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Yield to Maturity - Finance

  1. A zero-coupon bond with a face value of $1,000 and 7 years to maturity is currently trading for $713. What is the bond's effective annual yield to maturity?
    Answer: 4.95% For a zero-coupon bond, the price formula is P=FV(1+YTM)n P = \frac{FV}{(1+YTM)^n} . We need to solve for YTM. $713=$1000(1+YTM)7 \$713 = \frac{\$1000}{(1+YTM)^7} . Rearranging gives (1+YTM)7=$1000$713≈1.4025 (1+YTM)^7 = \frac{\$1000}{\$713} \approx 1.4025 . Taking the 7th root of both sides gives 1+YTM=(1.4025)17≈1.0495 1+YTM = (1.4025)^{\frac{1}{7}} \approx 1.0495 . Therefore, YTM ≈ 1.0495 - 1 = 0.0495, or 4.95%.
  2. Consider a bond with a coupon rate of 5% trading at a discount. Which of the following provides the best conceptual breakdown of its yield to maturity (YTM)?
    Answer: The current yield plus the annualized capital gain from the price accreting to par value. The total return from a discount bond held to maturity comes from two sources: the coupon payments and the capital gain as the bond's price increases (accretes) towards its par value at maturity. The YTM incorporates both. The current yield (Annual Coupon / Price) captures the first part. The remainder of the YTM is the annualized capital gain the investor will receive by holding the bond until it matures at par.
  3. Two bonds, Bond A and Bond B, are identical in all respects (coupon rate, par value, credit quality) except for their maturity. Bond A matures in 5 years and Bond B matures in 25 years. If the general level of market interest rates rises by 150 basis points, what is the most likely impact on the bonds' yields and prices?
    Answer: The YTM of both bonds will increase by approximately 150 basis points, but the price of Bond B will fall more than the price of Bond A. When market interest rates rise, the yield to maturity (YTM) required by investors for all comparable bonds also rises. Thus, the YTM for both bonds will increase by approximately 150 basis points (1.5%). Due to interest rate risk, longer-maturity bonds are more sensitive to changes in interest rates. Therefore, the price of Bond B (25-year maturity) will experience a larger percentage decrease than the price of Bond A (5-year maturity).
  4. A bond's price is quoted at 102.5. It has a 6% coupon paid semi-annually and 8 years remaining to maturity. Which of the following statements is correct?
    Answer: The bond's yield to maturity is less than its coupon rate. A price quote of 102.5 means the bond is trading at 102.5% of its par value, or $1,025. Since the price is above par, the bond is trading at a premium. For any premium bond, there is a fixed relationship between its yields: Coupon Rate > Current Yield > Yield to Maturity. Based on this, the yield to maturity (YTM) must be less than the coupon rate of 6%.
  5. A bond's yield to maturity is 5.5%. If the general market expectation is that interest rates will become significantly more volatile in the future, how will this affect the required YTM on a newly issued, otherwise identical bond?
    Answer: The required YTM will be higher, because investors will demand more compensation for increased interest rate risk. Increased volatility of interest rates means greater uncertainty and greater price risk for bondholders. Rational investors are risk-averse and will demand a higher return to compensate them for bearing this additional risk. This additional compensation is reflected in a higher risk premium, which increases the overall required yield to maturity for a new bond issuance.
  6. The primary difficulty in calculating a meaningful yield to maturity (YTM) for a floating-rate note (FRN) is that:
    Answer: its future coupon payments are unknown. When analyzing floating-rate notes (FRNs), you need to understand how their variable interest payments create unique valuation challenges compared to fixed-rate bonds. The fundamental problem with calculating YTM for an FRN lies in the uncertainty of future cash flows. Answer A is correct because floating-rate notes have coupon payments that reset periodically based on a reference rate (like LIBOR or SOFR). Since you cannot predict what interest rates will be at future reset dates, you cannot determine the exact dollar amounts of upcoming coupon payments. YTM calculations require knowing all future cash flows, making this uncertainty the primary obstacle. Looking at the incorrect choices: Answer B is wrong because FRNs maintain a stable par value of $1,000 (or face value) regardless of interest rate movements—this stability is actually one of their key features. Answer C is incorrect since FRNs have clearly defined maturity dates just like other bonds; the floating aspect affects coupon rates, not the repayment schedule. Answer D misses the mark because while credit risk may change over time for any bond, this isn't the primary computational challenge for YTM calculations, nor is it unique to FRNs. Remember that FRNs are designed to trade near par value precisely because their coupon rates adjust with market conditions. When you encounter questions about floating-rate securities, focus on how the variable payment structure affects valuation—the unpredictability of cash flows is almost always the key issue, not changes to principal value or maturity terms.
  7. A corporation issues two bonds on the same day with the same maturity date. Bond A is a standard non-callable bond. Bond B is identical to Bond A in all respects except that it is callable by the issuer at any time after five years. An investor purchasing these bonds at issuance should expect that:
    Answer: Bond B will have a lower price and a higher yield to maturity than Bond A. When evaluating bonds with embedded options, you need to understand how these features affect investor compensation. A callable bond gives the issuer the right to redeem the bond before maturity, which creates additional risk for investors. The call option represents a disadvantage to bondholders because issuers typically call bonds when interest rates fall below the bond's coupon rate. This means investors face reinvestment risk - they'll receive their principal back early and must reinvest at lower prevailing rates. Additionally, the bond's price appreciation is limited (called "price compression") because as interest rates fall, the likelihood of early redemption increases. Since Bond B carries this additional call risk that Bond A doesn't have, investors will demand compensation in the form of a higher yield. To provide this higher yield at issuance, Bond B must be priced lower than Bond A. This makes answer A correct - Bond B will have both a lower price and higher yield to maturity. Answer B is wrong because identical bonds with different risk profiles cannot have the same pricing. Answer C gets the relationship backwards - the callable bond cannot command a premium price when it offers less favorable terms to investors. Answer D incorrectly suggests inflation determines the yield relationship, when the call feature itself drives the pricing difference regardless of inflation expectations. Study tip: Remember "CHIP" - Callable bonds have Compensation (higher yields), Heightened risk, Inferior price appreciation, and Price discounts compared to non-callable equivalents.
  8. A 15-year bond with an 8% annual coupon and $1,000 par value is currently priced to yield 8%. If its yield to maturity immediately rises to 9%, the bond's price will decrease by approximately:
    Answer: $80.85 This is a multi-step problem. First, determine the initial price. Since the coupon rate (8%) equals the YTM (8%), the bond is priced at par: $1,000. Second, calculate the new price with the higher YTM. Using a financial calculator with N=15, I/Y=9, PMT=80, FV=1000, the new price (PV) is $919.15. Finally, calculate the price decrease: $1,000 - $919.15 = $80.85.
  9. A 10-year bond with a $1,000 face value and a 7% coupon is issued at par. Five years later, the bond's yield to maturity (YTM) has fallen to 5%. Which of the following statements about the bond's characteristics at that time (five years after issuance) is most accurate?
    Answer: The bond is trading at a premium, and its current yield is between 5% and 7%. Five years after issuance, the bond has 5 years remaining to maturity. Since its coupon rate (7%) is greater than its current yield to maturity (5%), the bond must be trading at a premium (price > $1,000). For a premium bond, the yields are ordered as follows: Coupon Rate > Current Yield > YTM. Therefore, the current yield must be between the 7% coupon rate and the 5% YTM.
  10. An investor buys a 10-year, 7% annual coupon bond at par value. For the investor's realized yield to be exactly equal to the 7% yield to maturity promised at purchase, which condition must be met?
    Answer: All coupon payments must be reinvested at a rate of 7% until the bond matures. The yield to maturity (YTM) is the promised rate of return only if two key conditions are met: 1) the bond is held to maturity, and 2) all coupon payments are reinvested at a rate equal to the original YTM. If the coupons are reinvested at a different rate, the investor's actual, or realized, yield will differ from the YTM calculated at the time of purchase. This is known as reinvestment risk.
  11. A zero-coupon bond has a face value of $1,000 and a yield to maturity of 6.0%. The bond is priced at $558.39. Using this information, what is the approximate number of years until the bond matures?
    Answer: 10 years When you encounter zero-coupon bond problems, you're working with bonds that pay no periodic interest but are sold at a discount to face value. The key relationship is that the current price equals the face value discounted back at the yield to maturity. The zero-coupon bond formula is: PV=FV(1+r)nPV = \frac{FV}{(1 + r)^n}, where PV is present value (current price), FV is face value, r is yield to maturity, and n is years to maturity. Rearranging to solve for time: n=ln⁡(FV/PV)ln⁡(1+r)n = \frac{\ln(FV/PV)}{\ln(1 + r)} Plugging in the values: n=ln⁡(1000/558.39)ln⁡(1.06)=ln⁡(1.791)ln⁡(1.06)=0.5830.058≈10n = \frac{\ln(1000/558.39)}{\ln(1.06)} = \frac{\ln(1.791)}{\ln(1.06)} = \frac{0.583}{0.058} ≈ 10 years. You can verify this works backwards: 558.39=1000(1.06)10=10001.791≈558.39558.39 = \frac{1000}{(1.06)^{10}} = \frac{1000}{1.791} ≈ 558.39 ✓ Choice B (8 years) would give a price of about $627, which is too high. Choice C (6 years) would yield approximately $705, far exceeding our given price. Choice D (12 years) would result in a price around $497, which is too low compared to $558.39. Study tip: For zero-coupon bond problems, remember that longer maturity periods mean deeper discounts (lower current prices). If you're short on time, you can estimate by testing the middle answer choices first, then adjust based on whether you need a higher or lower price.
  12. A 10-year, semi-annual coupon bond has a par value of $1,000 and is currently priced at $1,067.79. If the bond's yield to maturity (Bond Equivalent Yield) is 5%, what is its annual coupon rate?
    Answer: 6.0% This problem requires working backward to find the coupon payment. For a semi-annual bond, the inputs for a financial calculator are: N = 10 2 = 20; I/Y = 5% / 2 = 2.5%; PV = -1,067.79; FV = 1,000. Solving for the payment (PMT) gives $30. This is the semi-annual coupon payment. The annual payment is $30 2 = $60. The annual coupon rate is the annual payment divided by the par value: $60 / $1,000 = 6.0%.
  13. A 30-year callable bond with an 8% coupon is issued at par. The bond is callable in 10 years at $1,050. Five years after issuance, market interest rates have dropped significantly, and the bond is now trading at $1,250. For an investor considering purchasing the bond today, which yield calculation is the most relevant for decision-making?
    Answer: Yield to call, because the bond is trading at a significant premium and is likely to be called by the issuer. The bond is trading at a significant premium ($1,250) to both its par value ($1,000) and its call price ($1,050). This is because its 8% coupon is much higher than current market rates. The issuer has a strong economic incentive to call the bond at the first opportunity (in 5 more years) and refinance at a lower rate. Therefore, an investor buying the bond today should assume it will be called, making the Yield to Call the most realistic and relevant measure of potential return.
  14. The issuer of a 10-year bond with a 7% coupon experiences a sudden, unexpected credit rating upgrade from a major rating agency. Assuming no other market changes, what is the most likely immediate impact on the bond's market price and its yield to maturity (YTM)?
    Answer: Price will increase and YTM will decrease. A credit rating upgrade signifies a decrease in the perceived default risk of the issuer. With lower risk, investors will demand a lower rate of return to hold the bond. This lower required return is the bond's new, lower yield to maturity (YTM). There is an inverse relationship between a bond's price and its YTM. As the YTM decreases, the present value of the bond's future cash flows increases, causing its market price to rise.
  15. An investor purchases a 20-year, 6% annual coupon bond at a price that gives it a yield to maturity of 8%. The investor holds the bond for one year, during which market interest rates for comparable bonds fall to 7%. Assuming the investor sells the bond after one year, the investor's realized one-year holding period return will be:
    Answer: greater than the original yield to maturity of 8%. This is a multi-step problem. First, calculate the purchase price (PV) with N=20, I/Y=8, PMT=60, FV=1000, which is $803.64. Second, calculate the selling price one year later (PV) with N=19, I/Y=7, PMT=60, FV=1000, which is $899.34. The one-year return is (Ending Price - Beginning Price + Coupon) / Beginning Price = ($899.34 - $803.64 + $60) / $803.64 = $155.70 / $803.64 ≈ 19.38%. This return is significantly greater than the original YTM of 8% due to the capital gain from falling interest rates.
  16. A portfolio manager is considering a 12-year bond with a $1,000 par value and a 5% coupon paid annually, currently trading at $890. Which of the following statements correctly ranks the bond's yields?
    Answer: Yield to Maturity > Current Yield > Coupon Rate The bond is trading at $890, which is less than its $1,000 par value, so it is a discount bond. For any discount bond, there is a fixed relationship between its yields. The coupon rate is given as 5%. The current yield is the annual coupon payment divided by the market price: ($1000 * 0.05) / $890 = $50 / $890 ≈ 5.62%. The yield to maturity (YTM) for a discount bond is always the highest of the three yields because it includes both the current yield and the annualized capital gain from the price accreting to par. Therefore, the correct order is YTM > Current Yield > Coupon Rate.
  17. The yield to maturity (YTM) calculation for a bond implicitly assumes that all interim coupon payments are reinvested at a rate equal to:
    Answer: the YTM itself. A critical assumption underlying the yield to maturity calculation is that the investor is able to reinvest all coupon payments received over the life of the bond at a rate of return equal to the bond's YTM at the time of purchase. If future reinvestment rates are lower than the YTM, the investor's actual realized yield will be less than the promised YTM, and vice versa. This is known as reinvestment risk.

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