Question

Consider a bond with annual coupon payments. You purchased the bond when it was originally
issued. Immediately thereafter, the YTM had changed and remained at this new level
indefinitely. Today, at the end of year 4 (immediately after the 4th coupon payment), your bond
investment has the following characteristics:

Total Interest (Coupons) = Interest-on-Interest (I2) = Capital Gains = Realized Return (annual) =

$5,476.75 $1,047.89 $759.06 13.773973%

Hint: Do not assume any face value or any time to maturity at issue

You must show ALL work – including any calculator keystrokes to receive credit. Please, find
the following:
a. The annual coupon (in dollars and cents)
b. The new YTM (as a percentage with 3 digits after the decimal point)
c. The purchase price of the bond (in dollars and cents)
d. The face value of the bond (in dollars and cents)
e. The coupon rate (as a percentage with 3 digits after the decimal point)
f. The market value of the bond at the end of year 4 (in dollars and cents)
g. The time to maturity at issue (round to the nearest year)
h. The realized return at the end of year 10 (as a percentage with 3 digits after the decimal
point)
i. The realized yield at the end of year 10 (as a percentage with 3 digits after the decimal
point)

Answer 1

a) Annual Coupons=$5476.75/4=1369.19$

let the coupon rate is 10% so 1000 will be coupon for one year and 369 will be interest on the coupon

b)Realised return-Coupon rate =yield

13.7739-10=3.774

c)Purchase price=10000

d)Selling price of bond-purchase price of bond=capital gain

Sp=759.06+10000

Selling price=10759.06

so the face value is at par.

e)Coupon rate as explained in solution a by trail and error method 10%

f)market value=10759.06

g)4 years

h)face value/coupons yield for year

1369.19+261.97=1631.16

10000/1631.16=6.130%

i)Realized yield

yield to maturity-Gain in principal of bond

3.774%-2.369%

=1.40%