM 6 ½ 28 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.

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YTM Estimate for IBM Bond

• Assuming 1000 Par (or Face) Value and
  semi-annual coupons
• Price 98.25 (1000) 982.50,
  INT/21000(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/YYTM/23.32 YTM(APR) 2(3.32) 6.64

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The Financial Pages Treasury Bonds

• Maturity Ask
• Rate Mo/Yr Bid Asked Chg Yld
• 6 Feb 26 10425 10426 -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

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Bond Valuation What have we learned? 5 Important
Relationships

• Our Example 1 Duffs Beer bonds
• 12-year bond
• kb6, V 1,167.68
• kb8, V 1,000
• kb10, V 863.73
• These values illustrate the First Second
  Important Relationships

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First Relationship Bond Prices and Interest
Rates have an inverse relationship!
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Second Important Relationship

• From example 1 The coupon rate was 8
• kb6, V 1,167.68
• kb8, V 1,000
• kb10, V 863.73
• When required rate coupon rate Bond Value
  Par Value (M)
• When required rate gt coupon rate Bond Value lt
  Par Value (M)
• When required rate lt coupon rate Bond Value gt
  Par Value (M)

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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

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What is the bonds 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

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

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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. Lets compare with
  a 2-yr, 8 annual coupon bond.
• 12-year bond 2-year bond
• kb6, V 1,167.68 V 1,036.67
• kb8, V 1,000 V 1,000
• kb10, V 863.73 V 965.29

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Bond Price Sensitivity Graph
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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

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Fifth Relationship

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

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Duration

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

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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 bondholders required return,
• P0 the bonds present value (or todays price).

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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?

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Suggested Duration Calculation Steps

• First, calculate todays 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
  todays bond value duration.

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Krusty Burger Duration

• Since Krustys required return and coupon rate
  are equal, todays value 1,000.
• 80 PMT, 1000 FV, 8 I/Y, 3 N, CPT PV
  1000
• t C t x C PV(tC)
• 80 80 C01 74
• 80 160 C02 137
• 1080 3240 C03 2572
• NPV I 8, CPT NPV 2783
• Krusty Burger Duration 2783/1000 2.783

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Burns Power Duration

• Todays Burns Power Bond Value 0 PMT, 1000
  FV, 8 I/Y, 3 N, CPT PV 793.83
• t C t x C PV(tC)
• 0 0 C01 0
• 0 0 C02 0
• 1000 3000 C03 2381.50
• 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.

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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.