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1
CHAPTER 6: BONDS, BOND PRICES, AND THE
DETERMINATION OF INTEREST RATES
A. T
HE
B
ASICS
Chapter 6 shows how the work done in Chapter 4 on present values can be used to
determine the prices of various kinds of bonds. Looking beyond just bonds, Chapter 6
lays the foundation for pricing a wide variety of other financial assets as well. Core
Principle 1 that time has value is the key concept used in establishing prices of the
various financial assets. Equation (3) on text page 127, reproduced below, uses the
present value concept to illustrate the price of a coupon bond,
CB
P
. Importantly, it can be
easily modified to show the prices of zerocoupon bonds, fixed payment loans, and
consols. By understanding this particular result you can learn quickly other, related
results.
n
n
2
)
i
1
(
Value
Face
)
i
1
(
Payment
Coupon
)
i
1
(
Payment
Coupon
)
i
1
(
Payment
Coupon
P
Specifically, to find the price of a zero coupon bond (also called a discount bond), simply
set the coupon payments to zero:
n
COUPON
ZERO
)
i
1
(
Face
P
.
Or, consider the price of a fixed payment loan, in which n fixed payments are made to
retire the loan. Each of the fixed payments is part principal repayment and part interest
payment. Accordingly, set the face value term to zero since principal repayment is
directly included as part of the fixed payment, and change the terminology from “coupon
payment” to “fixed payment,” obtaining
n
2
PAYMENT
FIXED
)
i
1
(
Payment
Fixed
)
i
1
(
Payment
)
i
1
(
Payment
P
Or, finally, to find the price of the consol, let the number of years, n, until return of
principal grow arbitrarily large (in mathematical lingo, let n → ∞). For a given face
value, this makes the denominator of the last term in the coupon bond expression
arbitrarily large (pick an interest rate, even as low as 1%, and compute 1/(1+i)
n
using a
large value of n, such 1,000 or 10,000, and see what you obtain). So,
n
2
CONSOL
)
i
1
(
Payment
Coupon
)
i
1
(
Payment
Coupon
)
i
1
(
Payment
Coupon
P
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View Full DocumentChapter 6: Bonds, Bond Prices, and the Determination of Interest Rates
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2
where the sum goes on forever. (You learned to evaluate this expression in the appendix
to chapter 4, text pages 9495; if you don’t remember the details, they are worth
reviewing.)
In addition, notice that for any of these expressions for a given value for n,
1.
if you know the price of the asset and the payments, which are known when the
bond or loan is issued, you can solve for the interest rate;
2.
if you know the interest rate and the payments, you can find the price; and
3.
the interest rate is always in the denominator, which implies that a rise in the
interest rate
must
imply a fall in the price of the asset and vice versa.
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 Spring '05
 Staff
 Interest Rates

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