# Yield to Call

Yield to call (YTC) is the rate of interest earned on a bond when it is called. It is the rate of interest that equates the present value of its future coupon payment and call price to the current market price of the bond.

When the current market interest rate is lower than the stated interest rate on a callable bond, it is likely that the bond will be called because it is financial beneficial for an issuer to retire a high rate debt and issue a low rate bond (while accounting for the related flotation costs). In such a situation, yield to call (YTC) is a better estimate of expected return on the bond than the yield to maturity (YTM).

## Calculation

The formula used to calculate yield to call is very similar to that of yield to maturity (YTM). We just need to replace the maturity value with the call price and take into account only those coupon payments that are expected to be received by the call date.

Market Price of Bond = Coupon payment × | 1 − (1+r)^{-n} | + | Call Price |

r | (1+r)^{n} |

Where,

Coupon Payment = | Stated Rate on the Bond | × Face Value of Debt |

Number of Payments per Year |

r = | Yield to Call |

Number of Periods per Year |

n = Number of Coupon Payments till Expected Call Date = Number of Periods per Year × Years till Call Date |

Yield to call is expressed as an annual APR i.e. yield to call is equal to number of payments per year multiplied by r.

Using a financial calculator, yield to call can be calculated by using the IRR function.

## Example

Izmir Construction is a company engaged in construction in Turkish west. On 1 January 2012 it issued 5,000 5-year bonds with a par value of $1,000 per bond. They have a current market price of $975, carry annual coupon rate of 9% and are callable at 105 anytime in 3rd, 4th or 5th year. The interest rate in year 3, 4 and 5 are 10%, 8% and 9%. Estimate the yield to call (YTC) and yield to maturity (YTM) and tell which rate is a better estimate of the expected rate of return on the bond.

## Solution

We use the following formula to estimate yield to maturity (YTM):

$976 = $90 × | 1 − (1+r)^{-5} | + | $1,000 |

r | (1+r)^{5} |

r in the above equation is the yield to maturity and it equals: 9.65%

Izmir Construction is most likely to call the bond in 4th year because this is then the market interest rate is below the coupon rate on the bond. In order to find yield to maturity assuming the bond is called at the end of year 4, we need to replace the face value with call price and enter n = 4 in the yield to maturity equation given above and we will get r = yield to call.

$975 = $90 × | 1 − (1+r)^{-4} | + | $1,050 |

r | (1+r)^{4} |

This gives r = yield to call of 10.48%.

Since the bond is likely to be called, yield to call is a better of expected return on the bond as compared to yield to maturity.

Written by Obaidullah Jan, ACA, CFA