Chapter 10
Bond Prices and Yields
Bond Characteristics
• Face or par value
• Coupon rate
– Zero coupon bond
• Compounding and payments
– Accrued Interest
– invoice price versus quoted price
• Indenture
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Provisions of Bonds
• Secured or unsecured (debenture)
• Call provision
– refunding
– call price
– deferred callable bond
– coupon rates and promised ytm
at issuance
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Provisions of Bonds
• Convertible provision
– conversion ratio
– market conversion value
– conversion premium
– coupon rate & ytm at issuance
– Convertible example
»conversion ratio = 25
»market price of stock = $42
»callable bond price = $1150
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Provisions of Bonds
• Put provision (putable bonds)
– coupon rate & ytm at issuance
• Floating rate bonds
– changing credit condition of
issuer
• Sinking funds
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Other innovations
• Pay in kind bonds (pik)
• reverse floaters
• indexed bonds (TIPS -Treasury
Inflation Protection bonds)
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Default Risk and Ratings
• Rating companies
•
– Moody’s Investor Service
– Standard & Poor’s
– Duff and Phelps
– Fitch
Rating Categories
– Investment grade
– Speculative grade
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Factors Used by Rating
Companies
•
•
•
•
•
Coverage ratios
Leverage ratios
Liquidity ratios
Profitability ratios
Cash flow to debt
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Protection Against Default
•
•
•
•
Sinking funds
Subordination of future debt
Dividend restrictions
Collateral
– mortgage bond
– equipment obligation
– collateral trust
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Bond Pricing
ParValue
T
C
t
PB  

T
t
(1 r )
t 1 (1 r )
T
PB = Price of the bond
Ct = interest or coupon payments
T = number of periods to maturity
y = semi-annual discount rate or the semiannual yield to maturity
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Solving for Price: 10-yr, 8%
Coupon Bond, Face = $1,000
20
P B = 40
t=1
1
1
+ 1000
(1+.03) t
(1+.03)
20
PB = $1,148.77
Ct
P
T
r
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= 40 (SA)
= 1000
= 20 periods
= 3% (SA)
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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
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Prices and Coupon Rates
Price
Yield
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Yield to Maturity
YTM = the discount rate that makes the present
value of the bond’s promised payments equal
to its price.
Bond is priced at $1067.95, it has a coupon rate
of 9% paid semiannually, a par value of $1000,
and 10 years to maturity. Find the bond’s ytm.
What is the current yield?
Bond is priced at $945.40 , it has a coupon rate
of 6% paid semiannually, a par value of $1000,
and 14 years to maturity. Find the bond’s ytm.
What is the current yield?
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YTM versus current yield
versus coupon rate
• Bond selling at par
– coupon = YTM = current yield
• Bond selling at a premium
– coupon > current > YTM
• Bond selling at a discount
– coupon < current < YTM
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Yield to call (YTC)
• Similar to YTM, but use time to first
call date and call price as future
value.
• Bond with 15 years to maturity, par
of $1000, a coupon rate of 8% (paid
semiannually), price of $1025,
callable in 5 years at $1080. Find
YTC.
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Realized compound yield
versus yield to maturity
• YTM will equal the realized return
over the life of the bond if all
payments are reinvested at an
interest rate equal to the bond’s
yield.
– Consider a bond with 10 years to
maturity, coupon rate of 9 percent
paid annually, and a price of
$1067.10.
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Realized compound yield (RCY)
versus yield to maturity (YTM)
• Consider a bond with 10 years to maturity,
coupon rate of 9 percent paid annually,
and a price of $1067.10.
– What is its ytm?
– Realized compound yield if you
reinvest at ytm?
– RCY if you reinvest at 3 percent?
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Time
1
2
3
4
5
6
7
8
9
10
CF
FV(CF)@8% FV(CF)@3%
$90.00
$179.91
$117.43
$90.00
$166.58
$114.01
$90.00
$154.24
$110.69
$90.00
$142.82
$107.46
$90.00
$132.24
$104.33
$90.00
$122.44
$101.30
$90.00
$113.37
$98.35
$90.00
$104.98
$95.48
$90.00
$97.20
$92.70
$1,090.00
$1,090.00
$1,090.00
Total
$2,303.79
$2,031.75
RCY
8.00%
6.65%
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Holding period return (HPR)
versus YTM.
• Consider a bond with 10 years to maturity,
•
•
coupon rate of 9 percent paid annually,
and a price of $1067.10. Note: ytm = 8%
Suppose you hold the bond one year and
interest rates decline to 7 percent.
Calculate your HPR.
Suppose instead that rates had risen to 9
percent. What is your HPR?
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Original Issue Discount (OID)
• Consider a 10 year Treasury strip with a
yield of 5 percent and face of $10,000.
– Price = $6,139.13
– After one year (yield = 5%)
»P = $6,446.09
»Difference = implicit interest = $306.96
»If you sold the strip for $6,500, then
you would have interest income of
$306.96 and capital gain of $53.91
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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
– Usually Treasury Bonds
– Have to be similar risk or other
factors would be influencing yields
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Yield Curves
Yields
Upward
Sloping
Downward
Sloping
Maturity
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Theories of Term Structure
• Expectations
• Liquidity Preference
– Upward bias over expectations
• Market Segmentation
– Preferred Habitat
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