Yield to Maturity and Yield to Call

What YTM measures

Yield to maturity is the discount rate that equates a bond's current price with the present value of scheduled coupon payments and principal due at maturity. It combines coupon income with the expected change from purchase price to maturity value. It is broader than coupon rate or current yield because it considers the full payment schedule.

YTM is an estimate based on assumptions: the issuer makes promised payments, the investor holds to maturity, and interim coupons can be reinvested at the yield used in the calculation. Actual return can differ if the investor sells early, the issuer defaults, coupons are reinvested at different rates, or the bond's terms change cash flows.

The bond's price is the present value of future cash flows discounted at YTM. For annual coupons, Price = Σ[C ÷ (1 + y)^t] + F ÷ (1 + y)^n. C is annual coupon dollars, y is YTM, F is face value, and n is years remaining. With semiannual coupons, use half the annual coupon, a per-half-year yield, and twice as many periods under the stated convention.

For a bond at par with coupon equal to the required yield, YTM is near the coupon rate under standard assumptions. For a premium bond, YTM is generally below the coupon rate because the investor pays more than face value and may receive par at maturity. For a discount bond, YTM is generally above coupon because the investor pays less than face value.

Calculate YTM from price and cash flows

YTM is usually found by solving an equation rather than by a simple division. A financial calculator or spreadsheet can find the rate that makes the present value of future cash flows equal the bond's price. For an exam, identify the cash flows and direction of the relationship even when the question supplies a yield.

Consider a $1,000-face bond with a 6% annual coupon, three years remaining, and a market price of $950. It pays $60 in each of years one and two, then $1,060 in year three. The YTM solves $950 = $60/(1+y) + $60/(1+y)^2 + $1,060/(1+y)^3.

Try 8%: the present values are about $55.56, $51.44, and $841.46, totaling $948.46, slightly below the $950 price. A slightly lower rate makes the present value larger. The YTM is roughly 7.9% under this annual-payment example. A calculator provides more precision.

The yield is above the 6% coupon because the investor pays $950 and, if paid at maturity, receives $1,000 principal in addition to coupons. If the bond traded above $1,000, the principal repayment would be below the purchase price and YTM would generally fall below the coupon rate.

For semiannual bonds, follow the market or question convention. If the annual coupon is 6%, each semiannual coupon is $30. Discount each payment at the periodic yield over twice as many periods. The quoted annual yield may be a nominal annual rate compounded semiannually or another basis; use what is specified.

What YTC measures

Yield to call is the yield calculated using an applicable call date and call price instead of the stated maturity date and face value. It estimates return if the issuer exercises its call right on that date and makes the required payments. It uses the same present-value logic as YTM but a different final cash flow and holding period.

A callable bond gives the issuer, not the investor, the right to redeem early under specified conditions. Issuers may call bonds when refinancing is advantageous, often after market yields fall. The investor receives the call price and must reinvest the proceeds. A high coupon may end earlier than expected.

A bond trading at a premium is vulnerable to call risk because the issuer may repay at a call price near par, below the investor's purchase price. YTC can be lower than YTM. Investors compare both rather than assuming the stated maturity controls.

Suppose a $1,000-face bond with a 5% annual coupon trades at $1,050 and is callable in two years for $1,020. The investor receives $50 at the end of year one and $1,070 at the call date, including the coupon and call price. YTC solves $1,050 = $50/(1+y) + $1,070/(1+y)^2, giving a yield of roughly 3.4%.

The coupon rate is 5%, but YTC is lower because the investor pays a premium and may receive less than the purchase price when called. If the bond were not called, its YTM could differ. The issuer's option changes which cash-flow path may occur.

Yield to worst and multiple call dates

Callable bonds can have several call dates and prices. Yield to worst is commonly the lowest yield among specified redemption scenarios, including maturity, under the calculation convention. It helps show the least favorable contractual yield path for the investor, but it is not a guarantee that the bond will be called at that date.

A bond may be callable at a premium on one date and at par later. Calculate yield to each relevant call date using its redemption price and coupon schedule. The earliest call does not automatically produce the lowest yield; price and call premium affect the result.

Some bonds have sinking funds or extraordinary redemption provisions. These can retire part or all of the issue under specified conditions. Review the prospectus for redemption possibilities and use the appropriate cash-flow scenario. A simple YTM may not capture all expected outcomes.

Yield to worst is a comparison statistic, not a probability-weighted forecast. It does not indicate which call scenario is most likely. An investor should also consider the issuer's incentives, market yields, call protection, and the effect of reinvestment.

How price, coupon, and time affect yield

Holding cash flows constant, a lower purchase price raises YTM, while a higher price lowers YTM. A discount investor receives a larger maturity amount relative to purchase cost; a premium investor pays more than the principal due at maturity. Price changes can reflect interest rates, credit spreads, liquidity, or issuer expectations.

A higher coupon can produce more current income but does not always mean higher YTM. A premium price may offset the coupon. Compare bonds using yield measures and cash-flow terms, not coupon alone. The investor's total return also depends on actual reinvestment and holding period.

Time to maturity affects the number and timing of payments. If a bond is callable, time to call may be more relevant than final maturity. Yield calculations use the payment dates and redemption amount, so a small change in call date or price can alter YTC.

Credit risk changes the interpretation. YTM assumes scheduled payments. If the issuer defaults, actual cash flows can differ materially. A high YTM may reflect a market assessment of default, liquidity, or call risk rather than a reliable return opportunity.

YTM, current yield, and coupon rate

Coupon rate equals annual coupon divided by face value. Current yield equals annual coupon divided by current market price. YTM considers coupons, market price, principal at maturity, and time. YTC substitutes an applicable call price and date. Each measure answers a different question.

A $1,000-face bond with a $50 coupon trading at $900 has a 5% coupon rate and current yield of about 5.56%. Its YTM is higher than current yield if the investor receives $1,000 at maturity and all else is standard, because the $100 discount contributes to return. A callable version may have lower YTC if redeemed at an earlier date or price.

Current yield may be useful for a snapshot of coupon income relative to price, but it ignores capital gain or loss and timing. YTM and YTC are more complete cash-flow measures, but they depend on assumptions. Do not present any of them as guaranteed realized returns.

Reinvestment and sale before maturity

YTM calculations typically assume interim coupon payments can be reinvested at the yield used in the calculation. If rates fall and coupons are reinvested at lower yields, realized compound return may be lower. If rates rise, reinvestment may be higher, but the bond's market price may have fallen if sold early.

Selling before maturity makes the investor's return depend on the sale price. The quoted YTM is not a forecast of the one-year return or a promise of market value. Credit spreads, interest rates, liquidity, accrued interest, and transaction costs can change the result.

A client with a defined cash need should consider whether the bond's maturity or call schedule aligns with that date. A callable bond may repay earlier than planned; a noncallable bond may still need to be sold at a fluctuating price. Match cash flows to objectives where possible.

Worked case: compare callable and noncallable bonds

Two bonds each have $1,000 face value and a 6% coupon. Bond A is noncallable and has five years to maturity. Bond B is callable after two years at $1,000 and trades at a premium because market yields have fallen. Bond B's YTM may look attractive based on its five-year maturity, but the issuer may call it and return only par sooner.

For Bond B, calculate YTC using coupon payments through the call date and the call price. Compare that result with YTM and any other relevant redemption scenario. The lower yield may be the more conservative comparison. The actual call depends on issuer incentives and terms.

Bond A avoids the issuer's early call option, but its price can fluctuate with rates and credit spreads. Bond B may have more reinvestment risk. A client should compare cash-flow certainty, market price, credit, maturity, and planned holding period rather than selecting only the higher quoted yield.

A practical yield calculation workflow

Write down purchase price, face value, coupon amount, payment frequency, time to maturity, and call dates and prices. Confirm whether the quoted price includes accrued interest. Use the appropriate redemption amount for YTM or YTC and align the periodic yield with payment frequency.

Solve for the rate that equates price with the present value of the scheduled cash flows. Use a financial calculator or spreadsheet if needed, and check the result by repricing the cash flows. Ensure the calculator's payment and compounding settings match the bond.

Compare YTM with YTC and yield to worst for callable securities. Review credit, liquidity, tax, and reinvestment assumptions. Explain that quoted yield is conditional on payment and holding assumptions and may differ from realized return.

For a client, consider whether the bond's payment schedule and call risk fit the need for income or principal. A high yield is not automatically attractive; it may compensate for issuer risk or a likely call. Suitability depends on the full portfolio and client circumstances.

Check calculator settings and quoted conventions

A calculator can return a plausible rate even when its settings do not match the bond. Confirm whether the price is entered per $100 of face or as a dollar amount, whether the coupon is annual or semiannual, and whether the quoted annual yield is nominal or effective. Set the number of periods and coupon amount consistently. A semiannual bond with five years remaining normally has ten coupon periods in a basic model, not five.

Settlement between coupon dates adds another detail. A quoted clean price excludes accrued interest, while the investor's settlement payment generally includes it. Many standard yield conventions account for settlement date and accrued interest internally. For an exam question, use the simplified inputs it supplies; for a real quote, check the pricing convention and calculator specification before comparing yields.

A useful reasonableness check is to compare the result with the coupon and the price relative to par. If a standard discount bond has a coupon below market and trades below face value, YTM is generally above coupon. If a standard premium bond trades above face, YTM is generally below coupon. An unexpected result may signal an input error, a call feature, a different redemption value or a nonstandard cash flow.

Compare yields with the investor's actual horizon

Suppose an investor expects to hold a noncallable bond for only two years even though it has ten years to maturity. Its YTM describes the full maturity cash-flow model, not the return over the investor's planned period. To estimate a two-year holding-period result, the analyst needs the coupons received, the expected sale price at the end of year two, accrued interest and costs. The future sale price is uncertain.

For a callable bond, the investor's horizon can be shortened by the issuer. A client planning to hold five years may receive principal after two if a call occurs. In that case, YTC and other call scenarios matter alongside YTM. Even if the bond is not called, the client may sell early at a price affected by rates and credit.

A yield comparison should match security features and the decision being made. Comparing a callable bond's YTM with a noncallable bond's YTM can hide the cost of the call option. Compare call-adjusted yields, credit quality, maturity, liquidity and expected cash-flow timing. The highest displayed yield may rely on a maturity scenario that is less relevant to the client's situation.

How to answer Series 65 questions

YTM uses scheduled coupon payments and principal at maturity. YTC uses cash flows to an applicable call date and call price. Both are discount rates that equate price with present value of cash flows under their assumptions.

A premium bond's YTM is generally below its coupon rate; a discount bond's YTM is generally above coupon, all else equal. For callable premium bonds, YTC can be lower than YTM because the bond may be redeemed early.

Do not treat yield as guaranteed return. The issuer must pay, the investor's holding and reinvestment assumptions must fit, and a call may change cash flows. Use the specific call schedule and price from the question.

Sources

TreasuryDirect, Understanding Pricing and Interest Rates; OpenStax Principles of Finance, Bond Valuation; NASAA Series 65 Test Specifications, Section I. Yield examples are hypothetical and approximate.