Time Value of Money Homework Solutions

Dr. Stanley D. Longhofer
MBA 800 – Financial Statement Analysis
Bond Valuation Practice Problems – Solutions
Note: Some of the problems below came from Corporate Finance, 6 th edition by Ross,
Westerfield, and Jaffee.
1) Consider a semi-annual bond with a 7 1/8 percent coupon trading at 104 with ten
years remaining until maturity.
a) What is the yield to maturity on this bond?
P/Y = 2, N = 20, FV = 1,000, PMT = 35.625, PV = − 1,040
⇒ I = YTM = 6.57%.
b) What will happen to the price of this bond if the market required return is 6
percent?
I = 6 ⇒ PV = − 1,083.69. The new price would be 108.37.
2) Suppose a pure discount bond with a par value of $100 and maturing in one year sells
for $93.46, while a similar two-year discount bond sells for $84.17.
a) What is the current one-year spot interest rate? (Hint: It is the yield to maturity
on the one-year bond.)
P/Y = 1, N = 1, PV = − 93.46, PMT = 0, FV = 100 ⇒ I = 7.00%.
b) What is the current two-year spot interest rate?
P/Y = 1, N = 2, PV = − 84.17, PMT = 0, FV = 100 ⇒ I = 9.00%.
c) Bonus: What is the implied one-year forward interest rate (i.e., the one year
interest rate between years one and two)?
The two-year spot rate is simply the geometric average of the one-year rates
for each year. Thus, you can use this relationship to solve for the one-year
forward rate:
( 1
+ r
0−
2
)
1.
09
1+
r
2
2
1−2
r
1−2
1
=
( 1
+ r
0−1
) × ( 1+
r
= 1.
07 × ( 1+
r
= 1.
1104
= 11.
04%
3) A bond is sold at 93.2 percent of par. The bond has twelve years remaining to
maturity and investors require a 6.75 percent yield on the bond. What is the coupon
rate for the bond if the coupon is paid semiannually?
Enter P/Y = 2, N = 24, PV = − 932, I = 6.75, FV = 1,000 and solve for
PMT = $29.57. The annual coupon payment is therefore $59.14, for an annual
coupon rate of 5.914%.
1−2
)
1−2
)

4) The Sue Fleming Corporation has two different bonds currently outstanding. Bond A
has a face value of $40,000 and matures in 20 years. The bond makes no payments
for the first six years and then pays $2,000 semiannually for the subsequent eight
years, and finally pays $2,500 semiannually for the last six years. Bond B also has a
face value of $40,000 and a maturity of 20 years; it makes no coupon payments over
the life of the bond. If the required rate of return is 12 percent compounded
semiannually, what is the current price of
a) Bond A?
Use the irregular cash flow function in your financial calculator to value this
bond:
b) Bond B?
Dates Payment Frequency
1-12 0 12
11-28 2,000 16
29-39 2,500 11
40 42,500 1
There are several points to note about these entries. First, the periods are 6month
intervals because of the semiannual payments. Second, it is important
to put in the 12 periods without payments; otherwise, your financial calculator
won’t discount the later payments correctly. Finally, when the bond matures
it pays back its face value of $40,000. At the same time, it makes its final
coupon payment. These two payments are added together and listed as the
final cash flow. Don’t simply put the $40,000 payment as an additional cash
flow in period 41. You will get the wrong answer!
When you solve for the PV, you need to give your calculator the periodic rate,
not the annual rate. This is because your payments occur at semiannual
intervals. Solving for the PV of these cash flows with a 6 percent discount
rate gives us PV = $18,033.86.
You can use the TVM function in your calculator to solve for the value of this
pure discount bond: P/Y = 2, N = 40, I = 12, PMT = 0, FV = 40,000 ⇒
PV = − 3,888.89.
5) Assume the following spot rates:
Maturity Spot Rates (%)
1 5
2 7
3 10
What are the forward rates over each of the three years?
f 5.
00%
, the current spot rate over the first year.
1 =
2

3
%
04
.
9
1
05
.
1
07
.
1
1
)
1
(
)
1
(
2
1
2
2
2
=
−
=
−
+
+
=
r
r
f .
%
25
.
16
1
07
.
1
10
.
1
1
)
1
(
)
1
(
2
3
2
2
3
3
3
=
−
=
−
+
+
=
r
r
f .