Question

Bond A and bond B both pay annual coupons, mature in 8 years, have a face value of $1000, pay their next coupon in 12 months, and have the same yield-to-maturity. Bond A has a coupon rate of 6.5 percent and is priced at $1,050.27. Bond B has a coupon rate of 7.4 percent. What is the price of bond B?

Answer 1

Price of a bond is the present value of future coupons and redemption amount discounted at yield to maturity of the bond. It can also be presented in the following manner:

Here: I is the periodic coupon amount,

r is the yeild to maturity,

n is the periods to maturity,

F is the redemption amount of the bond,

PVAF is the present value annuity factor which may also be represented by and

PVIF is the present value intrest factor which may also be represented by

Step: 1. We have been given following for bond B:

Years to maturity : 8 years

Face Value : $ 1,000

Coupon Rate : 7.4% annual

Annual Coupon Amount: $ 74

Yield to maturity : ?

Side Note:1. Yield to matuiry of Bond B is missing but as given in the question Bond A and Bond B have the same Yield to maturity, we can derive Yield to maturity of Bond A.

Step: 2. Yield to maturity of Bond A

Side Note: 2. Yield to Maturity may be derived by financial calculator or Trial and Error method but we can derive the same by following formula as well.

YTM

Here: r = Yield to maturity,

I = 6.5% of $ 1,000

= $ 65

F = $ 1,000

P = $ 1,050.27

n = 8 years

%

Step: 3 Price of the Bond B

Therefore price of the Bond B is $1,104.78.

Please Upvote. Thank You.