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Present Value
Financial Economics
Bruce C. Dieffenbach
Question 1
When the price of a bond equals the maturity value, then the yield to
maturity equals the current yield. Show this property for a twoyear bond.
The bond price
P
equals the present value of the coupon payments
C
and
the maturity value 1000:
P
=
C
1
+
R
+
C
+
1000
(
1
+
R
)
2
.
When
P
=
1000, show
R
=
C
/
1000. (Hint: Substitute
R
=
C
/
1000 into
the righthand side, and show that
C
cancels out, to give a value of 1000.)
Answer 1
Evaluate the present value by substituting
R
=
C
/
1000:
PV
=
C
1
+
R
+
C
+
1000
(
1
+
R
)
2
=
C
1
+
C
/
1000
+
C
+
1000
(
1
+
C
/
1000
)
2
=
1000
C
1000
+
C
+
1000
2
(
1000
+
C
)
(
1000
+
C
)
2
=
1000
,
as desired.
Alternatively, one could solve
1000
=
C
1
+
R
+
C
+
1000
(
1
+
R
)
2
for
R
, using the quadratic formula.
Question 2
Consider the following, quoted from an article in the
Wall Street Journal
:
Disney Amazes Investors With Sale of 100Year Bonds
The corporate race to lock in low credit costs hit a fever pitch as Walt Dis
ney Co. began marketing the first sale of 100year bonds by any borrower
since 1954. Bond traders were stunned to hear that the entertainment
concern is expecting to sell $150 million of 100year bonds at a yield of
only about 7.5%, barely .
.. above 30year U. S. Treasury bonds. “It’s
crazy,” said William Gross. “Look at the path of Coney Island over the
last 50 years and see what happens to amusement parks.” Investors buy
ing a 100year Disney issue will need to have a “lot of confidence in the
longevity of Mickey Mouse,” said John Lonski.
Do you agree with the reaction of these two men? Discuss the validity
of their comments, from the viewpoint of present value. Can one justify
buying the bonds only if Mickey will still be popular in 100 years?
Answer 2
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This note was uploaded on 04/20/2008 for the course ECO 466y taught by Professor Dieffenbach during the Spring '08 term at SUNY Albany.
 Spring '08
 Dieffenbach
 Economics

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