Question

In your own words Discuss in detail why bonds may be sold or traded at a discount or a premium. Also explain in your own words what the amortization of a bond discount or a bond premium is and how it works.

Answer 1

Why a Bond Trades at a Premium or a Discount

If a bond with a par value of $1,000 is selling at a premium when it can be bought for more than $1,000 and is selling at a discount when it can be bought for less than $1,000.

When a bond is first issued, it has a fixed coupon rate that is paid on its $1000 face value. A bond with a coupon of 3% pays $30 annually, and it will continue to be same $30 in future year as Interest is always paid on face value of bond and not on Issue Price of a bond.

Say the bond’s price rises to $1050 after a year (i.e. trades at a premium). At this time, the bond is still paying investors $30 a year, but it now trades with a yield to maturity of 2.86% ($30 divided by $1050). On the other hand, if the bond’s price falls to $950, the yield to maturity is 3.16% ($30 divided by $950).

With this in mind, we can determine that:

• A bond trades at a premium when its coupon rate i.e. 3% is higher than yield to maturity i.e. 2.86%
• A bond trades at a discount when its coupon rate i.e. 3% is lower than yield to maturity i.e. 3.16%

Amortizing of a Bond Discount or Bond Premium

Discount on Bond or Premium on a Bond is amortized under straight-line method of amortization. Under this method of accounting, the bond discount or premium is amortized over the life of the bond.

Considering the above example Where par value of Bond is $1000 and issue price is $1050 that means there is a premium of $50 ($1050-$1000). It will be amortized over the life of a bond. Assuming Life of a Bond is five years. In that case $10 will be amortized each year ($50/5)

Where par value of Bond is $1000 and issue price is $950 that means there is a discount of $50 ($1000-$950). It will be amortized over the life of a bond. Assuming Life of a Bond is five years. In that case $10 will be amortized each year ($50/5)