Question

1a. Thomas' Trains has bonds outstanding that mature in eleven years. The bonds pay interest semiannually and have a coupon rate of 7.82%. If the face value is $1,000 and the yield to maturity is 6.2%, what is the market price per bond?  

1b. Jalen's Roses Inc. has outstanding bonds with a current market price of $704. The bonds have a 6.2% coupon rate (paid annually) and a face value of $1,000. The YTM is 10.4%. How many years until these bonds mature?

1c. Navarro, Inc., plans to issue new zero-coupon bonds with a par value of $1,000 to fund a new project. The bonds will have a YTM of 6.03 percent and mature in 30 years. If we assume semiannual compounding, at what price will the bonds sell?

1d. Healthy Peeps offers 5.75 percent coupon bonds with semiannual payments and a yield to maturity of 6.84 percent. The bonds mature in 7 years. What is the market price per bond if the face value is $1,000?

1e. You own a bond that matures in 11 years. Currently, the bond is selling for $1,034.14. The face value is $1000 and the coupon rate is 5.2% (paid annually).  

What is the yield to maturity?

1f. Birds' Drive Inc. has bonds on the market making annual payments, with 12 years to maturity, a par value of $1,000, and a current price of $1,124.60. At this price, the bonds yield 6.2 percent. What is the coupon rate?

Answer 1

1a. The market price of a bond can be found by PV function in EXCEL

=PV(rate,nper,pmt,fv,type)

Payments are semi-annual,

rate=yield to maturity/2=6.2%/2=3.1%

nper=number of periods=2*11=22

pmt=semi-annual coupon payment=(7.82%*1000)/2=39.1

fv=1000

=PV(3.1%,22,39.1,1000,0)

PV=$1127.81

The market price of the bond=$1127.81

1b. The bonds to mature can be found using nper function in EXCEL

=nper(rate,pmt,pv,fv,type)

The payments are annual here

rate=YTM=10.4%

pmt=annual coupon payment=(6.2%*1000)=62

pv=704

fv=1000

=nper(10.4%,62,-704,1000,0)

nper=number of years to mature=13.3 years

1c. Again its same as 1a.

=PV(rate,nper,pmt,fv,type)

Payments are semi-annual,

rate=yield to maturity/2=6.03%/2=3.015%

nper=number of periods=2*30=60

pmt=0

fv=1000

=PV(3.015%,60,0,1000,0)

PV=$168.26

The bond should sell at $168.26

1d. the formula to calculate market price of the bond=PV(rate,nper,pmt,fv,type)

Payments are semi-annual,

rate=yield to maturity/2=6.84%/2=3.42%

nper=number of periods=2*7=14

pmt=semi-annual coupon payment=(5.75%*1000)/2=28.75

fv=1000

=PV(3.42%,14,28.75,1000,0)

PV=$940.16

The market price of the bond=$940.16

1e. The payments are annual

yield to maturity can be found by using RATE function in EXCEL

=RATE(nper,pmt,pv,fv,type)

nper=number of periods=11

pmt=coupon payment=(5.2%*1000)=52

pv=1034.14

fv=1000

=RATE(11,52,-1034.14,1000,0)

RATE=YTM=4.79%

1f. The payments are annual

We have to use PMT function to find the coupon and its rate

=PMT(rate,nper,pv,fv,type)

rate=6.2%

nper=12

pv=1124.60

fv=1000

=PMT(6.2%,12,-1124.60,1000,0)

PMT=$77.03

Coupon rate=$77.03/$1000=7.70%