This preview shows pages 1–3. Sign up to view the full content.
FIN340
HOMEWORK #3
SOLUTION
1.
If the term structure of interest rates is flat, all yields are the same (at 3%
in this problem). In general, the price of a bond is the present value of its
future cash flows (coupon payments and principal repayment). Since all
the yields are the same, we can use the annuity formula to find the value
of the coupons and then add in the present value of principal payment.
If the interest rates were not all the same, you can’t use the annuity
formula. You have to discount each cash flow individually using the
appropriate yieldtomaturity for each corresponding maturity/cash flow
and then add them up.)
a) 10year bond with a 2% coupon:
⎡⎤
×−
+
⎢⎥
⎣⎦
20
20
10
1
1,000
PV =
1
= 914.16
0.015
(1+0.015)
(1+0.015)
b) 10year bond with a 4% coupon:
+
20
20
20
1
1,000
PV =
1
=1,085.84
0.015
(1+0.015)
(1+0.015)
c) 10year bond with a 2% coupon:
+
20
20
15
1
1,000
PV =
1
=1,000
0.015
(1+0.015)
(1+0.015)
d) When the coupon rate is lower than the yield, the bond price is lower
than the face value and hence it is sold at a
discount
. When the
coupon rate is higher than the yield, the bond price is higher than the
face value and hence it is sold at a
premium
.
Only when the rates are
equal, the bond sells
at par
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2.
See also the Excel File for more calculations and for more details.
a) We begin by finding the price of the 6% coupon bond using the
mathematical definition of YTM:
⎡⎤
×−
+
⎢⎥
⎣⎦
22
60
1
1,000
PV =
1
=1,037.72
0.04
(1+0.04)
(1+0.04)
Next we can find the yield of the 1year zerocoupon bond given by.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '09
 Narg

Click to edit the document details