Yield To Call Calculator

What this yield to call calculator does

Most corporate and municipal bonds carry a call provision, which lets the issuer buy the bond back from you before it matures. They do not do this out of kindness. They do it when interest rates have fallen and they can refinance more cheaply, which is precisely when you would rather keep the bond.

So the yield you were quoted at purchase, calculated to maturity, may never happen. Yield to call is the return you would actually get if the bond is redeemed at the first call date instead.

Give this calculator the annual coupon in currency, the call price, the current market price, and how long until the call. It returns the yield to call as a percentage.

One thing to know up front: this uses the standard approximation rather than solving for the exact internal rate of return. It is close, and we have measured how close.

No currency is assumed and everything runs in your browser. Nothing typed here is stored.

How to use it

1. Annual interest. The coupon as a cash amount for one year, not a percentage. A 6 percent bond with a 1,000 face value pays 60, so enter 60.
2. Call price. What the issuer pays you if it calls. Often par, often par plus a premium such as 1,020 or 1,050. It is in the bond's prospectus, usually as a call schedule with the premium declining over time.
3. Market price. What the bond costs today, in the same currency terms as the call price. If your bond is quoted as a percentage of par, a quote of 107.5 on a 1,000 face bond means 1,075.
4. Number of years until call. Time to the call date. Use the dropdown to switch between years and months, and for anything under a year select months.

Press Calculate. Press Reset to clear it.

Keep the coupon, call price and market price in the same units. Mixing a percentage coupon with cash prices is the fastest way to a meaningless answer.

The formula, and that it is an approximation

What this calculator computes:

Yield to call ≈ (annual coupon + (call price − market price) ÷ years to call) ÷ ((call price + market price) ÷ 2) × 100

Read it as two pieces. The numerator is your annual income: the coupon, plus the gain or loss between what you paid and what you will be handed at the call, spread evenly across the years you hold it. The denominator is the average of what you paid and what you will receive, standing in for the money tied up over the period.

That is the approximation, and it is the version taught in most textbooks and used in most calculators.

The exact yield to call is an internal rate of return: the single discount rate that makes the present value of every remaining coupon plus the call price equal today's market price. There is no closed form solution for it. You have to solve it iteratively, which is what a bond calculator or a spreadsheet's rate function does.

The approximation exists because it can be done on paper. It is close enough for most purposes, and the next section but one shows exactly how close.

A worked example

A bond with a 6 percent coupon on a 1,000 face value, so 60 a year. It trades at 1,075 and is callable in five years at 1,050.

The capital loss, spread out: (1,050 − 1,075) ÷ 5 = −5 a year

Adjusted annual income: 60 − 5 = 55

Average price: (1,050 + 1,075) ÷ 2 = 1,062.50

Yield to call: 55 ÷ 1,062.50 = 5.18 percent

Notice what happened to the headline. The bond pays a 6 percent coupon and yields 5.18 percent to the call, because you paid 1,075 for something that will hand back 1,050. You are buying at a premium and that premium erodes over the five years.

Anyone reading the coupon as their return is overstating it by more than three quarters of a percentage point. Premium bonds do this constantly, and it is the main reason yield rather than coupon is the number that matters.

How close the approximation gets

We ran the formula against a properly solved internal rate of return across a range of cases:

For premium bonds, which is where call risk actually lives, the approximation is within about five hundredths of a percentage point. That is close enough to make decisions on.

The last row is the exception. On a bond trading at a discount the approximation runs low, by around a seventh of a point here, and the gap widens as the discount deepens. The reason is that averaging the two prices treats your capital gain as arriving evenly, when in a discounted bond more of the return is concentrated at the end.

So the practical guidance: trust it for premium and near-par bonds, treat it as indicative on deep discounts, and if a decision turns on a tenth of a percentage point, use a spreadsheet's rate function instead.

A separate note on coupon frequency. Most bonds pay semi-annually rather than annually, and this calculator does not model that. The effect on the approximation is small, generally under a tenth of a point, because the formula was never tracking payment timing precisely in the first place.

Yield to worst, and the number on your confirmation

Yield to call on its own is only half the picture. The bond might be called, or it might run to maturity, and you do not get to choose.

So the convention is to work out both and take the lower one. That is the yield to worst, the most conservative return the bond can produce short of a default.

Take our example bond again, and suppose it matures in fifteen years rather than five:

There is a useful rule of thumb behind that. For a bond trading at a premium, the yield to worst is usually the yield to call, because there is less time for the premium to amortise. For a bond at a discount, it is usually the yield to maturity. Which makes intuitive sense: an issuer calls a bond when doing so is good for the issuer, and that tends to be when you paid over par for it.

This is not just a convention among analysts. Yield to worst is the yield that has to be reported to you on your trade confirmation when you buy or sell a bond. So if you have ever wondered why the yield on your confirmation is lower than the yield the broker quoted, this is very often why.

A bond with several call dates has a yield to call for each one. Yield to worst is the lowest across all of them plus maturity, and a full call schedule needs checking rather than just the first date.

Why bonds get called, and what it costs you

The call option belongs to the issuer, and they exercise it when it suits them.

The usual trigger is falling interest rates. A company that issued at 6 percent when rates were high can, once rates drop to 4 percent, call the old bonds and issue new ones more cheaply. Perfectly rational, and it happens at exactly the worst moment for you.

Because the moment rates fall is the moment your 6 percent bond becomes valuable. Its price rises, and just as it does, you get handed the call price and your money back. Then you have to reinvest it in a market that now pays 4 percent.

That is reinvestment risk, and it is the real cost of a call feature. You keep the downside if rates rise, since nobody calls a bond that has become cheap, and you lose the upside if rates fall. The option runs one way.

Issuers compensate for this. A callable bond generally pays a higher coupon than an otherwise identical non-callable one, and call prices often start above par and step down toward it over the years. Whether that compensation is adequate is exactly the judgement yield to call is meant to inform.

Two practical consequences. If a bond trades well above its call price and the call date is close, the price is being anchored by the call rather than by maturity, and your realistic return is the yield to call. And if you want none of this, Treasury securities are generally not callable, and STRIPS in particular cannot be called at all.

Questions people ask

What is yield to call?

The annual return you would receive if the issuer redeems the bond at its call date rather than letting it run to maturity, accounting for the coupons received and the difference between what you paid and the call price.

How does it differ from yield to maturity?

Same idea, different endpoint and different final payment. Yield to maturity assumes you hold to the end and receive par. Yield to call assumes redemption at the call date at the call price.

Why is my yield to call lower than the coupon?

Because you paid a premium. If you buy at 1,075 and get back 1,050, that 25 loss eats into the coupon income over the holding period.

Do I enter the coupon as a percentage or an amount?

An amount. A 6 percent coupon on a 1,000 face value bond is 60 a year, so enter 60.

Which yield should I actually use?

The lower of yield to call and yield to maturity, which is the yield to worst. That is also the figure your confirmation is required to show.

Is this the exact yield to call?

It is the standard approximation, which is within about five hundredths of a percentage point on premium bonds and drifts further on deep discounts. See the comparison table.

My bond has several call dates. What do I do?

Run it once for each and take the lowest result, then compare that against the yield to maturity.

References

A note on sourcing. The definitions of yield to call and yield to worst, and the requirement that yield to worst appear on a customer's trade confirmation, come from the Financial Industry Regulatory Authority and the Municipal Securities Rulemaking Board. The exact yield to call has no closed form and is solved iteratively; the formula used by this calculator is the standard approximation.

1. Financial Industry Regulatory Authority, Bonds. https://www.finra.org/investors/investing/investment-products/bonds
2. Municipal Securities Rulemaking Board, Municipal Bond Basics. https://www.msrb.org/Education/Municipal-Bond-Basics-0
3. U.S. Securities and Exchange Commission, Bonds, Investor.gov. https://www.investor.gov/introduction-investing/investing-basics/investment-products/bonds-or-fixed-income-products/bonds