Question

A coupon bond which pays interest semi-annually, has a par value of Rs.1,000, matures in 5 years, and has a yield to maturity of 8%. If the coupon rate is 10%, the intrinsic value of the bond today will be __________.

Answer 1

Rs.1,081.10

Step-by-step explanation:

The intrinsic value of the bond today is the present value of the bond's future cash flows discounted at the appropriate yield which in this case is the semiannual yield to maturity since the bond pays coupons twice a year.

Using the bond price formula below, the bond price is computed thus:

Bond price=face value/(1+r)^n+semiannual coupon*(1-(1+r)^-n/r

face value=Rs.1,000

r=semiannual yield to maturity=8%*8/12=4%

n=number of semiannual coupons in 5 years=5*2=10

semiannual coupon=face value*coupon rate*6/12=1000*10%*6/12=50

bond price=1000/(1+4%)^10+50*(1-(1+4%)^-10/4%

bond price=1000/(1.04)^10+50*(1-(1.04)^-10/0.04

bond price=1000/1.48024428 +50*(1-0.67556417 )/0.04

bond price=1000/1.48024428 +50*0.32443583 /0.04

bond price= 675.56+405.54 = Rs.1,081.10