Lecture 4: Bond Valuation and
the Term Structure of Interest Rates
RSM 332
Capital Market Theory
Rotman School of Management
University of Toronto
Mike Simutin
October 5/6, 2011
Bond Valuation
RSM 332, 1/32
Why Is This Important?
I
Bonds are an important component of an investment portfolio
I
Issuing bonds is the most common form of raising funds by
governments and corporations
I
Bond markets are larger than stock markets
I
Understanding bonds may help to understand and even predict
the health of an individual company and the overall economy
Bond Valuation
RSM 332, 2/32
DeFnition of a Bond
I
A bond is a legally binding contract between a borrower (bond
issuer) and a lender (bondholder)
I
Borrower promises to make interest and principal payments
I
All payments are determined in the contract
I
Bonds can diFer in several diFerent respects: repayment type,
issuer, maturity, collateral, priority in case of default
I
Abondspec
i±es
I
²ace (or par) value,
F
dollars, to be paid at maturity
I
Coupon rate,
c
, to be paid periodically
I
Fixed rate, e.g., 8% annually
I
Floating rate, e.g., 1year Treasury bill rate + 100 basis points
I
Maturity,
T
years
Bond Valuation
RSM 332, 3/32
Example of a Bond
Consider a fouryear Government of Canada bond with a 6%
annual coupon rate, issued on 1/1/2012 and maturing on
12/31/2015
I
The par value of the bond is $1,000
I
Coupons are paid semiannually: June 30 and December 31
I
The semiannual coupon payment is
$1
,
000
·
0
.
06
2
= $30
$0
1/1/2012
$30
6/30/2012
$30
12/31/2012
$30
6/30/2013
$30
12/31/2013
$30
6/30/2014
$30
12/31/2014
$30
6/30/2015
$1,030
12/31/2015
Bond Valuation
RSM 332, 4/32
How to Value Bonds
Value of Bond
=
PV of Expected Future Cash Flows
I
Identify the size and timing of cash ﬂows
I
Discount them at the correct discount rate, which depends on
the default risk of the bond
I
Intrinsic risk of the issuer (often rated by an agency, e.g.
Moody’s)
I
Collateralized or noncollateralized debt
I
Seniority
I
Is there default risk on government bonds?
Bond Valuation
RSM 332, 5/32
What If Bond Price
±
= PV of ±uture Cash ±lows?
I
Consider a bond that pays $1,000 next year and now trades at
$920. The relevant discount rate is
r
=5%
.
I
Bond price ($920) is not equal to PV of future cash ﬂows
($1
,
000
/
1
.
05 = 952
.
38)!
I
Let’s borrow $920 at 5% for one year and use it to buy the
bond at $920. This leads to the following cash ﬂows:
Today
Next Year
Borrow 920
+920
−
920
·
(1 + 0
.
05) =
−
966
Buy bond
−
920
+1
,
000
I
You get a sure future payoF of $1
,
000
−
966 = $34 without
paying anything today. This is a free lunch or
arbitrage
:a
t
least one cash ﬂow of an arbitragebased strategy is positive,
and all other cash ﬂows are zero (or also positive)
I
Can arbitrage persist?
Bond Valuation
RSM 332, 6/32
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View Full DocumentZeroCoupon Bonds
Zerocoupon
(or
pure discount
) bonds do not pay coupons (
c
=0)
I
Time to maturity,
T
= Maturity date
−
today’s date
I
Face value
F
I
Discount rate
r
P
=
F
(1 +
r
)
T
What is the value of a 30year zerocoupon bond with a $1,000 par
value and a discount rate of 6% (annual compounding)?
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 Spring '08
 RAYMONDKAN
 Interest Rates, Yield Curve, Zerocoupon bond

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