Problem Set #4  Solutions
GSI: Florent Rouxelin
81.
A 30year bond with a face value of $1000 has a coupon rate of 5.5%, with semiannual payments.
a.
What is the coupon payment for this bond?
b.
Draw the cash flows for the bond on a timeline.
a.
The coupon payment is:
Coupon Rate
Face Value
0.055
$1000
$27.50.
Number of Coupons per Year
2
CPN
b.
The timeline for the cash flows for this bond is (the unit of time on this timeline is sixmonth periods):
2
P
100/(1.055)
$89.85
82.
Assume that a bond will make payments every six months as shown on the following timeline (using
sixmonth periods):
a.
What is the maturity of the bond (in years)?
b.
What is the coupon rate (in percent)?
c.
What is the face value?
a.
The maturity is 10 years.
b.
(20/1000) x 2 = 4%, so the coupon rate is 4%.
c.
The face value is $1000.
87.
Suppose a fiveyear, $1000 bond with annual coupons has a price of $900 and a yield to maturity of
6%. What is the bond’s coupon rate?
2
5
C
C
C
1000
900
C
$36.26, so the coupon rate is 3.626%.
(1
.06)
(1
.06)
(1
.06)
We can use the annuity spreadsheet to solve for the payment.
1
$27.50
0
2
$27.50
3
$27.50
60
$27.50 +
$1000
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NPER
Rate
PV
PMT
FV
Excel Formula
Given:
5
6.00%
900.00
1,000
Solve For PMT:
36.26
=PMT(0.06,5,900,1000)
Therefore, the coupon rate is 3.626%.
88.
The prices of several bonds with face values of $1000 are summarized in the following table:
For each bond, state whether it trades at a discount, at par, or at a premium.
Bond A trades at a discount. Bond D trades at par. Bonds B and C trade at a premium.
811.
Suppose that General Motors Acceptance Corporation issued a bond with 10 years until maturity, a
face value of $1000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond
when it was issued was 6%.
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 Spring '07
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