Bond Prices and Yields

1
Bond Prices and Yields

• Bond characteristics
• Bond pricing
• Bond yields
• Default risk and bond pricing
• The yield curve

2
Bond features

• Par value (face value) The principle payment to
  the bondholder at the maturity of the bond
• Maturity date when the principle is paid
• Coupon stated interest payment made on a bond
• Coupon rate the annual coupon divided by the
  face value of a bond
• Yield to maturity (or YTM) is the rate that
  makes the market price of the bond equal to the
  present value of its future cash flows

3
Bond Features

• If a bond has five years to maturity, an 50
  annual coupon, and a 1000 face value, its cash
  flows would look like this
• Time 0 1 2 3 4 5
• Coupons
• Face Value

4
Corporate Bonds

• Call provision
• The call provision allows the issuer to
  repurchase the bond at a specified call price
  before the maturity date
• When will firms use the call provision?
• How are investors compensated?
• Put provision
• Holder may choose either to exchange for par
  value at some date or to extend for a given
  number of years

5
Corporate Bonds

• Convertible bond
• A bond with an option allowing the bondholder to
  exchange the bond for a specified number of
  shares of common stock in the firm
• Conversion ratio
• If one bond can convert into 50 shares, the
  conversion ratio will be 150.
• Market conversion value current stock price
  conversion shares
• If stock price is 18 dollars, then market
  conversion value is ____
• Conversion premium bond price market
  conversion value
• If bond price 950, then conversion premium is
  _____
• Floating rate bonds
• Bond with coupon rate periodically reset
  according to a specified market rate

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Bond Pricing
T
Par Value
å
C
P
T
t


B

T

r
(
)
1
t
r
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• PB Price of the bond
• Ct coupon payments
• T number of periods to maturity
• r semi-annual discount rate or the
  semi-annual yield to maturity

7
Price of 8, 10-yr. with yield at 6, semi-annual
coupon

• Coupon _______ (Semiannual)
• Discount Rate ________ (Semiannual)
• Maturity ________
• Par Value _______

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Exercise

• A bond has a 10 percent coupon rate and a 1,000
  face value. Interest is paid semiannually, and
  the bond has 20 years to maturity. If investors
  require a 12 percent yield, what is the bonds
  present value?

9
Question

• Consider callable bond, put bond, convertible
  bond, and straight bond together.
• 1) Everything else being the same, which of them
  has the highest yield to maturity?
• 1) everything else being the same, which of them
  has the lowest price?

10
Bond Prices and Yields

• Prices and Yields (required rates of return)
  have an inverse relationship
• When yields get very high the value of the bond
  will be very low
• When yields approach zero, the value of the bond
  approaches the sum of the cash flows

11
The Inverse Relationship Between Bond Prices and
Yields (8 coupon bond with 30-year maturity and
semiannual coupon payment)
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Alternative Measures of Yield

• Yield to maturity
• Current Yield
• Yield to Call
• Call price replaces par
• Call date replaces maturity
• Holding Period Return
• Considers any change in price if the bond is held
  less than its maturity

13
Bond Yields Yield to Maturity

• It is the discount rate that makes the present
  value of a bonds payments equal to its price.
• YTM is reported on an annualized basis using
  simple interest techniques.
• Suppose an 8 coupon, 30-year bond is selling at
  1276.76 and it makes semiannual coupon payment,
  what is the yield to maturity?

14
Bond Yields Current Yield

• It is annual coupon divided by bond price
• Example for 8, 30-year bond currently selling
  at 1276.76, the current yield is _____

15
Bond Yields Yield to Call

• If the call price is less than the present value
  of the scheduled payments, the issuer can call
  the bond at the expense of the bondholder
• The yield to call is calculated just like the
  yield to maturity, except that the time until
  call replaces time until maturity and the call
  price replaces the par value.
• Investors in premium bonds often are more
  interested in the bonds yield to call rather
  than yield to maturity

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Bond Prices callable and Straight Debt
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Yield to Call Example

• Suppose the 8 coupon (semiannual coupon
  payment), 30-year maturity bond sells for 1150
  and is callable in 10 years at a call price of
  1100.

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Yield to Maturity and Holding-Period Return

• Consider a 30-year bond paying a semiannual
  coupon of 40 and selling at par value of 1,000.
  
• What is the initial yield to maturity
• If the yield remains the same over the year, what
  is the holding-period return for the year?
• If the yield falls to 7 at the end of the year,
  what is the holding-period return?

19
Premium and Discount Bonds

• Premium Bond
• Coupon rate exceeds yield to maturity
• Bond price will decline to par over its maturity
• Discount Bond
• Yield to maturity exceeds coupon rate
• Bond price will increase to par over its maturity

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Figure 9.6 Premium and Discount Bonds over Time
21
The Price of a Zero-Coupon Bond over Time
22
Default Risk and Ratings

• Rating companies
• Moodys Investor Service
• Standard Poors
• Fitch
• Rating Categories
• Investment grade
• Speculative grade

23
Factors Used by Rating Companies

• Coverage ratios
• Leverage ratios
• Liquidity ratios
• Profitability ratios
• Cash flow to debt

24
Protection Against Default

• Sinking funds
• Calls for the issuer to periodically repurchase
  some proportion of the outstanding bonds prior to
  maturity
• Subordination of future debt
• Restrict the amount of additional borrowing.
  Additional borrowing will be paid after the
  current bond is paid in case of bankruptcy
• Dividend restrictions
• Collateral
• If the firm defaults the bond, bondholders get a
  particular asset of the firm

25
Term Structure of Interest Rates

• Relationship between yields to maturity and
  maturity
• Yield curve - a graph of the yields on bonds
  relative to the number of years to maturity

26
Yield Curves
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Expectation Theory

• Yield to maturity is solely determined by
  expectation of future short-term interest rate
• Upward slope means that the market is expecting
  _____ future short term rates
• Downward slope means that the market is expecting
  _____ future short term rates

28
Liquidity Preference Theory

• Investors demand a risk premium on long-term
  bonds

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Term Spread