How to use the yield to call and yield to worst calculator
- Enter the price you paid for one bond, its face value, its coupon rate and how often coupons are paid.
- Enter the years to maturity, which must fit the coupon schedule, such as 10 or 10.5 for twice a year.
- Add each call date as years until the call and the price the issuer pays, or remove the call lines for a bond that cannot be called.
- Read the yield to worst, the yield to maturity and the table of yields for each way the bond can end.
Formula
price = sum over k = 1 to n of coupon / (1 + y)^k + redemption / (1 + y)^n
solve for y, the yield per period, separately for each call date and for maturity
yield shown = y x coupons per year, effective yield = (1 + y)^(coupons per year) - 1
yield to worst = the lowest of those yields
For a call, n is the number of periods until the call and the redemption is the call price. For maturity, the redemption is the face value.
A bond bought for $1,045 with three call dates
The bond has a $1,000 face value, a 6% coupon paid twice a year and 10 years left. It can be called in 3 years at $1,030, in 5 years at $1,015 and in 7 years at $1,000. The coupon is $30 each half year.
The yields are 5.294% to the 3 year call, 5.232% to the 5 year call, 5.224% to the 7 year call and 5.411% to maturity. The lowest is 5.224%, so the yield to worst is 5.224%, and the current yield is $60 / $1,045 = 5.742%. A discount bond bought for $940 has its lowest yield at maturity, 6.838%, because calling it early at par would pay more than the market price.
Why the lowest yield matters
A callable bond can end early, and an issuer is more likely to call when it would be cheaper to borrow again. For a bond bought above face value, a call usually cuts the return, so the yield to worst is the number to plan around. For a bond bought below face value, the early redemption helps and the worst case is usually the maturity date.
The Bond Yield Calculator covers a single bond with a price sensitivity table, the Present Value Calculator discounts any cash flows at a rate you pick, and the T-Bill Yield Calculator handles short term bills.
How the solver works
There is no formula that gives the yield directly, so the tool narrows it down by repeatedly halving a range until the price matches to many decimal places. It reports an error when the price cannot be matched by any yield, which usually means a typing mistake in the price or a call price.
Assumptions and limits
- The bond is bought on a coupon date, so there is no accrued interest to add.
- Coupons are paid at the end of each period and the bond is redeemed right after the last coupon.
- Each call is certain at the date you list, and make-whole calls, partial calls and sinking funds are not modeled.
- Taxes, fees and reinvestment of coupons are not included, and the yield is a bond equivalent yield.
Frequently asked questions
What is the difference between yield to call and yield to worst?
Yield to call is the yield if the bond is called at one particular date. Yield to worst is the lowest of the yields for every call date and for maturity, which is the least you would earn if the issuer chooses the date that is best for them.
Why do I have to match the coupon schedule?
The solver counts whole coupon periods. A call at 2.3 years on a semiannual bond falls between coupons, and the cash flows would need accrued interest that this tool does not model.
What is the effective yield?
The yield shown is the per period yield times the number of periods in a year. The effective yield compounds the periods, so for a semiannual bond it is a little higher than the stated one.
Does the price include accrued interest?
No. Enter the price without it and assume the purchase is on a coupon date. Between coupons the quoted price and the amount you pay differ, and this tool does not adjust for that.