Question

The semi-annual bonds of Delta Company have a coupon rate of 6%, a Yield to Maturity of 8%, a par value of $1,000, and 20-years to maturity.

a. Calculate the price of a Delta Company bond today.

b. What will be the price of a Delta Company bond in 1 year if the YTM decreases to 7%?

Answer 1

Coupon rate = 6%, YTM = 8%

Par value = 1,000 and period = 20 years

Since its semi-annual

a.

Here, C = 1000 x 6/100 x 1/ 2 = 30

R = 8%/2 = 4%

F = 1000 and t =40 (20 years x 2 semi-annual payment = 40)

Bond value = 30 x ((1 - (1/(1+4%)^40)) / 4%) + 1000 / (1+4%)^40

Bond Value = 30 x (1-0.208289)/0.04 + 1000 / 4.801021

Bond Value = 30 x 19.79277 + 208.289

Bond Value = 593.7832 + 208.289

Bond Value = 802.0723

b. When YTM = 7% and time = 19 years

Bond Value = 30 x ((1 - (1/(1+3.5%)^38)) / 4%) + 1000 / (1+3.5%)^38

Bond Value = 30 x (1-0.270562) / 0.035 + 1000 / 3.696011

Bond Value = 625.2326 + 270.5619 = 895.7946