Question

A 10-year bond has a face value of $1,000 with a 5% per annum coupon rate. The bond pays coupons semi-annually. The current yield to maturity of the bond is 4% per annum. After 5 years, the yield to maturity of the bond is predicted to increase to 6% per annum, what would be the value of the bond in Year 5?

Answer 1

Solution :

As given in question,

Face value of Bond = $1000

Annual coupon rate = 5%

Bond pays coupon = semi annually

So, Semi Annual coupon payment will be = $1000 * 5% * 6/12 = $25

Yield to maturity of the bond after 5 years = 6%

Semi annual yield to maturity rate = 6% / 2 = 3%................................. taken as " i " in formula

Total no. of periods = Remaining years after year 5 * 2

= 5 * 2

= 10 ............taken as " n " in formula

Calculation of Bond Price at year 5

Value of Bond at year 5 = [Semi annual coupon payment * [1 - ( 1/(1 + i)n] / i ] + [Face value of bond / (1 + i)n ]

Value of Bond at year 5 = $25 * [1 - ( 1/(1 + i)n] / i + 1,000/ (1 + i)n

= 25 * [1- (1/1+0.03)10] / 0.03 + 1000 / (1 +0.03)10

= 25 * [ 1- (1/1.344) ] /0.03 + 1000/1.344

= 25 * [ 1 - 0.7441 / 0.03 + 744.09

= 25 * 8.53 + 744.09

= 213.26 + 744.09

= $957.35