Question

In March, 2019, Volkswagen AG issued a ten-year bond with a face value of €4,000 and paying an annual coupon of 3 per cent. What is the price of the bond if the YTM is:

a. 1 percent.

b. 3 percent.

c. 6 percent.

(Assume interest is calculated at the beginning of the period and paid annually)

Answer 1

Given the interests are paid at the begining of the period and annually

The price of the bond needs to be calculated using PV function in EXCEL

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

a. rate=1%

nper=maturity time=10

pmt=coupon payment=(3%*face value)=(3%*4000)=120

fv=4000

type=1 (because the interest payments are paid at the begining of the year)

=PV(1%,10,120,4000,1)

PV=$4769.07

The price of the bond at 1% YTM=$4769.07

b. rate=3%

nper=maturity time=10

pmt=coupon payment=(3%*face value)=(3%*4000)=120

fv=4000

type=1 (because the interest payments are paid at the begining of the year)

=PV(3%,10,120,4000,1)

PV=$4030.71

The price of the bond at 3% YTM=$4030.71 (generally if YTM and coupon rate are same the price of the bond would be equal to the face value. But there the interests are paid at the begining the price is little higher due to interest received)

c. rate=6%

nper=maturity time=10

pmt=coupon payment=(3%*face value)=(3%*4000)=120

fv=4000

type=1 (because the interest payments are paid at the begining of the year)

=PV(6%,10,120,4000,1)

PV=$3169.78

The price of the bond at 6% YTM=$3169.78