Question

An AT&T bond carries a coupon rate of 6%, has 7 years until maturity, and sells at a yield-to-maturity (YTM) of 8%.

1. What interest payments do bondholders receive each year?
2. At what price does the bond sell? (Assume annual interest payments.)
3. What would likely happen to the bond price if the yield-to-maturity fell to 6%?

Answer 1

Solution

Considering Par value=$1000

Intrest payment=Coupon rate*par value=6%*1000=$60

Current price of bond=Present value of coupon payments+Present value of face value

Current price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

where

n=number of periods=7

r-discount rate per period=YTM=8%

Face value =1000

Coupon payment=60

Current price of bond=60*((1-(1/(1+.08)^7))/.08)+1000/(1+.08)^7

=$895.8726

If the yield price fell to 6% the price of the bond will increase and this is due to the fact that the bond price increases with fall in intrest rates.

In this case if the YTM falls to 6% at the current time itself

Price of the bond will be=60*((1-(1/(1+.06)^7))/.06)+1000/(1+.06)^7=$1000

Then the bond price will increase and become equal to par value.