Average-Price Call Approximation

This worksheet applies a transparent average-price shortcut to a callable-bond scenario. Enter an annual interest amount in dollars, call price, market price, and years until call. The result is an average-price annualized call approximation—not conventional yield to call and not a coupon-date internal rate of return (IRR).

Exact equation

For entered annual interest I, call price K, market price P, and years Y:

$\text{annual call-price change} = \frac{K-P}{Y}$

$\text{average-price annualized call approximation} = \frac{I + (K-P)/Y}{(K+P)/2} \times 100\%$

For comparison, current yield uses only entered annual interest and market price:

$\text{current yield} = \frac{I}{P} \times 100\%$

The displayed interest until call is undiscounted arithmetic, I× Y. The gain or loss at call is K-P. Call price, market price, and horizon must be positive; entered annual interest may be zero but cannot be negative.

Recomputed example

For $60 entered annual interest, a $1,000 call price, $950 market price, and 5 years:

• annual call-price change is (1,000-950)/5= $10.00;
• average price is (1,000+950)/2= $975.00;
• approximation is (60+10)/975×100=7.179487…%, displayed as 7.18%;
• current yield is 60/950×100=6.315789…%, displayed as 6.32%;
• undiscounted interest is 60×5= $300.00, and gain at call is $50.00.

A premium scenario can produce a negative approximation. For example, zero annual interest, a $1,000 call price, a $1,100 market price, and two years gives -50/1,050×100=-4.76%.

Important exclusions

The shortcut ignores coupon dates and frequency, reinvestment, accrued interest, settlement, taxes, day count, clean versus dirty price, and the issuer’s actual call schedule. Entering a coupon rate instead of an annual interest amount is a unit mistake. Treating the call date as certain is another: this worksheet only describes the entered scenario.

It does not model dated cash flows and should not be described as a conventional yield or investment-return calculation. Check the security’s call terms and dated cash flows and obtain an appropriate fixed-income calculation when conventional yield to call is required.

For yield based on a bond’s maturity date rather than an entered call scenario, use the bond YTM calculator. Maturity yield is a different task.

Sources and limits

• FINRA, Bonds — authoritative investor context for callable-bond risk; it does not establish this shortcut as conventional yield to call.
• U.S. SEC Investor.gov, Yield glossary — Version: federal glossary at access. It supports the mapped general yield definition; it does not validate this generic shortcut as conventional yield to call.