Fina3001
Solution #5
2. Plan:
We can see that the bond consists of an annuity of 20 payments of $20, paid every
6 months, and one lumpsum payment of $1000 (face value) in 10 years (twenty 6month periods).
We can rearrange Eq. (6.1) in order to find the coupon rate knowing the coupon payment of $20.
By rearranging Eq. (6.1) we come up with: coupon rate
(coupon payment/face value)
number
of coupon payments per year.
Execute:
a. The maturity is 10 years.
b. (20/1000)
2
4% so the coupon rate is 4%.
c. The face value is $1000.
Evaluate:
The maturity of the bond is the final repayment date of that bond, at which point
payments on the bond will terminate. In this case, the bond will make 20 semiannual payments
terminating in 10 years. We can find the coupon rate if we know the coupon payment, face
value, and number of coupon payments per year by using and rearranging Eq. (6.1). Finally,
we know that the face value of the bond is the amount repaid at maturity, in this case $1000.
3. Plan:
We can use Eq. (6.2) to compute the yield to maturity for each bond. We can then use
Excel to plot the zerocoupon yield curve, which will plot the yield to maturity of investments
of different maturities using the yield to maturity on the
y
axis and the maturity in years on the
x
axis.
Execute:
a. Using Eq. (6.2) for the first five years to compute the yield to maturity:
1/
1 /1
11
1 / 2
1 / 3
33
1 / 4
44
1 / 5
55
FV
1
YTM
100
1
4.70%
95.51
1
4.80%
91.05
1
5.00%
86.38
1
5.20%
81.65
1
5.50%
76.51
n
n
n
P
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View Full Documentb. The yield curve is
Zero Coupon Yield Curve
4.6
4.8
5
5.2
5.4
5.6
0
2
4
6
Maturity (Years)
Yield to Maturity
c. The yield curve is upward sloping.
Evaluate:
The yield to maturity of the bond is the discount rate that sets the present value of the
promised bond payments equal to the current market price of the bond. We can use Eq. (6.2)
knowing the face value, price, and year of each bond in order to find the yield to maturity. We
can plot the zerocoupon yield curve using Excel, which will compare the yield to maturity of
investments of different maturities.
8. Plan:
The bond consists of an annuity of 20 payments of $40, paid every six months, and one
lumpsum payment of $1000 in 10 years (20 sixmonth periods). We can use Eq. (6.3) to solve
for the yield to maturity. However, we must use sixmonth intervals consistently throughout
the equation. We can also use an annuity spreadsheet in Excel (also shown below) to find the
bond’s yield to maturity. Also, given the yield, we can compute the price using Eq. (6.3). Note
that a 9% APR is equivalent to a semiannual rate of 4.5%. Again, we can use a spreadsheet in
Excel to find the new price of the bond.
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 Spring '08
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 Annuity, YTM

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