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# Bond Interest Annually

I. The Sampson Company issued a \$1,000 bond 5 years ago with an initial term of 25 years
and a coupon rate of 6%. Today's interest rate is 10%.
1) What is the bond's current value if interest is paid semiannually as it is on most bonds?
2) What is the value of the bond if the bond's interest is paid annually?

II. Assume that you wish to purchase a bond with a 30-year maturity, an annual coupon rate
of 10 percent, a face value of \$1,000, and semiannual interest payments. If you require a 9
percent nominal yield to maturity on this investment, what is the maximum price you should
be willing to pay for the bond?

III. A bond has an annual 8 percent coupon rate, a maturity of 10 years, a face value of
\$1,000, and makes semiannual payments. If the value of the bond is \$934.96, what is the
annual yield to maturity (i.e., kd) on the bond?

IV. A bond has an annual 11 percent coupon rate, an annual interest payment of \$110, a
maturity of 20 years, a face value of \$1,000, and makes annual payments. It has a yield
to maturity of 8.83 percent. If the price is \$1,200, what rate of return will an investor
expect to receive during the next year?

V. A 20-year, 10 percent semiannual coupon bond, with a par value of \$1,000 sells for
\$1,200(assume that the bond has just been issued today).
1) What is the bond's yield to maturity?
2) What is the bond's current yield?
3) What is the bond's capital gain or loss yield if the bond is purchased today and sold
next year. (Hint: Find the values of the bond today and one year after. Or you can use the
general relationship among 'yield-to-maturity,' current yield,' and 'capital gain/loss.' )

VI. Red Frog Brewery has \$1,000-par-value bonds; 5 years until final maturity; and a 9
percent coupon rate(with interest paid semiannually). Interestingly, Old Chicago Brewery has
a very similar bond issue outstanding. In fact, every bond feature is the same as for the Red
Frog bonds, except that Old Chicago's bonds mature in exactly 15 years. Now, assume that
the market's nominal annual required rate of return for both bond issues suddenly fell from 9
percent to 8 percent.
2-2
Calculate the values of the two bonds, Red Frog Brewery and Old Chicago Brewery 1) when
the required rate of return is 9 percent 2) 8 percent.

#### Solution Preview

1.
a. n =20?2= 40
I/Y = 10/2 = 5.00%
PMT = 60/2=30
FV = 1,000;
CPT PV = 656.82

b. n =20
I/Y = 10%
PMT = 60
FV = 1,000
CPT PV = 659.45

2.
n =30x2=60
I/Y = 9/2 = 4.50%
PMT = 100/2=50
FV = 1,000;
CPT PV = 1103.19

3.
n =10x2=20
PMT = 80/2=40
PV = 934.96;
FV=1000
CPT I/Y = 4.5% -> ...

\$2.19