Question

Suppose that a bond is purchased at a discount (meaning that it is sold for less than face value). Could the yield to maturity ever be less than the coupon rate? Could the rate of return be less than the coupon rate? Explain.

Answer 1

When the coupon rate is less than the yield to maturity then the price of the bond will be less than the face value. That is the bond is issued at a discounted price.

Let us assume FV = $ 1000, C = 10%, MATURITY = 10 Years

Price of bond,

Price = $ 887 (Less than face value, discount bond).

When YTM = Coupon rate = 10%

Then face value = price

Thus, when YTM = Coupon, thus the bond is issued at par.

When YTM is less than Coupon rate then the price of the bond is greater than the face value.

Assume YTM = 8%,

Thus, when YTM is less than coupon then bond is issued at a premium price.

Using the example I have attempted to explain. Please contact of having any query will be obliged to you for your generous support. Thank you.