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Yield To Maturity – Meaning, Steps to Calculate and Coupon Rate

Yield To Maturity
Yield To Maturity

What is the yield?

Yield is the measure of cash flow of an investment over a period of time. It is expressed as a percentage. It considers all dividends or interest received from the investment during the term of the investment.

Yield is different from the total return. Yield is a complete measure of return of an investment as it includes all cash flows from an investment. It can be calculated based on cost and current price.

Yield on cost: When the yield is calculated on the purchase price, it is called the yield on cost.

Current yield: When the yield is calculated on the current market price, it is called the current yield.

Yield based on the asset class

There are two types of yields based on the asset class.

In the case of stocks

Yield in case of stocks is the return the stockholder earns on the dividend. It does not include the profit from selling the shares. Below is the general formula for yield on stocks:

Yield in case of stocks = (Price increase + Dividend Paid)/Price

In the case of bonds

Bond yield is the return one earns on the interest. Interest is also known as the coupon rate. Hence bond yields depend on the coupon rate. In the case of bonds, it is called normal yield. This is the annual return from investing in fixed income securities.

Normal yield = Annual interest earned/Face value of the bond

What is the current yield?

Current yield is an investments’ annual cash flows divided by the current market price of the security. It shows the current return an investor would get if it is purchased and held for a year. Current yield is not the actual yield an investor would get it is held to maturity. However, it is the annual return from an investment.

Current yield = Annual Cash Flows/ Current price.

Annual cash flows = Price increase in the security plus the dividend

Current yield is mostly used in terms of bonds. This is because the bonds trade at premium or discount to par value. When investors buy the bond, they would want to calculate the return they might likely earn on their investment. In such cases, the current yield is mostly used.

However, current yield can also be used in terms of stocks or equities. The dividend is divided by the current market price to get the current yield.

What is yield to maturity?

YTM is nothing but the internal rate of return (IRR) of a bond. However, the investment must be held until maturity, and all the proceeds must be reinvested at a constant rate. YTM is similar to current yield where it determines the return one can expect by holding the security for a year. However, YTM is slightly advanced and accounts for the time value of money.

Yield to maturity meaning

Yield to maturity (YTM) is the total expected return for an investor if the bond is held to maturity. YTM factors all the present values of future cash flows from an investment which equals the current market price. However, this is based on the assumption that all the proceeds are reinvested back at a constant rate, and the investment is held until maturity. The price of the bond, the coupon payments and maturity value are known to an investor. However, the discount rate has to be computed. This discount rate is the yield to maturity. Often trial and error basis is used to calculate this. Below is the formula for yield to maturity.

Yield to Maturity Formula

Below is the YTM formula

yield to maturity formula
yield to maturity formula

Where, bond price = the current price of the bond.

Coupon = Multiple interests received during the investment horizon. These are reinvested back at a constant rate.

Face value = The price of the bond set by the issuer.

YTM = the discount rate at which all the present value of bond future cash flows equals its current price.

One can calculate yield to maturity only through trial and error methods.

However, one can easily calculate YTM by knowing the relationship between bond price and its yield. When the bond is priced at par, the coupon rate is equal to the bond’s interest rate. If the bond is selling at a premium (above par value), then the coupon rate is higher than the interest rate. And if the bond is selling at discount, the coupon rate is lower than the interest rate. This information will help an investor to calculate yield to maturity easily.

Terms related to YTM

Following are few important terms in yield to maturity formula

Face value/ Par value

Face value or par value is the value of the bond upon maturity. In other words, this is the price paid to the bondholder at the maturity date.

Present value/ Market value

Present value or market value of the bond is the current market price. The bond prices are subject to fluctuations on the basis of the interest rate changes. Both price and yield have an inverse relationship.

Coupon rate

The coupon rate is the interest rate paid to the bondholder by the bond issuer. The coupon rate is paid on the bond’s face value and not on the market value.

Interest rate

The interest rate of a bond is not the same as its coupon rate. Let’s understand this with an example. Mr Ananth buys a bond at INR 1,000 (face value), and the coupon rate is 10%. Mr Ananth gets INR 100 (10% of INR 1,000) every year for his investment as annual coupon payments. The effective interest rate for him is 10%.

On the other hand, Ms Sushma buys a bond at INR 2,000 (at a higher price to its face value). The face value of the bond is INR 1,000, and the coupon rate is 10%. Here, Ms Sushma also gets a yearly payment of INR 100 (10% of INR 1,000) as annual coupon payments. However, since she bought the bond at INR 2,000, the rate of interest for her investment is 5% (INR 100 of INR 2,000).

Similarly, had an investor bought the bond below its face value, the interest rate would be higher than the coupon rate.

Discount and Premium

Bonds trade either at discount or premium. When,

Market value = Face value, the bond is trading at par

Face value < Market value, the bond is trading at a premium

Face value > Market value, the bond is trading at a discount

Time to maturity

Maturity is the duration or date when a bond’s principal amount is repaid with interest. For example, a 10-year government bond matures in 10 years. The bondholder receives the principal amount along with interest at that time. Most commonly, maturity is referred to as time to maturity. This depicts the amount of time between now and the bond maturity date.

How to calculate the Yield to Maturity?

One can calculate yield to maturity using trial and error basis. 

Yield to maturity example

Let’s take an example of a bond with a par value of INR 1,000. The current market price of the bond is INR 950. The bond pays a coupon of 4% annually. The bond matures in 3 years. This bond’s yield to maturity can be calculated by following the steps below.

First one has to calculate the coupon payment, which is INR 40 (4% of INR 1000)

Then determine the face value and bond price. The face value is INR 1000. Price of the bond is INR 950.

Since the bond is selling at a discount, the coupon rate will be lower than the interest rate or YTM. Using the YTM formula, the required yield to maturity can be determined.

950 = 40/(1+YTM)^1 + 40/(1+YTM)^2 + 40/(1+YTM)^3+ 1000/(1+YTM)^3

We can try out the interest rate of 5% and 6%. The bond prices for these interest rates are INR 972.76 and INR 946.53, respectively. Since the current price of the bond is INR 950. The required yield to maturity is close to 6%. At 5.865% the price of the bond is INR 950.02

Hence, the estimated yield to maturity for this bond is 5.865%.

Importance of yield to maturity

Yield to maturity helps in estimating whether buying bonds (fixed income securities) is a good investment or not. Also, yield to maturity is a popular metric for comparison. In other words, YTM helps investors to compare returns from different securities. It helps in shortlisting the securities one can invest in.

YTM is expressed as an annual rate. Therefore, irrespective of the maturity of the bond, YTM can be used to compare bonds with different maturities and coupons.

Furthermore, YTM is useful to understand the change in prices of the securities with respect to the changing market conditions. Both price and yield have an inverse relationship. For example, with a fall in prices of the securities, the bond yields rise and vice versa.

Limitations of YTM

  • Yield to Maturity YTM doesn’t account for taxes that an investor has to pay on their bond investments.
  • YTM calculations do not consider the costs associated with buying and selling of the bond.
  • The YTM calculations are based on assumptions about the future. Estimated yield to maturity doesn’t account for the following instances:
    • The investor might not be able to reinvest all the coupon payments.
    • One may not be able to hold the bond until maturity.
    • The bond issuer may default the payments.
Published on September 15, 2020