Question

What will be the relationship between coupon rate and yield to maturity for bonds selling at discount? Give reason to support your answer.

Answer 1

We can understand the problem with an example

Case 1

Bond face value 100

Coupon rate 12%

Bond Maturity 2 years

YTM 12 %

Calculation bond current price

Year 1 Cash flow/(1+ytm)^1 + Year 2 cash flow/(1+ytm)^2

12/(1.12)^1 + 112/(1.12)^2

10.714 + 89.286 = 100

Case 2

Bond face value 100

Coupon rate 12%

Bond Maturity 2 years

YTM 10 %

Calculation bond current price

Year 1 Cash flow/(1+ytm)^1 + Year 2 cash flow/(1+ytm)^2

12/(1.10)^1 + 112/(1.10)^2

10.909 + 92.562 = 103.471

Case 2

Bond face value 100

Coupon rate 12%

Bond Maturity 2 years

YTM 14 %

Calculation bond current price

Year 1 Cash flow/(1+ytm)^1 + Year 2 cash flow/(1+ytm)^2

12/(1.14)^1 + 112/(1.14)^2

10.526 + 86.180 = 96.706

Coupon Rate = YTM (Bond price will be at par (at face value) in above example 100)

Coupon Rate < YTM (Bond price will be at premium from face value in above example 103)

Coupon Rate > YTM (Bond price will be at discount from face value in above example 96.706)