In: Finance
1) A Sprint bond has a face value of $1,000, a coupon rate of 7.75%, with coupons paid semi-annually, and 15 years to maturity. If the effective annual return for bonds of comparable risk is 7.75%, the price that you should be willing to pay for this bond is?
2) A corporate bond with a face value of $1,000 and coupons paid semi-annually, sells for
$1,058.39. The term to maturity is 14.5 years. If the yield to maturity of similar bonds is
9.5%, what is the coupon rate of this bond?
1. Here both the coupon rate and market rate is same at 7.75%. Hence, the price of the bond sells at face value of $1000.
You can also test this by using the PV function in EXCEL.
=PV(rate,nper,pmt,fv,type)
please remember that coupons are paid semi-annually (2 times in a year)
rate=effective annual return/2=7.75%/2=3.875%
nper=number of periods=2*15=30
pmt=semi-annual coupon=(coupon rate*face value)/2=(7.75%*1000)/2=38.75
fv=face value=1000
=PV(3.875%,30,38.75,1000,0)
PV=$1000
2. To find the coupon rate, use PMT function in EXCEL
=PMT(rate,nper,pv,fv,type)
please remember that coupons are paid semi-annually (2 times in a year)
rate=yield to maturity/2=9.5%/2=4.75%
nper=number of periods=2*14.5=29
pv=bond value=1058.39
fv=face value=1000
=PMT(4.75%,29,-1058.39,1000,0)=$51.25
PMT=semi-annual coupon payment=$51.25
Annual coupon payment=2*$51.25=$102.50
Coupon rate=coupon payment/face value=$102.50/$1000=10.25%
Therefore, coupon rate=10.25%