Question

In: Finance

1) A Sprint bond has a face value of $1,000, a coupon rate of 7.75%, with...

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?

Solutions

Expert Solution

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%


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