Question

) ABC Inc.’s Class A bonds sell at par, have a 12-year maturity, $1,000 par value and a 6% coupon paid semiannually. ABC Inc.’s Class B bonds have the same risk, maturity and par value, but pay a 7% semiannual coupon. What is the price of the Class B bonds?

no excel and no financial calculator, so please show all the numbers and how u get to them

Answer 1

If class A bond is selling at par, yield to maturity will be equal to coupon rate

Therefore, yield to maturity of bond A = 6%

Since bond B has the same risk, yield to maturity of bond B = 6%

It is semi annual bond. There are two coupon payments in a year.

Semi annual rate = 6% / 2 = 3%

Number of periods = 12 * 2 = 24

Semi annual coupon = [(7 / 100) * 1000] / 2 = 35

Price of class B bonds = Coupon * [1 - 1 / (1 + rate)^time] / rate + par value / (1 + rate)^time

Price of class B bonds = 35 * [1 - 1 / (1 + 0.03)^24] / 0.03 + 1000 / (1 + 0.03)^24

Price of class B bonds = 35 * [1 - 0.491934] / 0.03 + 491.933736

Price of class B bonds = 35 * 16.935542 + 491.933736

Price of class B bonds = $1,084.68