Yield to Call (YTC) Calculator
This calculator estimates the annual rate of return you would receive if you purchase a bond today and hold it until its specified call date, at which point the issuer redeems it at the call price.
It considers the bond's current market price, face value, coupon rate, frequency, the call price, and the time remaining until the call date.
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Understanding Yield to Call (YTC)
What is Yield to Call?
Yield to Call (YTC) is a measure of the return on a bond if it is held until its call date and redeemed by the issuer at the call price. Many corporate and municipal bonds have a call provision, which allows the issuer to redeem the bond before its scheduled maturity date.
YTC is calculated similarly to Yield to Maturity (YTM), but it assumes the bond is called on the first possible call date rather than held until maturity. It takes into account the bond's current market price, the periodic interest payments (coupons), the call price, and the time remaining until the call date.
YTC vs. YTM
YTC is usually calculated when a bond is selling at a premium (above its face value). In this scenario, the issuer is likely to call the bond to refinance at a lower interest rate. If the bond is called, the investor receives the call price (which is often face value or slightly above) instead of the higher market price they paid, plus the remaining coupon payments until the call date.
- If a bond is trading at a premium, YTC is generally lower than YTM.
- If a bond is trading at a discount, YTC is generally higher than YTM (but YTM is more relevant as the bond is less likely to be called early).
- If a bond is trading at par, YTC is generally close to YTM and the coupon rate.
Bond investors typically calculate both YTM and YTC and use the lower of the two figures (known as Yield to Worst) to make investment decisions, as this represents the minimum potential return.
How YTC is Calculated
Calculating YTC is an iterative process (like YTM) because there isn't a direct formula. It involves finding the discount rate that equates the present value of the bond's expected future cash flows (the remaining coupon payments until the call date plus the call price) to its current market price.
The cash flows include:
- Periodic coupon payments until the call date.
- The lump-sum call price received on the call date.
The calculator finds the annual yield (discount rate) that makes the sum of the present values of these cash flows equal to the current market price.
Yield to Call Examples
These examples illustrate how YTC is calculated in different scenarios:
Example 1: Bond Trading at a Discount
Scenario: A bond with Face Value $1000, 5% Annual Coupon (Semi-Annual payments), is trading at $950. It's callable in 3 years (6 semi-annual periods) at $1000 (par).
Inputs: Market Price = 950, Face Value = 1000, Annual Coupon Rate = 5%, Frequency = Semi-Annually (2), Periods Until Call = 6, Call Price = 1000.
Analysis: Since the bond is trading at a discount, YTC is likely higher than the coupon rate. Calling the bond wouldn't benefit the issuer as they'd pay $1000 for a bond worth $950 in the market. YTM is the more relevant yield here, but we can still calculate YTC based on the call assumption.
Expected YTC: Higher than 5%.
Calculation (via calculator): YTC ≈ 6.80%
Conclusion: If, hypothetically, the bond were called, the return would be ~6.80% per year. But since it's trading below par, it's unlikely to be called.
Example 2: Bond Trading at a Premium
Scenario: A bond with Face Value $1000, 6% Annual Coupon (Semi-Annual payments), is trading at $1050. It's callable in 4 years (8 semi-annual periods) at $1000 (par).
Inputs: Market Price = 1050, Face Value = 1000, Annual Coupon Rate = 6%, Frequency = Semi-Annually (2), Periods Until Call = 8, Call Price = 1000.
Analysis: Since the bond is trading at a premium, YTC is likely lower than the coupon rate. The issuer might call this bond if interest rates have fallen, allowing them to refinance at a lower rate.
Expected YTC: Lower than 6%.
Calculation (via calculator): YTC ≈ 5.08%
Conclusion: If the bond is called in 4 years, the investor's annual return is estimated to be ~5.08%.
Example 3: Bond Trading at Par
Scenario: A bond with Face Value $1000, 4% Annual Coupon (Semi-Annual payments), is trading at $1000. It's callable in 5 years (10 semi-annual periods) at $1000 (par).
Inputs: Market Price = 1000, Face Value = 1000, Annual Coupon Rate = 4%, Frequency = Semi-Annually (2), Periods Until Call = 10, Call Price = 1000.
Analysis: When a bond trades at par and is callable at par, the YTC should be approximately equal to the coupon rate.
Expected YTC: Around 4%.
Calculation (via calculator): YTC ≈ 4.00%
Conclusion: If the bond is called at par when trading at par, the yield is essentially the coupon rate.
Example 4: Bond with a Call Premium
Scenario: A bond with Face Value $1000, 5.5% Annual Coupon (Semi-Annual), trading at $1030. It's callable in 2 years (4 semi-annual periods) at $1020.
Inputs: Market Price = 1030, Face Value = 1000, Annual Coupon Rate = 5.5%, Frequency = Semi-Annually (2), Periods Until Call = 4, Call Price = 1020.
Analysis: This bond is trading at a premium, but is callable at a price slightly above par ($1020). The call premium reduces the potential loss compared to a call at par, resulting in a slightly higher YTC than if called at par.
Expected YTC: Lower than 5.5%, but potentially higher than YTC if Call Price was 1000.
Calculation (via calculator): YTC ≈ 4.98%
Conclusion: Accounting for the $1020 call price, the estimated YTC is ~4.98%.
Example 5: Annual Coupon Frequency
Scenario: A bond with Face Value $1000, 7% Annual Coupon (Annual payments), trading at $1080. It's callable in 3 years (3 annual periods) at $1000.
Inputs: Market Price = 1080, Face Value = 1000, Annual Coupon Rate = 7%, Frequency = Annually (1), Periods Until Call = 3, Call Price = 1000.
Analysis: Same principles apply with annual payments. Trading at a premium ($1080 vs $1000 call price) means YTC will be less than the coupon rate.
Expected YTC: Lower than 7%.
Calculation (via calculator): YTC ≈ 4.02%
Conclusion: With annual coupons, the estimated YTC is ~4.02% if called in 3 years.
Example 6: Longer Time Until Call (Semi-Annual)
Scenario: A bond with Face Value $1000, 4% Annual Coupon (Semi-Annual), trading at $970. It's callable in 7 years (14 semi-annual periods) at $1000.
Inputs: Market Price = 970, Face Value = 1000, Annual Coupon Rate = 4%, Frequency = Semi-Annually (2), Periods Until Call = 14, Call Price = 1000.
Analysis: Trading at a discount over a longer period until call. Again, YTM is more likely the relevant yield.
Expected YTC: Higher than 4%.
Calculation (via calculator): YTC ≈ 4.61%
Conclusion: The estimated YTC over 7 years is ~4.61%.
Example 7: Short Time Until Call (Semi-Annual)
Scenario: A bond with Face Value $1000, 5% Annual Coupon (Semi-Annual), trading at $1015. It's callable in 6 months (1 semi-annual period) at $1000.
Inputs: Market Price = 1015, Face Value = 1000, Annual Coupon Rate = 5%, Frequency = Semi-Annually (2), Periods Until Call = 1, Call Price = 1000.
Analysis: Trading at a premium with a very near call date. The premium paid ($1015) versus the amount received ($1000 call price + 1 coupon payment of $25) heavily impacts the YTC.
Expected YTC: Significantly lower than 5%.
Calculation (via calculator): YTC ≈ 1.48%
Conclusion: The short time horizon and premium paid result in a low estimated YTC of ~1.48%.
Example 8: Higher Coupon Rate, Trading at Premium
Scenario: A bond with Face Value $1000, 8% Annual Coupon (Semi-Annual), trading at $1120. It's callable in 5 years (10 semi-annual periods) at $1000.
Inputs: Market Price = 1120, Face Value = 1000, Annual Coupon Rate = 8%, Frequency = Semi-Annually (2), Periods Until Call = 10, Call Price = 1000.
Analysis: High coupon bond trading at a significant premium. Very likely to be called if interest rates are lower than 8%.
Expected YTC: Much lower than 8%.
Calculation (via calculator): YTC ≈ 5.33%
Conclusion: Despite the high coupon, the premium paid reduces the YTC to ~5.33% if called.
Example 9: Lower Coupon Rate, Trading at Discount
Scenario: A bond with Face Value $1000, 3% Annual Coupon (Semi-Annual), trading at $920. It's callable in 6 years (12 semi-annual periods) at $1000.
Inputs: Market Price = 920, Face Value = 1000, Annual Coupon Rate = 3%, Frequency = Semi-Annually (2), Periods Until Call = 12, Call Price = 1000.
Analysis: Low coupon bond trading at a discount. YTM is the more relevant yield here.
Expected YTC: Higher than 3%.
Calculation (via calculator): YTC ≈ 4.52%
Conclusion: The estimated YTC is ~4.52% if called, but it's unlikely to be called.
Example 10: Callable at Par, Short Term, Premium
Scenario: A bond with Face Value $1000, 6% Annual Coupon (Semi-Annual), trading at $1005. It's callable in 1 year (2 semi-annual periods) at $1000.
Inputs: Market Price = 1005, Face Value = 1000, Annual Coupon Rate = 6%, Frequency = Semi-Annually (2), Periods Until Call = 2, Call Price = 1000.
Analysis: Small premium, short time until call. YTC will be close to, but slightly less than, the coupon rate.
Expected YTC: Slightly less than 6%.
Calculation (via calculator): YTC ≈ 3.98%
Conclusion: The slight premium over a short period results in an estimated YTC of ~3.98%.
Frequently Asked Questions about Yield to Call
1. What is Yield to Call (YTC)?
YTC is the estimated annual rate of return an investor receives if they hold a callable bond from the purchase date until the bond's first possible call date, assuming the bond is redeemed by the issuer at the call price on that date.
2. How is YTC different from Yield to Maturity (YTM)?
YTM calculates the return if the bond is held until its original maturity date, assuming no early call. YTC calculates the return if the bond is called on the earliest possible call date. YTC is typically calculated for bonds trading at a premium, while YTM is more relevant for bonds trading at a discount.
3. Why is YTC important?
For callable bonds trading at a premium, YTC is a critical measure because it represents the likely minimum yield an investor will receive. If interest rates fall, the issuer is likely to call the bond, limiting the investor's return to the YTC.
4. What is "call risk"?
Call risk is the risk that a bond will be called by the issuer before maturity. This usually happens when interest rates have fallen, allowing the issuer to refinance their debt at a lower rate. Call risk is highest for bonds trading at a premium.
5. What inputs do I need for this calculator?
You need the bond's Current Market Price, Face Value, Annual Coupon Rate, Coupon Frequency (how often payments are made per year), the number of coupon Periods until the first possible Call Date, and the Call Price.
6. What is the "Periods Until Call"?
This is not the number of years, but the number of individual coupon payment periods remaining until the call date. For example, if it's semi-annual and the call date is 3 years away, there are 3 years * 2 payments/year = 6 periods until call.
7. What is the "Call Price"?
The call price is the price at which the issuer can redeem the bond on the call date. It's often set at the bond's face value ($1,000 for typical bonds), but it can sometimes include a "call premium," meaning the call price is slightly above face value.
8. What does a high or low YTC indicate?
A higher YTC (compared to the coupon rate) usually occurs when the bond is trading at a discount below the call price. A lower YTC (compared to the coupon rate) usually occurs when the bond is trading at a premium above the call price.
9. Can I use this for bonds that are not callable?
No, this calculator is specifically for callable bonds and estimates the yield assuming it *is* called. For bonds without a call provision, you should calculate the Yield to Maturity (YTM) instead.
10. What is "Yield to Worst"?
Yield to Worst is a concept where investors calculate all possible yields for a callable bond (YTM and YTC on all possible call dates) and take the lowest yield. This represents the most conservative estimate of the potential return and helps manage expectations regarding call risk.
