Yield to Maturity (YTM)
What is Yield to Maturity and how to calculate it?
The term ‘Yield to Maturity’ is used to indicate the annual rate of return that an investor can expect, by holding an investment till maturity date. It is perhaps the most important concept in the Bond markets, as it communicates the Internal Rate of Return (IRR) of the investment. The YTM is also known as ‘Book yield’ or ‘Redemption yield’.
In fact, this concept can be applied for calculating the returns of any Fixed Income security, if the cash flows are known. Since it is a rate of return, the yield is usually communicated in percentage terms. Calculation of the yield requires understanding of the Time Value of Money, so investors should be aware about Discount Factors and their usage.
When calculating the yield, it is assumed that all coupon and interest payments will happen on time. Example: Suppose an investor holds a corporate bond which pays annual coupon on 01-January. For calculation, it is assumed that the payments will be received around this date, each year. Any material delays in payments can change the investment returns.
Difference between Yield to Maturity and Coupon rate
In case of bonds, the ‘Coupon’ refers to the fixed interest amount that is paid out to the bondholders at regular intervals. The Coupon rate will indicate the amount to be paid, as a percentage of the Face Value of the bond. This amount does not change during the life of a normal bond.
Example: Suppose a company has issued a 7-year bond, with Face Value of INR 1,000 and a Coupon Rate of 8% with annual payments.
So, if investors buy this bond, they will receive a coupon of INR 80 every year (8% of INR 1,000), for first six years and INR 1,080 at maturity time. This translates into annual interest payments of 8% (ignoring the compounding effect).
Real Rate of Return?
But what happens if the investor had bought the above bond from the Stock Exchange at INR 1,500?
In this case, the investor still receives INR 80 coupon (8% of INR 1,000) every year. But the actual return on the investment will be much lower than 8 % as the initial investment amount is higher.
Since the coupon rate is calculated on the Face Value, it might not give the effective rate of return of the investment. Instead, the Yield to Maturity is more useful as it is calculated using the investment price (INR 1,500 in this case).
Similarly, if a bond is bought significantly below the par value, the yield will be higher than the coupon rate. So, it can be imagined that the Yield to Maturity of a Bond is a dynamic value, which changes regularly depending on the price of the bond and the time left till maturity.
Effect of compounding
When calculating the yield for any Fixed Income instrument, an important factor at play is the compounding effect. Let us again consider our above example, where INR 80 was received each year, for first six years and INR 1,080 is received in the seventh year.
There are 2 ways in which the interest of INR 80 can be used each year:
1. Interest is not re-invested
If the bond was bought at INR 1,000 and held till maturity, then the investor can hope to achieve a total interest of INR 80 * 7 = INR 560. The rate of return on the investment will be 8 % in this case. This is also equal to the Current Yield of the bond.
2. Interest is Re-invested
The first coupon payment of INR 80 is received at the end of one year. It is possible to re-invest this amount for the remaining six years. Similarly, the second payment can be re-invested for remaining five years, and so on.
In this case, the rate of return at the end of seven years, will be greater than the returns received in above scenario 1. When re-invested, the returns will be as follows:
At the end of first year, interest received is INR 80 (8 % of INR 1,000).
(Now, we will assume that all future interests can be re-invested at 8 % for remaining time)
At the end of second year, interest received is INR 86.4 (8 % of INR 1,080).
At the end of third year, interest received is INR 93.312 (8 % of INR 1,166.4).
… and so on …
The final amount received at end of seventh year will be INR 1,713.824.
As it can be seen, the interest received after compounding (INR 713.824) is greater than the interest received without compounding (INR 560). So, the concept of YTM allows us to calculate the actual, compounded rate of return of the investment. When calculating the yield, it is always assumed that the interest will be re-invested in the future.
Calculating Yield to Maturity (with automatic reinvestment)
Let us first look at investments where the amount is received only at maturity time and there is no interest payments in between. For these investments, it is assumed that any accrued interest is automatically re-invested for the remaining period.
Here are some investment options, where no separate interest payments are received:
- Zero Coupon Bonds
- NCDs with cumulative payment
Etc.
YTM Formula
Calculating the yield in such cases is relatively easy as there is only one cash flow to the investor, which is at the maturity time. (Below formula assumes annual compounding. The formula will change if compounding frequency is changed)
Where,
t: the duration of investment (In years. Since we are calculating annual yield and assuming annual compounding)
FV: Final Value or Maturity amount
PV: Present Value or Initial value
Sample Calculation
Suppose a company is offering an NCD with the below borrowing terms:
Tenure: 5 years
Face value: INR 1,000
Interest payment: Cumulative payment at maturity
Amount paid at maturity: INR 2,000
Which gives us a yield of ~ 0.1487, which means ~ 14.87 % compounded annual return.
Calculating Yield to Maturity (Regular interest payments)
Calculations get more complicated for any Fixed Income instrument with payments at different time intervals. This is because we have to discount all the cash flows separately. The most important input parameters to consider are: Expected Cash Flows and Compounding frequency.
Below, we mention some investments which give regular payments to the investor. For calculating the YTM in these cases, we assume that the investor will be able to re-invest the money in the future and there will be no additional costs, taxes etc.
- Bonds, NCDs and Government securities
- Fixed Deposits
- PPF account
- National Savings
- Certificates (NSCs)
Etc.
Yield to Maturity Formula
As mentioned before, we need to discount all the future cash flows to obtain the current fair value of the bond. When calculating the YTM, we will already know the current price of the bond, which is P(0,T) in below formula.
{{P}}\left({0},{T}\right)=\sum\limits_{{n}={1}}^{{T}}\left({C}_{n}\times{Z}\left({0},{n}\right)\right)
\)
Where,
\(P(0,T)\): Price of the bond at time 0, with a maturity at time T
\(C_n\): Cash flow at time ‘n’
\(Z(0,n)\): Discount factor, for discounting the \(C_n\) (cash flow at time ‘n’) to time 0
The Discount Factor depends on the compounding frequency, which in this case is the frequency of interest payments. For example, if we assume annual compounding / payment of interest, the discount factor will be given by the below formula,
If we know the present trading price of the investment, then we can solve the above equations to calculate the current Yield to Maturity.
Sample Calculation
Suppose a company has issued an NCD with the following borrowing terms:
Tenure: 3 years
Face value: INR 1,000
Interest payment: 10 %, paid annually
Assume that the current trading price of the bond is INR 950. We want to find the YTM if an investor buys the bond at this price.
The cash flows for the corporate bond will be as follows: INR 100 in year 1 (10% of INR 1,000), INR 100 in year 2 and INR 1,100 in year 3.
Assuming annual compounding, the equation that we need to solve for finding the YTM will be:
To prevent the readers from losing interest, we will skip ahead to the final answer. For Math savvy readers, the value can be calculated using: ‘RATE’ function or ‘Solver’ feature in MS Excel. (Refer: How to use Solver in Excel?)
Solving the above-mentioned current yield formula will give us a YTM of ~ 0.1208, which means ~ 12.08 % return. So, if an investor buys the above bond at INR 950 and holds it till maturity, he / she will get a yield of 12.08 % on the invested amount.
Using the Yield to Maturity
The main usage of YTM is to help the investors in choosing the best investment option. Here are some ways in which the yield is used:
- Helps to calculate the real rate of return of investments which have multiple interest payments in the investment period.
- Helps to analyze the riskiness of the investment. For example, a Junk Bond will typically have a much higher yield than less risky bonds.
- Helps to find better investment options, when the risk of different investments is same.
- Used for calculating the 10-year bond yield of government securities. This is a very important indicator to judge the prevailing lending environment in a country.
- The yields of multiple bonds having different maturities can be plotted on a graph to obtain the Yield Curve.
Etc.
Disclaimer
- This page is for education purpose only
- Some information could be outdated / inaccurate
- Investors should always consult with certified advisors and experts before taking final decision
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