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Approximate Bond Yield to Call

Estimate callable-bond yield using annual coupon income and average price, with an explicit approximation rather than a cash-flow IRR.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

Annual coupon income 50, a call price of 1,000, a purchase price of 900 and five years to call give an approximate annual yield of 7.3684 percent.

Approximate yield = [annual coupon + (call price − purchase price)/years] / [(call price + purchase price)/2]

Worked example

Enter these known values and leave the other values blank.

Annual coupon amount
50 USD
Redemption amount at the assumed call
1000 USD
Bond purchase price on the same basis
900 USD
Years until the assumed call
5 yrs
Approximate annual yield to call
7.368 %

Assumptions and limitations

  • This is the average-price approximation. It does not solve the present value of dated coupon and redemption cash flows, so it is not an exact yield-to-call IRR.
  • Call price, purchase price and annual coupon use the same per-bond or per-face-value scale. Prices and time are positive; annual coupon may be zero.
  • The calculation assumes the bond is called at the specified time and price. It does not choose the first call date, assess likelihood of a call, or calculate yield to worst.
  • Coupon frequency, settlement timing, accrued interest, taxes and transaction costs are not modeled. A premium and low coupon can produce a negative approximate yield.

Common questions

Why does a broker’s exact yield differ?

An exact yield solves discounted cash flows with coupon timing and settlement conventions. This shortcut averages prices and annualizes the gain or loss linearly.

Does the result mean the issuer will call the bond?

No. The entered call date is a scenario assumption.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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