Question

The following statements are true. Explain why. a. If a bond’s coupon rate is higher than its yield to maturity, then the bond will sell for more than face value. b. If a bond’s coupon rate is lower than its yield to maturity, then the bond’s price will increase over its remaining maturity.

Answer 1

Answer:

A Bond's current market value represented by $B_{0}$ is the present value of a bond as on today. Present value of a bond is it's future cash flows in the form of coupon payments and principal repayment discounted at investor's expectation in the market also referred to as Yield to maturity(YTM).

Present value of a bond is given by the following equation,

$B_{0} = \frac{C}{(1\ +\ YTM)^{1} } +\ \frac{C}{(1\ +\ YTM)^{2} } \ +\ ......+\ \frac{C}{(1\ +\ YTM)^{n} } \ +\ \frac{RV}{(1\ +\ YTM)^{n} }$

where C= Annual coupon payments

YTM = Yield to maturity/ cost of debt/ market rate of return on similarly priced bonds

RV = Redemption value of bond

n = number of years to maturity

a. A bond's coupon rate is higher than it's yield to maturity, then the bond will sell for more than face value.

Hence, if the company pays more interest than what is paid in the market on similarly priced bonds, such bonds shall sell at more than their face value.

b. If a bond's coupon rate is lower than it's yield to maturity, then the bond's price will increase over it's remaining maturity.

Similarly, if a bond pays lower rate of interest than the market rate of interest on similarly priced bonds, the bond shall sell at lower than it's face value and the price will increase over the remaining life of such bonds.