Question

Microhard has issued a bond with the following characteristics: Par $1000 time to maturity 30 years, coupon rate 7 percent, semi annual payments. Calculate the price of this bone if the YTM is 7% 9% 5%

Answer 1

Given

Face value F=$1000

Maturity =30 years

N=30*2=60 semi annuals

Coupon rate =7%

Semi annual coupon C=7%*1000=$35

If YTM = 7%

r=YTM/2=7%/2=3.5%

then Price of Bond P=C*(1-(1+r)^-N)/r +F/(1+r)^N

P=35*(1-(1+3.5%)^-60)/3.5% + 1000/(1+3.5%)^60

P=$1000

If YTM = 9%

r=YTM/2=9%/2=4.5%

then Price of Bond P=C*(1-(1+r)^-N)/r +F/(1+r)^N

P=35*(1-(1+4.5%)^-60)/4.5% + 1000/(1+4.5%)^60

P=$793.62

If YTM = 5%

r=YTM/2=5%/2=2.5%

then Price of Bond P=C*(1-(1+r)^-N)/r +F/(1+r)^N

P=35*(1-(1+2.5%)^-60)/2.5% + 1000/(1+2.5%)^60

P=$1309.09