Question

Grohl Co. issued 18-year bonds a year ago at a coupon rate of 10 percent. The bonds make semiannual payments. If the YTM on these bonds is 9 percent, what is the current bond price?

Answer 1

Since the face value of the bond is not given in the question, i am assuming the face value to be $1000. generally bonds have a face value of $1000 or $100

Face value = 1000

Number of periods = 17 * 2 = 34 ( since it is a semi annual bond, we multiply by 2. also we use 17 becaue 17 years are left.)

Coupon payments = 0.1 * 1000 = 100 / 2 = 50 ( since it is a semi annual bond, we divide by 2)

Rate = 0.09 / 2 = 0.045

Price of bond = ?

Bond price = Coupon * [1 - [ 1 / ( 1 + r)ⁿ ] / r + FV / ( 1 + r)ⁿ

Bond price = 50* [1 - [ 1 / ( 1 + 0.045)³⁴ ] / 0.045 + 1000 / ( 1 + 0.045)³⁴

Bond price = 50* [1 - 0.2239 ] / 0.045 + 1000 / 4.4664

Bond price = 50* [ 17.2467 ] + 223.89396

Bond price = 862.335 + 223.89396

Bond price = 1,086.23

You can also use a financial calculator to solve this

Keys to use in a financial calculator: 2nd I/Y = 2, FV = 1000, PMT = 50, I/Y = 9, N = 34, CPT PV