Yield to Call (YTC)
What is Yield to Call and how to measure it for Callable Bonds?
The term ‘Yield to Call’ refers to the annual rate of return that can be expected, by holding an investment till the earliest Call Date. Here, the Call Date refers to the day on which the bond issuer has the option to redeem the bond, by repaying the principal amount before the actual maturity date.
The YTC in bond market helps to indicate the Internal Rate of Return (IRR) of a Callable Bond, in case the Bond issuer decides to use the Call Option. Usually, the Call Date of the Bond happens before the actual Redemption Date. If there are multiple Call dates in the Bond, then the earliest date is used for the calculation.
Since this is a rate of return, the yield is usually communicated in percentage terms. The measurement of the yield requires an understanding of the Time Value of Money concept. So, the investors should be aware about Discount Factors and their usage.
Working of Callable Bond
A Callable Bond or Redeemable Bond is a special type of bond, where the issuer of the instrument has an option to redeem the bond, before the actual redemption date. This means that the borrower can repay the principal amount before the redemption date. In case of early redemption, the interest will only have to be paid till the earlier Call Date, instead of the entire duration of the Bond.
Example: Suppose that a company has issued new Bonds, with the below-mentioned borrowing terms.
Face Value: INR 1,000
Annual Coupon Rate: 9%
Tenure of bond: 5 years
Call Date (optional): At completion of 3 years
In this case, the company will pay INR 90 at the end of 1st year, and again pay INR 90 at the end of 2nd year. At the end of third year, the company has an option to Call the Bond early. This means that the company has 2 options at this stage:
Option 1: Choose to pay INR 1,090 and redeem the bond. In this case, the investors get the Principal amount back, and the Bond gets extinguished. So, the company does not have to pay anything for the 4th and 5th year.
Option 2: Not Call the Bond and just make the Coupon Payment of INR 90, at the end of third year. So, the company will pay INR 90 at end of 4th year also, and the Bond will be redeemed at the end of 5th year, when the company pays INR 1,090.
Yield to Call vs Coupon Rate
In Bond Market, the Coupon Rate refers to the fixed interest that is paid out to the bondholders at regular intervals. The Coupon Rate is measured in percentage terms, and the actual amount is calculated from the Face Value of the bond.
But this rate/amount remains fixed during the life of a normal bond, and it is not impacted by the Market Price or redemption date of the bond. So, the Coupon Rate might not give the effective rate of return of the investment.
On the other hand, the Yield to Call will assume that the received Coupon amount is re-invested for the remaining duration of the Bond (at the same Coupon Rate). So, when the Bond is purchased at Face Value, the Yield to Call will usually be higher than (or equal to) the Coupon Rate.
Note: If the Bond is purchased at a price that is different from the Face Value, then the actual return on investment will be different. But the Coupon Rate will remain same.
Effect of Compounding
Suppose that a company has issued a bond that is callable at the end of 5 years. It has a Face Value of INR 1,000 and an annual Coupon Rate of 10%.
If investors buy this bond, then they will receive a coupon of INR 100 every year (10% of INR 1,000) for first 4 years, and INR 1,100 at maturity time. This translates into annual interest payments of 10% (ignoring the compounding effect).
But if the Bond was purchased at INR 1,500 for example, then the return on investment will be much lower than 10%. Because the Cash Flow of Coupons from the Bond will not change.
When measuring the Yield to Call, it is assumed that the INR 100 received after 1st year will be invested at 10% for remaining 4 years. Similarly, INR 100 received after 2nd year will be assumed to be invested for the remaining 3 years etc. So, the actual rate of return till the Call Date will be higher than 10% (when bond is purchased at INR 1,000 or below).
Calculating Yield to Call
This section will explain how to calculate Yield to Call for any Fixed Income instrument, with payments at different time intervals. The main idea is that we have to discount all the expected Cash Flows separately.
When calculating the yield, it is assumed that all coupon and interest payments will happen on time. In addition, it is also assumed that the received amount can be reinvested at the same interest/Coupon rate, for the remaining duration of the bond.
Yield to Call Formula
As mentioned before, we need to discount the future Cash Flow to get the Present Value. All these values can then be added to obtain the current Fair Value of the Bond. When calculating YTC, we will already know the current price of the bond, which is P(0,T) in below formula.
\(P(0, T) = \sum\limits_{n=1}^{T} (C_n \times Z(0, n))\)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 will depend on the compounding frequency, which in this case is the frequency of Coupon payments. For example, if we assume annual compounding / annual payment of interest, then the Discount Factor will be given by the below formula,
\(Z(0,n)=\frac{1}{(1+YTC) ^ n}\)Where,
\(YTC\): Yield to Call
So, if we know the current price of the bond, then we can solve the above equations to calculate Bond Yield to Call. On the other hand, if we know the YTC of the Bond or if there is a target YTC, then it can be used to measure the Fair Value of the Bond.
Yield to Call example
Suppose that a company has issued a Non-Convertible Debenture (NCD) with the following borrowing terms:
Tenure: 5 years (Callable at end of 3 years, and at end of 4 years)
Face value: INR 1,000
Interest payment: 8%, paid annually
Let us assume that the investor purchases these bonds at a price of INR 900, and we want to find the YTC at this price.
The cash flows for this Corporate Bond will be: INR 80 in year 1 (8% of INR 1,000), INR 80 in year 2 and INR 1,080 in year 3. For calculation of Yield to Call equation, we have assumed that the Bond will be Called at the earliest possible redemption date (end of 3 years). If we assume annual compounding, then the equation that we need to solve will be:
\(900=\frac{80}{(1+YTC)} +\frac{80}{(1+YTC)^2} +\frac{1,080}{(1+YTC)^3}\)To simplify the information on this page, let us skip ahead to the final answer. (For Math savvy readers, the value can be calculated by using ‘RATE’ function in MS Excel, or by using the ‘Solver’ feature in MS Excel. Refer: How to use Solver in Excel?)
Solving the above equation will give us a Yield to Call of ~ 0.1218, which means a ~ 12.18% return. So, if an investor buys the above bond at INR 900, and the Bond gets Called at the end of 3 years, then he/she will get a yield of 12.18% on the invested amount.
Yield to Call vs Yield to Maturity
The main difference between Yield to Call and Yield to Maturity is the date that is used as the maturity of the bonds. The Yield to Maturity is measured by using the last/actual maturity date of the bond. Whereas the YTC will measure the expected returns till the earliest Call date.
The Yield to Maturity concept is more generic, and it can be applied to almost any type of Fixed Income instrument. But the Yield to Call is primarily used for Bonds that have a Call date, which is before the maturity date.
The Call feature in such bonds is usually optional, and it might or might not be used. Also, long duration bonds could even have multiple Call Dates. But for the measurement of YTC, it is assumed that the Bond will get Called at the earliest possible date. That is why, this yield is a type of the Yield to Worst (YTW) measurement.
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