Premium Bonds

A premium bond refers to a financial instrument that trades in the secondary market at a price exceeding its face value. This occurs when a bond's coupon rate surpasses its prevailing market rate of interest. For instance, a bond with a face value (par value) of $750, trading at $780, will reflect that the bond is trading at a premium of $30 ($780-750).

Premium bonds help in generating higher earnings in the bond market. Bonds are relatively safer than shares because bonds are essentially a debt to the issuer. As such, they carry lesser risk and usually have fixed returns. For example, a $2000 bondholder with a 5-year maturity and 10% annual interest or coupon rate will earn $200 in interest for five years. If the bond is held till maturity, $2000 will be repaid to the bondholder.

Some bonds have floating coupon rates, changing periodically. Investors try to make higher gains in a bond’s market by taking advantage of the changing coupon rates. When new bonds provide lower interest rates, the older bonds of the same category with higher interest rates attract investors.

Resultantly, older bonds start trading at a premium in the secondary market. For example, if a bond with a $2000 face value and 10% coupon rate is trading at $2200, it is a premium bond. However, the bondholder will still get $200 interest, as mentioned in the bond contract. At the time of maturity, the bondholder will still be repaid $2000.

Only when investors trade the premium bond before maturity would they feel the weight of interest change. When investors buy a premium bond, they pay a higher price than their cheaper alternatives in hopes that they’d eventually make more, especially if the interest continues to rise.

When bonds trade at a premium, it requires adjustments to compute their present value in the accounting books. The present value will help one understand the current issue price of the bond. Moreover, to compare the profitability of similar category bonds, they must be brought at the same level.

The adjustments require computation of yield to maturity (YTM), which helps in comparing bonds. YTM depicts the annual return one makes on the bond and eventually till maturity. Interestingly, if the coupon rate is lesser than YTM, the bond price will be less than its face value.

If the coupon rate is higher than YTM, the bond's price will be higher than its face value, reflecting that it is trading at a premium. Conversely, when YTM is equal to the coupon rate, the bond trading will be at its face value. This suggests an inverse relationship between YTM and bond prices.

Investors often wonder about the new issue price of bonds if their interest rate changes or if they are trading at a premium. Issue price or the bond price can also be understood as the bond value. To find the bond value or issue price, we need to add the present value of the bond and the present value of interest. Let us take a look at the formula below.

We will break down the formula for better clarity.

• BV = Bond Value or Bond Price
• BV = Present value of the bond + Present value of the interest

Present value of the bond

Present value of the interest

• F = Face Value of the bond;
• r = Yield to Maturity (YTM) or Discount Rate;
• n = Number of Periods till Maturity;
• Coupon = Bond Interest Rate

Let us take an example to understand the bond price formula better.

Suppose that IBM Corporation has issued a bond with a face value of $1,000, a coupon rate of 6%, and a maturity of 5 years. The coupon payments on the bond are made annually. If the discount rate or yield to maturity is 4%, what should be the bond’s price?

Solved Solution

Present value of the bond

= 821.9

Since the total time period or n is 5 years, we need to separately calculate the present values of the interest earned at the end of each year and add them all. We have converted both the interest rates into decimals at 0.06 and 0.04 for ease in calculations. The present value of the interest =

= 57.7+55.47+53.34+51.28+49.31

BV or Bond Price = 821.9 + 57.7+55.47+53.34+51.28+49.31

= $ 1089.04

In this example, the IBM bond is trading at a premium of $89 (1089 - 1000).

MS - Excel Solution

Additionally, with huge numbers, it becomes easier to find the bond price using MS Excel. Using the same example and formula, the bond price calculation on MS Excel is explained below.

This is the traditional way of calculating the bond value. This can also be calculated in MS Excel by using the PV (present value function).

Credit rating, market conditions and financial performance of the bond issuing company can influence a bond’s interest rate. If interest rates fall in the long run, the bond’s price will be affected. The longer the maturity, the more sensitive it is to fluctuations. As such, premium bonds could at times seem overvalued if their returns struggle to match the price paid.

Premium bond refers to a debt instrument which trades in the secondary market at a price more than its par value. It signifies a lower yield to maturity than the instrument's coupon rate and indicates over-pricing. Usually, these bonds have a high credit rating.

In contrast, a discount bond is a debt instrument available for exchange at a price below its par value. Discount bonds have a higher yield to maturity than their coupon rate, and they indicate under-pricing. The credit rating of discount bonds is often poor.