Question

1. A 30-year maturity bond makes annual coupon payments and has a coupon rate of 8%. What are the bond’s current yield and yield to maturity if the bond is selling for:

   a. $900 b. $1,000 c. $1,100

2. Recalculate yields in problem 1 assuming semiannual coupon payments.

Answer 1

For annual coupon payments:

Suppose the face value of the bond=$1000
Coupon rate=8%
Annual coupon payment=Face value*Annual coupon rate=$1000*8%=$80

Time period or number of periods when coupon payment is made annually=30 years

Current yield=Annual Coupon payment/Current Bond Price
a) When current price of the bond is $900, current yield=$80/$900=8.89%
b) When current price of the bond is $1000, current yield=$80/$1000=8.00%
c) When current price of the bond is $1100, current yield=$80/$1100=7.27%

Note: As present value is a cash outflow, it is taken as negative in the excel.

We have calculated yield to maturity using excel and the values are:
a) When current price of the bond is $900, yield to maturity= 8.97%
b) When current price of the bond is $1000, yield to maturity=8.00%
c) When current price of the bond is $1100, yield to maturity=7.18%

For semi annual coupon payments:
Suppose the face value of the bond=$1000
Coupon rate=8%, so the semiannual coupon rate=8%/2=4%
Semi annual coupon payment=Face value*Semi annual coupon rate=$1000*4%=$40

Time period or number of periods when coupon payment is made semiannually=30*2=60 years

Current yield=Annual Coupon payment/Current Bond Price
a) When current price of the bond is $900, current yield=$40/$900=4.44%
b) When current price of the bond is $1000, current yield=$40/$1000=4.00%
c) When current price of the bond is $1100, current yield=$40/$1100=3.64%

We have calculated yield to maturity using excel and the values are:
a) When current price of the bond is $900, yield to maturity=4.48%
b) When current price of the bond is $1000, yield to maturity=4.00%
c) When current price of the bond is $1100, yield to maturity=3.59%