Valuation and Characteristics of Bonds

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Valuation and Characteristics of Bonds

• Chapter
• Seven

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Terminology and types of bonds
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Definitions

• Bond
• Par value (face value)
• Coupons and Coupon rate
• Maturity and Time to maturity
• Yield or Yield to maturity
• Which of these will vary across bonds depending
  on riskiness?

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The bond indenture

• Contract between the company and its bondholders
  (represented by a trustee)
• The indenture includes
• Basic terms of the bonds
• Total amount of bonds issued
• Description of property used as security
• Sinking fund provisions
• Call provisions (call premium)
• Convertibility options
• Protective covenants
• Negative - i.e. firm can not merge, sell assets,
  pay dividend
• Positive - i.e. firm must maintain certain
  financial ratios, provide maintenance of assets

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Bond classifications

• Security
• Seniority
• Rate and/or payment
• Quality (ratings)
• Issuer

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Bond classifications - security

• Collateral secured by financial securities
• Mortgage secured by real property, normally
  land or buildings
• Debentures unsecured
• Notes unsecured debt with original maturity
  less than 10 years

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Bond classifications - seniority

• Senior
• Junior
• Subordinated

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Bond classifications rate zeros

• Make no periodic interest payments (coupon rate
  0)
• The entire yield-to-maturity comes from the
  difference between the purchase price and the par
  value
• Cannot sell for more than par value
• Sometimes called zeroes, or deep discount bonds
• Treasury Bills and principal only Treasury strips
  are good examples of zeroes

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Bond classifications rate floating rate

• Coupon rate floats depending on some index value
• Examples adjustable rate mortgages and
  inflation-linked Treasuries
• There is less price risk with floating rate bonds
• The coupon floats, so it is less likely to differ
  substantially from the yield-to-maturity
• Coupons may have a collar the rate cannot go
  above a specified ceiling or below a specified
  floor

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Bond classifications quality investment grade

• High Grade
• Moodys Aaa and SP AAA capacity to pay is
  extremely strong
• Moodys Aa and SP AA capacity to pay is very
  strong
• Medium Grade
• Moodys A and SP A capacity to pay is strong,
  but more susceptible to changes in circumstances
• Moodys Baa and SP BBB capacity to pay is
  adequate, adverse conditions will have more
  impact on the firms ability to pay

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Bond classifications quality junk

• Low Grade
• Moodys Ba, B, Caa and Ca
• SP BB, B, CCC, CC
• Considered speculative with respect to capacity
  to pay. The B ratings are the lowest degree of
  speculation.
• Very Low Grade
• Moodys C and SP C income bonds with no
  interest being paid
• Moodys D and SP D in default with principal
  and interest in arrears

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Bond classifications - issuer

• Treasury Securities
• Federal government debt
• Maturities
• T-bills pure discount bonds with original
  maturity of one year or less
• T-notes coupon debt with original maturity
  between one and ten years
• T-bonds coupon debt with original maturity
  greater than ten years
• Municipal Securities
• Debt of state and local governments
• Varying degrees of default risk, rated similar to
  corporate debt
• Interest received is tax-exempt at the federal
  level

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Bond markets

• Primarily over-the-counter transactions with
  dealers connected electronically
• Extremely large number of bond issues, but
  generally low daily volume in single issues
• Makes getting up-to-date prices difficult,
  particularly on small company or municipal issues
• Treasury securities are an exception

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Bond valuation
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Definitions of value

• Book value value of an asset as shown on a
  firms balance sheet
• Liquidation value amount received if an asset
  were sold individually
• Market value observed value of an asset in the
  marketplace
• Intrinsic value economic or fair value of an
  asset
• Can the intrinsic value of an asset differ from
  its market value?

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Security Valuation

• In general, the intrinsic value of an asset the
  PV of an assets expected future cash flows
• So the value of an asset is a function of
• Amount timing of expected cash flows
• Riskiness of the cash flows
• Investors required rate of return

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The Bond-Pricing Equation

• It dollar interest to be received w/each pmt
• M par value of bond at maturity
• kb required rate of return for the bondholder
• N number of periods to maturity

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Bond prices interest rates

• Interest rates and bond prices are inversely
  related
• As interest rates increase, bond prices ______
• As interest rates decrease, bond prices ______
• Interest rate risk
• A change in _______ caused by a change in ______
  _______.

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Bondholders required returns

• If bondholder required return coupon rate, then
  the bond will sell at ______.
• The coupon rate depends on the risk
  characteristics of the bond when issued
• Discount bonds
• Premium bonds

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Bondholders required returns

• The coupon rate depends on the risk
  characteristics of the bond when issued
• Which bonds will have the higher required rate of
  return, all else equal?
• Secured debt vs. a debenture
• Subordinated debenture vs. senior debt
• A bond with a sinking fund vs. one without
• A callable bond vs. a non-callable bond

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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.
• Yield-to-maturity is the rate implied by the
  current bond price.
• If you have a financial calculator, enter N, PV,
  PMT and FV, remembering the sign convention (PMT
  and FV need to have the same sign, PV the
  opposite sign)

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Current Yield

• The ratio of the interest payment to the bonds
  current market price.
• Current Yield
• Annual interest payment/current market price of
  the bond
• A 1,000 bond with 8 coupon rate and market
  price of 700
• Current yield 80 / 700 11.4

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Bond prices relation between coupon and yield

• If YTM coupon rate, then
  par value bond price
• Why?
• If YTM par value
• Why?

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Relation between price andyield-to-maturity
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Price reinvestment risk

• Price Risk
• Change in price due to changes in interest rates
  (this is also known by itself as interest rate
  risk)
• Long-term bonds have more price risk than
  short-term bonds
• Reinvestment Rate Risk
• Uncertainty concerning rates at which cash flows
  can be reinvested
• Short-term bonds have more reinvestment rate risk
  than long-term bonds

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Default risk

• The risk that the bondholder will not receive all
  of the bonds promised cash flows
• Ceteris paribus, higher default risk implies a
  higher YTM
• Only U.S. Govt bonds have no default risk.
• Bondholders are better protected if
• they have senior claims
• there is collateral (security)
• the firm has established a sinking fund
• there are restrictive covenants

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Interest rate risk

• Interest rate risk has two components
• Time to maturity--All other things equal, the
  longer the time to maturity, the greater the
  interest rate risk.
• Coupon rate--All other things equal, the lower
  the coupon rate, the greater the interest rate
  risk

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Bond pricing theorems

• Bonds of similar risk (and maturity) will be
  priced to yield about the same return, regardless
  of the coupon rate
• If you know the price of one bond, you can
  estimate its YTM and use that to find the price
  of the second bond
• This concept can be transferred to valuing assets
  other than bonds

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Valuing a discount bond with annual coupons 1

• Consider a bond with a coupon rate of 10 and
  coupons paid annually. The par value is 1000 and
  the bond has 5 years to maturity. The yield to
  maturity is 11. What is the value of the bond?
• Using the formula
• B PV of annuity PV of lump sum
• B 100(1 1/(1.11)5 / .11) 1000 / (1.11)5
• B 369.59 593.45 963.04
• Using the calculator
• N 5 I/Y 11 PMT 100 FV 1000
• CPT PV -963.04

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Valuing a discount bond with annual coupons 2

• Suppose our firm decides to issue 20-year bonds
  with a par value of 1,000 and annual coupon
  payments. The return on other corporate bonds of
  similar risk is currently 12, so we decide to
  offer a 12 coupon interest rate.
• What would be a fair price for these bonds?

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Valuing a discount bond with annual coupons 2
(cont.)

• Suppose interest rates fall immediately after we
  issue the bonds. The required return on bonds of
  similar risk drops to 10.
• What would happen to the bonds intrinsic value?

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Valuing a discount bond with annual coupons 2
(cont.)

• Suppose interest rates rise immediately after we
  issue the bonds. The required return on bonds of
  similar risk rises to 14.
• What would happen to the bonds intrinsic value?
• Suppose coupons are semi-annual.

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Bond valuation with semiannual coupons

• To value a bond with semiannual coupons
• halve the annual coupon amount,
• halve the quoted YTM (market interest rate)
• double the number of periods (years).

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YTM example

• Suppose we paid 898.90 for a 1,000 par 10
  coupon bond with 8 years to maturity and
  semi-annual coupon payments. What is the yield to
  maturity?

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YTM with annual coupons

• Consider a bond with a 10 annual coupon rate, 15
  years to maturity and a par value of 1000. The
  current price is 928.09. What is the yield to
  maturity?

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YTM with semiannual coupons

• Suppose a bond with a 10 coupon rate and
  semiannual coupons, has a face value of 1000, 20
  years to maturity and is selling for 1197.93.
  What is the required return of investors?

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Valuing a premium bond with annual coupons

• Suppose you are looking at a bond that has a 10
  annual coupon and a face value of 1000. There
  are 20 years to maturity and the yield to
  maturity is 8. What is the price of this bond?

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Zero coupon bonds

• Value of a zero coupon PV of bond's par or face
  value
• What is the value of a 5 year zero coupon bond
  (1000 face value) if its YTM is 15?

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Quiz

• Eagle Co.s bonds mature in 8 years. The bonds
  have a 12 coupon rate and pay coupons on a
  semiannual basis. If the current price of
  Eagles bonds is 875, what is the YTM?