TFIN 601 Business Finance
Yulin Ma
VALUING BONDS
Chapter 4
WHAT COMPANIES DO
Forrest Gump bonds
Hotel Chocolat:
1) issued its own promissory notes,
2) raising money from existing customers who
were members of its ‘Tasting Club’.
What made these notes unique was that they did
not make interest payments in cash. Instead,
investors received a monthly box of chocolates.
VALUATION BASICS
Present value of future cash flows
Link risk & return
Expected return
on assets
Valuation
THE FUNDAMENTAL VALUATION MODEL
CF 1
CF 2
CF n
+
+ . . .+
P0 =
1
2
(1+ r ) (1+ r )
(1+ r )n
P0 = price of asset at time 0 (today)
CFt = cash flow expected at time t
r = discount rate (reflecting asset’s risk)
n = number of discounting periods (usually years)
This model can express the price of any asset at
t = 0 mathematically.
Marginal benefit of owning the asset: right to receive the
cash flows.
Marginal cost: opportunity cost of owning the asset.
BOND VOCABULARY
Principal
• The amount of money on which interest is
paid.
Maturity date
• The date when a bond’s life ends and the
borrower must make the final interest
payment and repay the principal.
Par value
• The face value of a bond, which the
borrower repays at maturity.
Coupon
• A fixed amount of interest that a bond
promises to pay investors.
Indenture
• A legal document stating the conditions
under which a bond has been issued.
BOND VOCABULARY
Coupon rate
• The rate derived by dividing the bond’s
annual coupon payment by its par value.
Coupon yield
• The amount obtained by dividing the bond’s
coupon by its current market price (which
does not always equal its par value). Also
called current yield.
BOND VALUATION: THE
BASIC EQUATION
Bond price = PV of coupons + PV of principal
Assuming annual interest:
C
C
C
M
+
+ . . .+
+
P0 =
1
2
n
(1+ r )
(1+ r )
(1+ r )
(1+ r )n
C
1
M
]+
P0 = X [1 n
r
(1+ r )
(1+ r )n
YIELD TO MATURITY (YTM)
Estimate of return investors earn if they buy
the bond at P0 and hold it until maturity.
The YTM on a bond selling at par will always equal
the coupon rate.
YTM is the discount rate that equates the
PV of a bond’s cash flows with its price.
BOND PREMIUMS
AND DISCOUNTS
What happens to bond values if the required
return is not equal to the coupon rate?
The bond’s price will differ from its par value.
r > coupon interest rate
P0 < par value
=
Discount
r < coupon interest rate
P0 > par value
=
Premium
ON DISCOUNT RATES
• Generally, the greater the uncertainty about an
asset’s future benefits, the higher the discount
rate investors will apply when discounting
those benefits to the present.
SEMIANNUAL COMPOUNDING
C
C
C
C
+F
Price = 2 + 2 + 2 + ... + 2
r 1
r 2
r 3
r 2n
(1 + ) (1 + ) (1 + )
(1 + )
2
2
2
2
An example …
Value a T-bond:
• Par value = $1000
• Maturity = 2 years
• Coupon rate = 4%
• r = 4.4% per year
$40
$40
$40
$40
+ 1000
2
2
2
P0 =
+
+
+ 2
1
2
3
4
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ç1 +
÷ ç1 +
÷ ç1 +
÷ ç1 +
÷
2
2
2
2
è
ø è
ø è
ø è
ø
= $992.43
=
$20
$20
$20
$1020
+
+
+
=
(1.022) (1.022) 2 (1.022)3 (1.022) 4
ECONOMIC FORCES AFFECTING
BOND PRICES
Time to maturity: bond prices converge to par value
(plus final coupon) with the passage of time.
Interest rates: bond prices and interest rates move in
opposite directions.
Changes in interest rates have a larger impact on
long-term bonds than on short-term bonds.
INTEREST RATE RISK
Interest rate
risk
• The risk that changes in market interest rates
will cause fluctuations in a bond’s price. Also,
the risk of suffering losses as a result of
unanticipated changes in market interest
rates.
Real return
• Approximately, the difference between an
investment’s stated or nominal return and
the inflation rate.
Nominal
return
• The stated return offered by an investment
unadjusted for the effects of inflation.
TYPES OF BONDS: BY ISSUER
Corporate
bonds
Australian
Government
bonds
• Usually with par $1000 and semiannual
coupon
• Bonds if maturity > 10 years; notes if
maturity < 10 years
• If < 1 year to maturity, short-term bonds are
called Treasury bills
• If between 1 year and 10 years to maturity:
Treasury notes
• If > 10 years to maturity: Treasury bonds
• Used to fund budget deficits
TYPES OF BONDS: BY FEATURES
Fixed vs
floating rates
Secured vs
unsecured
bonds
• Floating-rate bond: coupon tied to prime rate,
Australian Government Bond Rate , Bill Bank
Swap Rate, LIBOR, other interest rates.
• Floating rate = benchmark rate + spread.
• Floating rate can also be tied to the inflation
rate: Capital Indexed Bonds, for example.
• Unsecured bonds (debentures) are backed
only by general faith and credit of issuer.
• Debenture bonds are secured bonds backed by
specific assets (collateral).
• Examples are mortgage bonds, collateral trust
bonds, equipment trust certificates and bonds
secured by real estate , financial assets held in
trust or transportation equipment.
TYPES OF BONDS: BY FEATURES
Zero-coupon
bonds
Convertible
and
exchangeable
bonds
• Zero-coupon bonds pay no interest.
• Also known as discount bonds or pure
discount bonds.
• Sell below par value.
• Australian Government DINGO Bonds.
• In US, Treasury STRIPS.
• Convertible bonds, in addition to paying
coupon, offer the right to convert the bond
into ordinary shares of the issuer of the
bond.
• Exchangeable bonds are convertible in
shares of a company other than the issuer’s.
TYPES OF BONDS: BY FEATURES
Callable and
putable
bonds
• Callable bonds: bond issuer has the right to
repurchase the bonds at a specified price
(call price).
• Companies could retire and reissue debt if
interest rates fall.
• Putable bonds: the investors have the right
to sell the bonds to the issuer at the put
price.
Protection
from default
risk
• Sinking fund provisions: the issuer is
required to gradually repurchase outstanding
bonds.
• Protective covenants: requirements the
bond issuer must meet.
• Positive and negative covenants.
ASX BOND QUOTATIONS
Bond details
Coupon rate of 10%, paying interest every 3
months and maturing in 2019
Last sale: the price of the bond at last sale
Quote prices
and coupon rate
YTM
Quotes buy/sell spread: difference between ask
and bid prices
Coupon rate is noted as 10% quarterly (10.00q)
paid until 27 October 2014, with next payment on
17 November 2012
Yield to maturity on the ask price
BOND RATINGS
Bond ratings: grades assigned to bond issues based on
the degree of default risk
Investmentgrade bonds
• Moody’s Aaa to Baa3 ratings
• S&P and Fitch AAA to BBB− ratings
Junk bonds
• Moody’s Ba1 to Caa1 or lower
• S&P and Fitch BB to CCC+ or
lower
TERM STRUCTURE OF
INTEREST RATES
• Relationship between yield and maturity is called
the term structure of interest rates
– Graphical depiction called a yield curve
– Usually, yields on long-term securities are higher than on short-term
securities
– Generally look at risk-free Treasury debt securities
• Yield curve normally upwards-sloping
– Long yields > short yields
– Can be flat or even inverted during times of financial stress
What do you think a yield curve would look like
graphically?
ADVANCED BOND VALUATION
Liquidity
preference
theory
Preferred
habitat theory
• States that the slope of the yield curve is
influenced not only by expected interest rate
changes but also by the liquidity premium
that investors require on long-term bonds.
• A theory that recognises that the shape of
the yield curve may be influenced by
investors who prefer to purchase bonds
having a particular maturity regardless of the
returns those bonds offer compared with
returns available at other maturities.
VALUING BONDS
• Bond price = present value of coupons +
present value of principal.
• Bond prices are inversely related to interest
rates.
• Bonds can have features like convertibility and
callability.