Get documents about "Investments
Document Sample
Ch 11. Bond Prices and Yields
Objective:To review the principles of
bond pricing and to examine the
determinants of credit risk.
Bond characteristics
Bond Pricing and YTM
Taxation Issues
Default Risk and Ratings
1
1. Bond Characteristics
Bond: Typically a bond issuer makes
semi-annual coupon payments and pays
the bond’s par value at maturity.
Face or par value
Coupon rate
Zero coupon bond
Indenture: loan contract between the
bond issuer and bondholder.
2
Accured interest
invoice price = flat (stated, quoted)
price + accrued interest
Example: 10% coupon. 90 days have
passed since the last coupon payment.
There are 182 days between two
coupon payment dates.
Accrued
interest=$100*(90/365)=$24.66, or
=$50*(90/182) = $24.73
3
Issuers of Bonds
Canada bonds
Provincial government bonds
Corporate bonds
International bonds
Foreign bonds and Eurobonds
Recent innovations in the market
Indexed Bonds
RRB (Real Return Bonds)
TIPS (Treasury Inflation Protected Security)
Floaters and Reverse Floaters
4
Provisions of Bonds
Secured or unsecured
Registered or bearer bonds (Canada)
Call provision and deferred callable bonds
Convertible provision
Retractable and extendible (putable) bonds
Floating rate bond
5
2. Bond Pricing
T
P Ct F
t 1 (1 r )
t
(1 r )T
P = price of the bond
Ct = interest or coupon payments
F = face value
T = number of periods to maturity
r = the appropriate discount rate for a
period
6
Example: bond price
30-yr, 8% semiannual oupon Bond,
F = $1,000, with ytm=10% p.a.
Ct = 40 (semiannual payment)
P = 1000
T = 60 periods
r = 5% (semiannual rate)
60
1 1,000
P 40
t 1 (1 0.05) (1 0.05)60
t
P = $810.71
7
Bond Prices and Interest Rates
Prices and yields (required rates of
return) have an inverse relation
When yields get high the value of the
bond will be low
The longer the maturity is, the bond
price is more sensitive to changes in
interest rates.
To a large extent, treasury bill is
default free and interest rate risk free.
8
Prices and Interest Rates
Price
Interest Rate
9
3. Yield to maturity (ytm)
Interest rate that makes the present
value of the bond’s payments equal to
its price. It is the solution r:
P Ct t
T
F
t 1 (1 r ) (1 r )
T
Example: 10 year, 7% coupon bond,
P=$950. Solve for r = semiannual rate:
950=t=1,20 35/(1+r)t + 1000/(1+r)20
r=3.8635% for 6 months
10
Yield Measures
Bond equivalent yield: 3.86%*2=7.72% p.a.
Effective annual yield(1.0386)2 -1=7.88% p.a.
Current yield (annual interest/market price)
$70/$950 = 7.37 %
Current yield does not consider price
changes in the future. The ytm does.
The ytm is the average return over the life
of the bond, assuming that all coupons are
reinvested at the bond’s ytm.
11
Realized yield and ytm
Consider a bond: current price=$100, 10%
coupon, 2-year bond.
100 = 10/(1+r) + 110/(1+r)2
which is 100(1+r)2=10(1+r) + 110.
Definition of ytm assumes the reinvestment
of coupon at a rate of ytm.
Suppose the appropriate reinvestment rate
is z instead of r. Then we have
100(1+y)2 =10(1+z) + 110.
Solution y is called the realized compound
yield.
12
Example: Realized yield vs. ytm
Two-year bond selling at par, 10%
coupon paid once a year. First coupon
is reinvested at 8%. Then:
1000(1+y)2 = 100(1+0.08) + 1100.
Solving for y results in y=9.91% p.a.
13
4. Bond prices over time
Price Paths of Coupon Bonds
Price
Premium bond
1,000
Discount bond
Time
0 Maturity date
14
Holding period return
HPR = (Interest + P1)/P0 - 1
Example: Consider 10-year 8% semiannual
coupon bond selling at par. Suppose that the
yield falls to 7% in six months. What is
holding period return?
P1=$1068.55 (i.e., PV of coupons and par
value)
HPR = [40 + (1068.55-1000)]/1000
= 10.85% semiannual
15
Zero coupon bonds
For constant yields, discount bond prices
rise over time and premium bond prices
decline over time.
Strips: Synthetically created zero-
coupon bond by selling the rights to a
single payment backed by a coupon-
paying Treasury bond.
16
Zero-coupon bonds and taxation issues
Original issue discount bond: bonds
that are issued intentionally with low
coupon rates.
The price appreciation of original issue
discount bonds (based on constant
yield) is taxed as ordinary income
Price changes due to yield changes are
taxed as capital gains if the bond is
sold
17
Example
30-year 4% coupon bond with an 8% YTM.
Suppose you sold the bond one year later when
YTM=7%. Assume a 36% income tax and a 20%
capital gains tax.
P0=549.69; P1(8%)=553.66;
P1(7%)=631.67.
P at 8% yield = 553.66 - 549.69 = 3.97 (1)
P due to (yield)= 631.67 - 553.66=78.01 (2)
income tax on (1)+$40: 36%(3.97+40)=15.83
capital gains tax on (2): 20%*78.01=15.6
total tax: 15.83+15.6 = 31.43
After tax rate of return:
(40+631.67-549.69-31.43)/549.69 – 1 = 0.165
18
5. Default Risk
Rating companies
Dominion Bond Rating Service
(DBRS) in Canada, and in U.S. Moody’s
Investor Service and Standard & Poor’s
Rating Categories
Investment grade (BBB and above)
speculative (junk bond) grade bonds
Factors used by rating companies
Coverage; Leverage; Liquidity;
Profitability; Cash flow to debt
19
Financial ratios by rating class
US Industrial LT Debt, AAA A BBB B
1998-2000 Medians
EBIT interest coverage 21.4 6.1 3.7 0.8
EBITDA interest coverage 26.5 9.1 5.8 1.8
Funds flow/total debt (%) 84.2 15.0 8.5 (3.2)
Free operating CF/debt (%) 128.8 43.2 30.8 7.8
Return on capital (%) 34.9 19.4 13.6 6.6
Operating income/sales (%) 27.0 18.6 15.4 11.9
LT debt/capital (%) 13.3 33.9 42.5 69.7
Total debt/capital (%) 22.9 42.5 48.2 74.8
20
Altman discriminant analysis method
Compare bankrupt firms one year prior to
default with solvent (control) firms.
Find a line to separate bankrupt and solvent
firms
Sales Net Earnings
Z 0.234 0.972
Total Assets Total Debt
Current Assets Total Debt
1.002 0.531
Current Liabilitie s Total Assets
0.612 ( EquityGrowth AssetGrowth )
Firms with Z>1.626 were “safe”, and
firms with Z<1.626 were in risk of default
21
Indenture: Protection against default
Sinking funds
Subordination of future debt (“me-
first” rule)
Dividend restrictions
Collateral
Ytm and default risk
Expected yield vs promised yield on
corporate bonds would be different
due to default risk. Promised yield is
the maximum possible yield.
22
Ytm and default risk
Default premiums: The difference
between the promised yield on a
corporate bond and the yield of
comparable T-bond.
Risk structure of interest rates: pattern
of default premiums on risky bonds
Yield spreads tend to be wider during
economic recession (Flight to quality)
23
