Question

A $1000 par value bond with 4 years to maturity has a coupon payment of 9% pa paid annually. Suppose the yield to maturity is 11% pa cont. comp.

Compute the bond price and the duration??

Answer 1

Answer:

Computation of Bond Price :

This question needs to be solved using financial calculator (like Texas BA II plus)

In this Question Yield to maturity given is 11% p.a. Continuosly Compounded, so we first need to calculate effective YTM or interest rate:

In calculator:

Put 0.11 and then press 2ND and then press LN , this comes to 1.116278 , then deduct 1 from this and then multiply by 100 i.e. (1.116278 - 1)*100 = 11.63% . This is effective yield we will use to calculate the bond price.

Calculation of Bond Price:

In calculator:

Put 1000 and press FV : This is the amount we receive in future at maturity

Put 90 and press PMT : This is coupon amount we receive annually. ($1000*9%)

Put 11.63 and press I/Y : This is effective YTM or interest rate annualy (calculated above)

Put 4 and press N : This is number of years to maturity

Now press CPT and then PV

Answer comes to -919.49

Therefore $919.49 is the Bond's Price Today.

Calculation of Bond Duration :

Formula for Duration = ((1+YTM) / YTM)) - (1+YTM) + t(C-YTM) / C[(1+YTM)^t -1] + YTM

YTM = Effective yield to Maturity i.e. 11.63% or 0.1163

t = time to maturity i.e. 4

C = Coupon i.e 9% or 0.09

Duration = ((1+0.1163) / 0.1163)) - (1+0.1163) + 4(0.09-0.1163) / 0.09[(1+0.1163)⁴ -1] + 0.1163

= 9.60 - (1.0111 / 0.166)

= 9.60 - 6.09

= 3.51 Years

Therefore Duration of Bond is 3.51 years.