# How to Calculate the Yield of a Bond?

Bond yield refers to the return received by the investor. It can be calculated in different ways. The aim is to calculate the income through investment in bonds.

Investors can analyze return on investment in bonds through different bond yields. It can be used to analyze the inverse relationship between bond prices and yield as well.

Let us discuss bond yield and different ways to calculate it.

## What is the Yield of a Bond?

The yield of a bond is the return on investment. In simple terms, it refers to the coupon rate. However, the yield differs from the nominal interest rate for several reasons.

This yield is the actual return that an investor receives. It is denoted in percentage terms similar to the interest rate.

Since most investors buy bonds at a market price that is different from the face value, their actual returns vary. Thus, the coupon rate is not a sufficient indication of the return on investment for the investors.

## How to Calculate the Yield of a Bond?

This yield can be calculated in different ways. It can be equal to the current coupon rate in some cases too.

Simple yield analyses do not consider the compounding effect or the time value of money. Some forms of yield calculations consider the time value of money by taking into account the compounding option.

Here are a few important methods of calculating a bond yield.

### Current Yield

The current yield is the annual rate of return for an investor. It considers the current bond price instead of the face value.

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Current yield is the return an investor would receive for investing in a bond for one year. However, if the bond is held till maturity, the yield will be different.

#### Formula

The formula to calculate the current yield is to take annual cash inflows and divide them by the current market price of the bond.

Current yield = Annual cash inflows / Current Market Price

#### Example

Current market price = \$ 1,200      Coupon Rate = 10% Face Value = \$ 1,000

Total Cash inflows (01 year) = \$ 100

Current yield = 100/1,200 = 8.33%

### Yield to Maturity (YTM) and Bond Equivalent Yield (BEY)

Yield to maturity or the bond equivalent yield is the most widely used measure to calculate the return on bond investments.

An investor can use the YTM to calculate the total return on investment if the bond is held until the maturity date. It considers the time value of money as it compounds all cash flows at the current coupon rate.

#### Formula

The formula for YTM is given below.

Bond Price = [ C1/ (1+YTM)1 + C2/(1+YTM)2 + …. Cn / (1 + YTM)n]

The calculation of YTM requires a trial and error method. Since the current bond price and the future cash flows until maturity is known, YTM can be calculated that gives an equal return to the current bond price.

The bond equivalent yield is a simple variation of YTM. BEY is used for semiannual coupon payments. It does not consider the time value of money for the second half of the coupon payment. Thus, simply doubling the YTM will give us the BEY.

### Effective Annual Yield (EAY)

The effective yield is the rate of return an investor receives if all coupons are reinvested at the same interest rate.

Effective annual yield (EAY) is another variation of YTM or one step further calculation of BEY.

#### Formula

The formula to calculate the EAY is:

EAY = [1 + (r/n)]n – 1

#### Example

Suppose a bond with a face value of \$ 1,000 and a coupon rate of 5%. It pays coupon payments quarterly.

The effective annual yield of the bond can be calculated as below.

EAY = [1+ (5%/4)]4 – 1

EAY = [1+ 0.0125]4 – 1 = 1.0509 – 1 = 0.0509

Therefore, EAY = 5.09%

## Coupon Rate and Yield to Maturity

If an investor purchases a bond at its par value, the yield to maturity and its coupon rate will be the same. However, that is rarely the case, as most investors purchase bonds from the secondary markets where bonds trade at a different price than their face values.

If the bond is purchased at a discount to its par value, the YTM will be lower than the coupon rate. Conversely, the YTM will be higher than the coupon rate if the bond is purchased at a premium.

## Different Types of Bond Yields

This yield can be calculated in different ways. Then, there are different types or variations of the bond yield as well.

### Running Yield

The running yield considers the market price of a bond instead of the face value. It is the annual return received divided by the market value of the security.

Usually, the running yield refers to the annual income of all current investments held in a portfolio.

### Nominal Yield

It is the simplest form of yield. The nominal yield refers to the coupon received through a percentage rate of the face value of the bond.

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Simply put, the nominal yield is equivalent to the coupon rate of the bond. Nominal yield or the coupon rate can be fixed or variable depending on the bond type.

### Tax-Equivalent Yield (TEY)

Municipal bonds offer tax-free returns to investors. It means income received by investors through these bonds is non-taxable.

Other bonds can calculate a pre-tax yield so that it matches the tax-free yield of the municipal bonds. It is termed the tax-equivalent yield (YTM).

### Yield to Call (YTC)

This is the effective rate of return for investors if the bond is called before its maturity date. It is the yield that bondholders will receive until the call date of the bond.

It is calculated in a similar way to YTM but it uses the period until the call date instead of the maturity date.

### Yield to Worst (YTW)

The YTW is the lowest possible return for an investor if the bond issuer faces financial issues. It is the assumed return on bonds before the bond issuer goes to bankruptcy.

The YTW is calculated by considering call and put dates as well as the conditions that can be enacted.

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