Question

1. What is the present value of bond with the following characteristics:

Semi-Annual Coupon Rate = 5%

Par = $1,000

Maturity = 5 years

YTM = 8%

2.

What is the present value of bond with the following characteristics:

Semi-Annual Coupon Rate = 4%

Par = $1,000

Maturity = 15 years

YTM = 7%

3.

Suppose a bond with a 3% coupon rate and semiannual coupons, has a face value of $1,000, 30 years to maturity, and is selling for $945.82.

What is the yield to maturity?

4.

What is the present value of bond with the following characteristics:

Semi-Annual Coupon Rate = 2%

Par = $1,000

Maturity = 100 years

YTM = 3%

5.

Suppose a bond with a 2.55% coupon rate and semiannual coupons, has a face value of $1,000, 10 years to maturity, and is selling for $685.82.

What is the yield to maturity?

Answer 1

1. Use PV function in EXCEL to find the present value of bond

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

Please remember that the payments are semi-annual

rate=YTM/2=8%/2=4%

nper=5 years*2=10

pmt=semi-annual coupon=(semi-annual coupon rate*face value)=(5%*1000)=50

fv=face value=1000

=PV(4%,10,50,1000,0)=$1081.11

present value of bond=$1081.11

2. rate=7%/2=3.5%

nper=15*2=30

pmt=4%*1000=40

fv=1000

=PV(3.5%,30,40,1000,0)=$1091.96

present value of bond=$1091.96

3. Use RATE function in EXCEL to find the Yield to Maturity

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

nper=30 years*2=60

pmt=semi-annual coupon=(coupon rate*face value)/2=(3%*1000)/2=30/2=15

pv=945.82

fv=1000

=RATE(60,15,-945.82,1000,0)=1.64%

Yield to Maturity=2*1.64%=3.29%

4. Use same formula as Q1 and Q2.

rate=YTM/2=3%/2=1.5%

nper=100*2=200

pmt=2%*1000=20

fv=1000

=PV(1.5%,200,20,1000,0)=$1316.36

Present value of bond=$1316.36

5. nper=10 years*2=20

pmt=semi-annual coupon=(coupon rate*face value)/2=(2.55%*1000)/2=25.5/2=12.75

pv=685.82

fv=1000

=RATE(20,12.75,-685.82,1000,0)=3.48%

Yield to Maturity=2*3.48%=6.96%