Question

Three $1,000 face value, 10-year, non-callable, bonds have the same amount of risk, hence their YTMs are equal. Bond 1 has an 8% annual coupon, Bond 2 has a 10% annual coupon, and Bond 3 has a 12% annual coupon. Bond 2sells at par. Assuming that interest rates remain constant for the next 10 years, what can you say about the relative prices of Bond 1 and Bond 3? That is, indicate whether each bond should sell at par, discount or premium

Answer 1

As face value and present price of Bond 2 is same at $1,000 its YTM is simply the coupon rate of 10%

Now, for Bond 1, YTM = 10%, Coupon rate = 8% => Coupon payment = $80, Face value = $1000,

Find present value or current price = $877.109 (hence trading at discount)

Now, for Bond 3, YTM = 10%, Coupon rate = 12% => Coupon payment = $120, Face value = $1000,

Find present value or current price = $1122.891 (hence trading at premium)

You can use excel or a financial calculator to easily solve it. I have attached the excel with formulas: