# Difference Between Coupon Rate and Discount Rate

Edited by Diffzy | Updated on: April 30, 2023

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## Introduction

The provision of guarantees in any field helps gain both the individuals on either side of a bond gain trust and assurance. However, there are multiple ways to assure this while trying to gain a benefit through the same. These techniques can be as simple as paying interest rates and the two most common methods are coupon rates and discount rates.

## Coupon Rate vs Discount Rate

The main difference between a coupon rate and a discount rate lies in how the rates are charged and the factors upon which the rates depend. A coupon rate can be described as the annual rate of interest that the bond issuer pays to the bondholder on the fixed income security whereas a discount rate can be defined as the rate of interest chosen by the bank, paid to the lender by the borrower and is directly affected by the general economic conditions.

## What is a Coupon Rate?

Also referred to as the nominal yield, the Coupon rate on a particular bond is defined as the rate of interest applied on a particular bond whereas coupons are defined as the periodic payments of interest paid to the bondholder by the bond issuer. These payments must continue until the agreed date of maturity as stated by the bond agreement.

### How to Calculate Coupon Rate?

• We must first determine the face value of the bonds through official documentation or certificates.
• The number of periods for which the payments must be made by the bond issuer should be determined. It is typically done through the same document as mentioned above.
• The coupon rate that was established must be applied to the formula to determine the interest amount. This can either be represented as the amount to be paid periodically or directly calculated annually.
• This is done by multiplying the coupon rate with the face value of the bond and dividing it by a hundred to acquire the periodic payment.

### Types of Coupon Rates

Some common types of coupon rates could be applied to the fixed income securities and we will list them now.

Fixed Rate

Also known as plain vanilla bonds, fixed coupon rates are the most commonly used in the market of finance and real estate. To be explained simply, fixed coupon rates are those that require the issuer to pay a fixed rate of interest for the required period throughout the lifetime of the bond. This means that the conditions of the market or the economy will not affect the coupon rate. These types of bonds are usually fulfilled on a semi-annual basis but this does not mean that there are any limitations on the establishment of the periods. Thye can also be charged monthly, quarterly, or even annually.

Floating Rate

Operating exactly how the name sounds like, floating coupon rates are those that are expressed in terms of a benchmark. The interest rate on a certain bond can be expressed as the sum of the reference rate and the described margin. Let us say that a company ABC issues a bond with a floating coupon rate for 3 years and this can be described as a 3-year treasury yield with a quoted margin of 0.75%. This means that the Coupon rate = 3-year treasury yield + 0.75%. Another common example of floating coupon rates involves London Inter-Bank Interest Rate(LIBOR) which usually demands a 2% quoted margin from the bond issuers. The prime advantage of this type of interest rate is that it benefits both the bond issuers and the bondholders as there is protection against possible inflation in the market while providing the same rate of returns.

Zero-Coupon

Pretty self-explicable from the name, these types of coupon rates are don not charge any kind of coupon rates upon the bonds. They are widely offered by agencies owned by the government while still being calculated in the considered period such as monthly or semi-annually. Although this doesn’t make sense since it isn't exactly included in any overall payments, this technique is usually done to stand comparable to other kinds of bonds in the market. Typically, the bonds are sold at a large discount to their face value which would later be reclaimed at the age of maturity.

Step-up Coupon

In contrast to fixed coupon rates, step-up rates are those kinda coupon rates that can increase every year or periodically. This is typically used by those individuals or firms that do not have enough cash flow in the initial stages. Thus, they start with a small number and slowly build up as they flourish. Thus the bonds always start with a low coupon rate and step it up every year until the desired interest in accrued. While some of them have a fixed growth every year, some are planned irregularly since the market might sometimes demand higher interest under pressure. While the investors might not be benefitted at the start, it does provide them a sort of incentive to stay through a long-term plan.

Another popular technique of applying coupon rates is the credit-linked coupon rates which are similar to step-up coupon rates. Instead, the coupon rates can keep changing based on the credit the issuer receives. These credits can be quantifiable or more of an abstract measure where the firm or the individual can gain or lose credits based on how good and punctual they are with their performance. Thus, if the company performs poorly, they reduce its credits which leads to an increase in the coupon rates and parallelly, reduces the coupon rate upon acquiring higher credits.

## What is a Discount Rate?

A discount rate is a rate charged on the loans lent to a borrower whereas a bond discount is a difference in the value of the face worth of the bond and the value at which it is sold for. What exactly does the term face value or face worth mean? The face value of a bond is the principal amount due to be paid when the bond reaches its date of maturity. It is also called the par value of a bond and determines how worthy a bond is.  But what does the term maturity or Yield To Maturity mean?

### Discount rates and Yield To Maturity(YTM)

First of all, let us look at what Yield To Maturity(YTM) is. YTM can be described as the rate of return for a particular bond that the bond issuer has to pay until it reaches its date of maturity. It can also be explained as the Internal Rate of Return(IRR) of a certain asset or investment in a bond. However, it is much easier to explain the concept of YTM is a discount bond that does not include any coupon rates.

Let us look at the formula to calculate the yield to maturity when there is no inclusion of coupons:-

[(Yield To Maturity)+1]t=Face valuePresent Value

Now if we estimate it to calculate the exact value of YTM, we write Yield To Maturity=tFace valuePresent Value-1

Where t= Number of years left for maturity

Face value= The maturity value of the bond

Present value= Current worth of the bond.

However, when there are coupons involved, YTM can be defined as the rate of returns an investor can earn if he chooses to reinvest all the money he earned from the coupons until the bond reaches its maturity. We can say that the current price of the potential cash inflows in the future is the bond’s market value. Although there has been no direct method to arrive at the exact discount rate, there is a trial and error method that prevailed until now. Thus, we calculate the worth of the bond as BP=C1[(Yield To Maturity)+1]1+C2[(Yield To Maturity)+1]2+....+Cn[(Yield To Maturity)+1]n+Face Value[(Yield To Maturity)+1]n

Or

BP=C1[(Yield To Maturity)+1]1+C2[(Yield To Maturity)+1]2+....+Cn + Face Value[(Yield To Maturity)+1]n

Where BP= Bond Price

C1= First coupon

C2= Second coupon

Cn= nth coupon

How can we calculate the discount rate upon any bond? Let us proceed with an example!

Consider a company XYZ that issues a bond that is worth USD 100,000 for a 3-year term with quarterly payments. The present interest rate declared is 10%.

Let us first calculate the present value of the bond.

Interest rate=0.1 or 1%

Since the payments are done quarterly which means 4 times a year, then the market rate every period is 0.1/4=0.025

Number of periodic payments= 3*4=12

Present Value = principal*[1/(1+r)^n], where r is the rate of interest every period and n is the number of periodic payments.

Hence, PV= 100,000*[1/(1+0.025)^12]= USD 74,355

We can now calculate the present value of periodic payments:-

Each periodic payment= 100,000*0.025= USD 2500

Present value of periodic payments is interest*1-(1(1+r)n)r=2500*1-(1(1+0.025)12)0.025=10.256*2500=USD 25640

Therefore, the market price of the bond would be the sum of present values of principal and interest= 25640+74355= USD 99995.

Thus the bond discount= 100,000-99995= USD 5

## Main Differences Between Coupon Rate and Discount Rate In Points

• Coupon rate and discount rate can be differentiated primarily based on how and where the rates of interest are applied to a certain sum of money, investment or not. The former can be described as the rate of interest that is applied on fixed income security that is charged by the issuer of the bond until the date of maturity whereas the discount rate is the rate of interest applied on any sum that is lent to any borrower until the expiration date.
• The coupon rate on any bond is determined by the face value of the fixed security whereas the discount rate on a sum of money usually depends on how large the lent sum is.
• The individual who guarantees the sum or the investment is the one who gets to decide the coupon rate whereas the moneylender or the bank gets to decide the discount rate.
• The measure of a coupon rate can be sensitive to any variations in discount rate since they are chosen by the public authority. As mentioned, discount rates are directly chosen by the public authority while also being affected by changes in the market or economic conditions.
• The securities that are granted with low coupon rates tend to face the hazard of large discount rates. this can be applied parallelly.

## Conclusion

Summarizing our discussions, we can assert that both discount rates and coupon rates are techniques that help the bondholder gain benefits alongside handing out assets for investments. However, both of them differ primarily in the type of assets being handed out along with the type of bond agreement issued.

## References

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"Difference Between Coupon Rate and Discount Rate." Diffzy.com, 2024. Tue. 06 Aug. 2024. <https://www.diffzy.com/article/difference-between-coupon-rate-and-discount-rate-322>.

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