How to Calculate Bond Premium or Discount? (Explained)

A bond is a fixed-income instrument that allows companies to receive funds. On the other hand, it provides the acquirer with the right to obtain fixed interest payments in the future. In practice, however, bonds are more complex than that. These instruments come from multiple sources, for example, companies, local governments, etc. However, they hold similar features that make them a favorable investment option.

When a company issues a bond, it obtains the services of a trustee. Usually, this party includes a financial institution that acts as an intermediary. This institution facilitates the process between the bond issuer and the holder. The holder acquires those bonds and may hold them until maturity. During this period, they receive interest payments based on face value.

The face value of a bond represents the amount the bond issuer will repay the holder. In some cases, it may also be the value paid by the holder to acquire it. However, the issuer may also issue the bond at a higher or lower price. This price does not relate to the bond’s face value. Instead, it falls under bond premium or discounts. Calculating these amounts is straightforward. However, it requires the knowledge of both terms and their differences.

What is a Bond Premium?

A bond premium is a surplus that companies get on issuing bonds above their face value. This amount relates to premium bonds, which describe bonds trading above their face value. As mentioned, every bond has a face value, which dictates its coupon payments and obligation. However, it does not represent the price that the bondholder will pay for it.

Some issuers charge higher or lower to issue a bond based on several factors. When it’s the former case, the bond becomes a premium bond. In other words, when an issuer charges a price higher than the bond’s face value, it falls under the bond premium. However, this premium only defines the excess funds received for the issuance. It does not include the bond’s face value.

However, the term premium bond also includes bonds trading at a higher value than the face value. In this case, it does not relate to how much the company charged. While the initial price of the bond may be lower than the face value, it can still trade at a premium. Usually, this process does not depend on the issuer or the holder. Instead, it relates to market expectations.

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A bond premium may generate when the market interest rates fluctuate. Due to these fluctuations, the market may perceive the bond to have a higher or lower value. With the former case, the bond will start trading at a premium. Usually, when the bond’s actual interest rates are higher than the market, it will become a premium bond. This definition is crucial in understanding how to calculate the bond premium.

Overall, a premium in the context of a bond may cover two cases. The first includes when companies charge a higher price for their issued bonds. In that context, the issuer controls the premium. In the second case, a bond premium is when bonds trade at a higher price in the market than the face value. It occurs when the bond’s interest payments are higher than the market.

What is a Bond Discount?

A bond discount is the opposite of a bond premium. It refers to the deficit generated from issuing bonds below their face value. Similarly, it relates to discount bonds, which describe bonds trading below their face value. The bond discount is similar to the bond premium in that it differs from the par value. In this case, however, it is lower.

When an issuer charges a lower price for their bond, it falls under a bond discount. Usually, issuers prefer not to receive a lower amount. However, the circumstances may force them to charge a lower value. The bond discount, in this case, represents the deficit from the transaction. It does not include the face value or the market value.

Like the premium bond, the bond discount can also relate to bonds trading at lower than face value. Similarly, it does not relate to how much the company charges for the bond initially. As mentioned, the issuer may issue the bond at a premium. However, it can still fall under a bond discount due to market fluctuations. The issuer and holder do not control this process.

A bond discount generates when the market interest rates fluctuate, like premiums. These fluctuations change the market perception of the bond’s value. Like the premium, the bond discount considers the difference between interest rates. If the interest payments on a bond are lower than the market, it falls under a bond discount. Usually, this occurs when the market interest rates are higher than those offered by the bond.

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Overall, a bond discount covers two areas, like the premium. The first is when an issuer charges a lower price for their bonds than the face value. In contrast, it also includes when bonds trade at a lower price than the face value in the market. The former process falls under the issuer’s control, while the other relates to the market. These definitions can help calculate the bond discount as well.

How to Calculate Bond Premium or Discount?

As mentioned, bond premium and discount apply to two scenarios. The first involves issuers issuing their bonds at a higher or lower price. In that scenario, estimating the bond premium and discount are straightforward. Issues can use the following formula to do so.

Bond premium or (Bond discount) = Issue price – Face value

If the above formula returns a positive value, the issuer issued the bond at a premium. In contrast, the bond discount will apply when the face value is higher than the issue price. However, bond premiums and discounts do not apply to this scenario often. Instead, it relates to the trading aspect of the bonds in the market.

Calculating the bond premium or discount for trading bonds is more complex. It requires issuers to measure the present value of the payments from the bond using the market interest rate. Usually, issuers can predict whether this calculation will result in a bond premium or discount. As mentioned, the difference between the bond and market coupon rate can reveal that information.

After calculating the present value of the payments from the bond, issuers must compare it to its face value. If the former is higher, then it falls under a bond premium. In the latter case, it will be a bond discount. The above explanation only provides the basis for calculating bond premium or discount. It is better to understand it through an example.

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Example

A company, ABC Co., issues a bond with a face value of $100, promising a coupon rate of 5%. Similarly, the maturity date for the bond falls after three years. This coupon rate applies semi-annually. Therefore, the rate for each payment will be 2.5% (5% / 2 payments). However, the market coupon rate is 4%. The semi-annual market interest rate is 2% (4% / 2 payments).

For calculating bond premium or discounts, it is crucial to calculate the present value of its payments. Firstly, bonds include regular fixed interest payments. Bondholders will receive $5 each year, or $2.5 semi-annually from ABC Co. These payments will continue for three years. Therefore, it is crucial to discount these at the market interest rate of 2%.

The calculation of the present value of these payments is as below.

PaymentAmountDiscount factor (2%)Present value
1$2.51.02^-1$2.451
2$2.51.02^-2$2.403
3$2.51.02^-3$2.356
4$2.51.02^-4$2.310
5$2.51.02^-5$2.264
6$2.51.02^-6$2.220
Total$15 $14.004

On top of these, the bond will also include a payment of $100 to the bondholder at maturity. This amount is the face value of the bond that the issuer must repay. Similarly, the issuer must also calculate the present value of this payment based on the market value. The calculation is as below.

Present value of face value = $100 x (1.02^-6)

Present value of face value = $88.797

The total present value of the payments from the bond will be as follows.

Present value of cash flows from the bond = Present value of face value + Present value of interest payments

Present value of cash flows from the bond = $88.797 + $14.004

Present value of cash flows from the bond = $102.801

The last step involves comparing this present value to the bond’s face value. As this value exceeds the $100 face value, it will fall under a bond premium. In contrast, if it were lower, then it would be a bond discount.

Conclusion

A bond is a debt instrument that allows issuers to raise debt finance. Usually, these instruments trade at a higher or lower value than their face value. These fall under bond premiums and discounts. As mentioned, these terms cover various scenarios. Calculating these bond premium and discount are straightforward.