*Yield to worst* is the lowest potential rate of return an investor could receive on his or her investment in a callable bond, assuming the bond does not go into default.

**Yield to Worst Meaning**

Callable bonds are bonds that allow the issuing firm to redeem them prior to maturity if the firm so chooses. When investing in a callable bond, the investor is taking the risk that the bond may be redeemed early by the issuing firm. Although the investor will receive the promised cash flows up to the time that the bond is called, he will receive no cash flows from that investment thereafter. For bonds with a single call date specified, the yield to worst will be either the bond’s yield to maturity (YTM) or its yield to call (YTC), whichever is lower.

**Yield to Worst Calculation**

To determine the yield to worst, we need to compare the yield to maturity to the yield to call. The yield to maturity is the yield that equates the price paid for the bond to the present value of the expected future cash flows of the bond, assuming the bond is not called:

where M is the number of years to maturity. The yield to call is the yield that equates the price paid to the present value of the expected future cash flows, assuming the bond is called:

Where C is the number of years to the first call date.

So, as an example, let’s assume a certain bond pays an annual coupon of 10% ($100 a year), has 10 years to maturity, is selling for $1,134 today, and is callable at its face value of $1,000 at the end of five years. The equations we must solve to calculate the bond’s yield to maturity and yield to call are:

and

Fortunately, we have electronic calculators and/or spreadsheets to solve this equation for us. Using Excel, we can see that the yield to maturity for this bond is 8%, and the yield to call is 6.75%.

Bond Cash Flows to Maturity | |

Year | CF |

0 | ($1,134) |

1 | $100.00 |

2 | $100.00 |

3 | $100.00 |

4 | $100.00 |

5 | $100.00 |

6 | $100.00 |

7 | $100.00 |

8 | $100.00 |

9 | $100.00 |

10 | $1,100.00 |

YTM | 8.00% |

Bond Cash Flows to First Call Date | |

Year | CF |

0 | ($1,134) |

1 | $100.00 |

2 | $100.00 |

3 | $100.00 |

4 | $100.00 |

5 | $1,100.00 |

YTC | 6.75% |

Therefore, the yield to worst in this example is 6.75%, the yield to call. Assuming the issuing firm does not default on the bond, **6.75% is the lowest yield the investor can expect to receive on the bond**.

Note that this will not always be the case. The following illustration shows the YTM and YTC calculations for the same bond if it is selling for $900:

Bond Cash Flows to Maturity | |

Year | CF |

0 | ($900) |

1 | $100.00 |

2 | $100.00 |

3 | $100.00 |

4 | $100.00 |

5 | $100.00 |

6 | $100.00 |

7 | $100.00 |

8 | $100.00 |

9 | $100.00 |

10 | $1,100.00 |

YTM | 11.75% |

Bond Cash Flows to First Call | |

Year | CF |

0 | ($900) |

1 | $100.00 |

2 | $100.00 |

3 | $100.00 |

4 | $100.00 |

5 | $1,100.00 |

YTC | 12.83% |

In this instance the yield to maturity of 11.75% is lower than the yield to call of 12.83%. **Therefore, the yield to worst is 11.75%**, the bond’s yield to maturity. The fact that the investor is buying the bond at a discount from its face value of $1,000 serves to offset the fact that the bond may be redeemed early, eliminating cash flows from the bond after the fifth year.

**Why It Matters**

When a bond is likely to be called by the issuing firm prior to maturity, the yield to maturity can be misleading. Therefore, the yield to call should also be calculated, and the yield to worst determined. It is also wise to remember that firms will call in these bonds when interest rates drop since they can obtain financing at a lower rate. This also means that the investor will be forced to accept a lower rate of return when he reinvests the proceeds from the bond, assuming he wants to invest in an asset of equal risk.

This, of course, is factored into the price at which a callable bond will sell. Because the call feature on a bond benefits the issuing firm, the firm must pay for this benefit; otherwise investors would not purchase the bond. A callable bond will sell at a lower price than a non-callable bond, given the two bonds have the same risk, coupon rate, and time to maturity. Another way to say this is that callable bonds offer greater promised yields (i.e., yields to maturity) than identical non-callable bonds, which is another reason it is important to calculate the yield to worst on the callable bond.

Furthermore, the closer the call date, the greater the promised yields on the callable bonds will be. Thus, a bond that is callable in one year will offer a greater yield to maturity (sell for a lower price) than a bond with the exact same attributes that has a first call date five years from now. Calculating the yield to worst on these bonds provides a better benchmark for comparing them.

**When To Use YTW**

It is particularly important to calculate the YTW when a callable bond is selling for a premium—that is, when it is selling for more than its face value. Bonds sell at a premium when their coupon rates are higher than the current market rates offered on similar risk investments. Therefore, the probability that a firm will exercise its option to redeem (call in) the bond early is high since it will be able to obtain financing at a lower rate of interest. Thus, the yield to worst, which, in this case, will be the yield to call, is a better estimate of the expected annual yield the investor will receive. Bond dealers often provide both the yield to maturity and the yield to worst on a callable bond.

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