A yield to call (YTC) is the interest rate if a callable bond is called before the maturity date. It is the effective rate of return that an investor would receive instead of the usual yield to maturity.

The YTC accounts for similar considerations like the coupon rate, time to maturity, and market value of the bond. These are similar terms as considered in the YTM calculations.

Let us discuss the concept of yield to call and see how it can be used in the analysis by investors.

## Yield to Call – Definition

Yield to call is the rate of return an investor receives if a bond is called before the maturity date.

A common measure of the rate of return on a bond is yield to maturity. However, redeemable bonds can be called before their maturity dates. The YTC measures the minimum return that an investor will receive if the bond is called.

Yield to call is calculated in a way that the present value of the bond’s remaining coupon payments equals its current market price. In other words, it evaluates the effect of call on the return on investment for an investor as compared to yield to maturity (YTM).

Theoretically, most bonds can be called after a specified term, however, the concept of yield to call refers to callable (or redeemable) bonds. These bonds include municipality or corporation bonds.

## How Does Yield to Call Work?

By definition, the call date of a bond will fall before its maturity date. This date can be predefined by the bond issuer. In many cases, the bond issuer specifies a specific period after which a bond can be called.

Many bonds are callable by their issuers. Bond issuers would normally offer a premium above the par value. However, the market price of a callable bond falls at the call date.

In declining interest rate environments, it’s feasible for bond issuers to call their existing debt instruments and issue new ones. The aim is to take advantage of low interest rates.

Usually, bond prices move inversely against the interest rate movements. Bond issuers would offer a premium above the face value to keep bonds competitive with new bonds in declining interest rate environments. However, it does not happen with a callable bond.

The call feature is predefined in redeemable bonds. Thus, the investors would already know if the interest rates fall, the bond issuers would call these bonds without offering a premium.

## Formula

Yield to call is calculated with an iteration method. The formula is given below.

P = (C / 2) x {(1 – (1 + YTC / 2) ^ -2t) / (YTC / 2)} + (CP / (1 + YTC / 2) ^ 2t)

Where,

- P = Price of Bond
- C = Annual Coupon Payment
- CP = Call Price
- t= time to maturity, and
- YTC = Yield to Call.

The call price of the bond and the market price of the bond are known factors. Thus, we can use an iteration method where the YTC equals the current market price of the bond. The calculation can be performed through excel or any other software.

## Alternative Formula:

Yield to call can be calculated with the help of another formula as well:

YTC = {(Coupon Interest Payment + (Call Price – Market Value)} ÷ [(Number of Years Until Call) ÷ (Call Price + Market Value) ÷ 2]

This formula also uses the same components but with a different calculation method.

## Examples

Suppose the following data is available for a callable bond.

Face Value | $ 10,000 |

Callable Price | $ 11,000 |

Current Market Price | $ 12,000 |

Coupon Rate | 10% |

Coupon Frequency | Semi-Annually |

Maturity | 15 years |

Call to Maturity | 5 years |

YTC | ? |

The formula to calculate the YTC is:

P = (C / 2) x {(1 – (1 + YTC / 2) ^ -2t) / (YTC / 2)} + (CP / (1 + YTC / 2) ^ 2t)

12,000 = ((1,000 / 2) x {(1 – (1 + YTC / 2) ^ -2*5) / (YTC / 2)} + (12,000/ (1 + YTC / 2) ^ 2*5)

We’ll need to use the iteration method to find a YTC rate that equals the equation to 12,000. In our example, using the trial and error or iteration method, we found the YTC equal to 7.90%.

Thus, even when the coupon rate of the bond was 10% originally, its YTC fell to 7.90%. It happens because investors will be unwilling to pay a higher price than the current market price of the bond. As we can see, the callable is also lower than the prevailing market price.

The bond issuers would issue a new bond using the lower interest rates instead of paying a premium on existing callable bonds.

## Important Considerations with Yield to Call

There are some important points to remember when considering the YTC of a bond instead of its YTM.

- The bond comes with a callable feature and the investor assumes it will be called before the maturity date.
- The purchase price of the bond will be the prevailing market price instead of its par value.
- In the case of multiple call dates, the investor will assume that the bond issuer will call the bond at the earliest callable date.
- Investors consider three main points while comparing the YTC and YTM rates. These points include return on investment in the form of coupon payments, capital gains, and reinvestment amounts.
- As with other bond rate calculations, it is assumed that the investor will reinvest the coupon payments at the same rate.

Additionally, the conventional rule of the bond prices and the interest rate does not fully hold for callable bonds. It is for the fact that the bond issuers have an option to redeem the bond and issue a new one to take advantage of lower interest rates. Thus, when interest rates fall, the callable bond prices will not move as far as for a straight or zero-coupon bond.

Considering these points, the YTC of a bond will always be lower than the YTM of the bond. If interest rates move up, the bond issuers are unlikely to call the bond. It can affect bond prices though.

## Callable Bonds and Yield to Call – Why Bonds are Called?

Bonds have an inverse relationship with the interest rates. A change in the interest rates means a change in the bond’s price in the opposite direction. It happens to set the market price of the bond according to investors’ demands.

However, callable bonds have an embedded feature of call options. If interest rates rise, bond issuers do not need to issue new bonds. Contrarily, if interest rates decline, bond issuers can replace existing bonds to raise capital.

Callable bonds are easier to redeem in falling interest rate environments. Thus, bond issuers redeem these bonds before their maturity date to replace them with new bonds to save on the cost of debt.

## Yield to Call Vs Yield to Maturity

Yield to Maturity is the total return an investor would receive if the investment is held till maturity. It is the annual internal rate of return on investment for the investor.

Yield to maturity also considers the time value of money. It assumes that all coupons received are reinvested at the same coupon rate of the bond.

The calculation of yield to maturity considers the bond’s par value, coupon payments, and time to maturity. It assumes if the interest rate remains constant until maturity, the present value of cash inflows (coupon payments) will equal the current market price of the bond.

Thus, the YTM is similar to the YTC in several ways. Both calculations consider similar assumptions. The YTM considers a bond’s par value instead of the call price in its calculation though.

## Yield to Call Vs Yield to Worst

A bond will carry a yield to maturity and a yield to call. The yield to worst is the lower of these two yields at any given time.

Yield to worst is a conceptual calculation rather than an actual return rate. It helps investors calculate the minimum rate of return of a bond in the worst case.

Often when a bond is called, its yield to call is lower than its prevailing yield to maturity. In any case, the lower of these two yields will be the yield to worst for investors.

Suppose a bond has a YTM of 5% and it has 10 years from the maturity date. The bond comes with a call feature. If interest rates fall, bond issuers will call the bond. Suppose its YCT comes out to be 4%.

In that case, the investors will assume the YTC (4%) as the bond’s Yield to worst.

## Concluding Remarks

Yield to call is the return on investment until the call date of a bond. It assumes that the coupon payments are reinvested at the same interest rate. It can be compared with the YTM as it considers similar assumptions.

Since investors know the attached call feature, the price of bonds does not change significantly if the interest rates change. However, the YTC is a useful calculation to analyze the minimum return on a bond when it is redeemed before the maturity date.