# Investments

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```							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
   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

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
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

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