Stone Sour Corp Issued 30-Year Bonds 6 Years Ago At A Coupon

Stone Sour Corp Issued 30 Year Bonds 6 Years Ago At A Coupon Rate O

Stone Sour Corp. issued 30-year bonds 6 years ago at a coupon rate of 7.90 percent. The bonds make semiannual payments. If these bonds currently sell for 109 percent of par value, what is the YTM? (Round your answer to 2 decimal places. (e.g., 32.16)) YTM= ______%

Treasury bills are currently paying 6 percent and the inflation rate is 3.40 percent. What is the approximate real rate of interest? (Round your answer to 2 decimal places. (e.g., 32.16)) Approximate real rate:________%

What is the exact real rate? Exact real rate:_______%

Say you own an asset that had a total return last year of 11.6 percent. If the inflation rate last year was 6.7 percent, what was your real return? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Real return:________%

Bond J is a 6 percent coupon bond. Bond K is a 12 percent coupon bond. Both bonds have 19 years to maturity, make semiannual payments, and have a YTM of 9 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? (Negative amount should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16))) Percentage change in price of Bond J:___________% Percentage change in price of Bond K:__________%

What if rates suddenly fall by 2 percent instead? (Round your answers to 2 decimal places. (e.g., 32.16)) Percentage change in price of Bond J:___________% Percentage change in price of Bond K:__________%

Martin Software has 9.8 percent coupon bonds on the market with 18 years to maturity. The bonds make semiannual payments and currently sell for 107.7 percent of par. What is the current yield on the bonds? (Round your answer to 2 decimal places. (e.g., 32.16)) Current yield:______%

What is the YTM? (Round your answer to 2 decimal places. (e.g., 32.16)) YTM:_______%

What is the effective annual yield? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Effective annual yield:________%

Backwater Corp. has 7 percent coupon bonds making annual payments with a YTM of 6.3 percent. The current yield on these bonds is 6.65 percent. How many years do these bonds have left until they mature? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Maturity of bond:__________years.

The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY). a. Suppose that today you buy a bond with an annual coupon of 11 percent for $1,130. The bond has 18 years to maturity. What rate of return do you expect to earn on your investment? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Expected rate of return:_________%

b. Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Bond Price______$

b2. What is the HPY on your investment? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) HPY:_________%

Las Paletas Corporation has two different bonds currently outstanding. Bond M has a face value of $40,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $2,000 every six months over the subsequent eight years, and finally pays $2,300 every six months over the last six years. Bond N also has a face value of $40,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 8 percent compounded semiannually. What is the current price of bond M and bond N? (Round your answers to 2 decimal places. (e.g., 32.16)) Current Price Bond M $___________ Bond N $___________

Paper For Above instruction

The series of questions provided examines key concepts in bond valuation, interest rates, and investment returns, reflecting foundational principles in finance. The discussion covers the calculation of yield to maturity (YTM), the assessment of real interest rates versus inflation, the impact of interest rate fluctuations on bond prices, and the determination of yields for bonds and other fixed-income securities. These components are crucial for investors seeking to optimize their fixed-income portfolios and for understanding the broader bond market dynamics.

Introduction

Investors in bonds face numerous decisions informed by understanding how bond prices and yields relate to interest rates and inflation. The concepts of YTM, current yield, and effective annual yield provide insight into the profitability of bonds under various market conditions. Additionally, grasping the effects of interest rate changes on bond prices helps investors manage interest rate risk efficiently. This paper explores these concepts through detailed calculations and explanations based on the given scenario questions.

Calculating Yield to Maturity (YTM)

The bond issued by Stone Sour Corp illustrates how YTM can be computed when bonds are traded at a premium or discount. The current price and coupon rate provide inputs to solve for YTM using the present value of the bond’s future cash flows. Specifically, the semiannual bond's present value equates to its current market price, which is 109% of par. Using the bond pricing formula and iterative methods such as financial calculators or Excel, we can derive the YTM. This computation accounts for the semiannual coupon payments, the number of periods remaining, and the bond’s face value.

Real Rate of Interest and Inflation

Understanding the real interest rate—reflecting the actual earning after adjusting for inflation—is essential in evaluating investment returns. The approximate real rate can be obtained through the Fisher equation approximation, which subtracts inflation from nominal interest rates. For more precision, the exact Fisher equation considers compounding effects, providing a slightly different result. In this context, treasury bills offer a risk-free benchmark for the nominal rate, and adjusting for inflation yields the real rate which indicates the true cost of borrowing or return.

Real Return on Assets

The real return calculation considers the nominal total return and inflation. If an asset yields 11.6% nominally but the inflation rate was 6.7%, the real return estimates the true gain in purchasing power. Using the Fisher equation, the approximate real return is the nominal minus inflation. For more accuracy, the exact Fisher equation accounts for the compounding effect, resulting in a slightly adjusted value that more accurately reflects behavioral economic principles.

Effect of Interest Rate Movements on Bond Prices

The sensitivity of bond prices to changes in interest rates is measured by duration and convexity. When interest rates rise or fall by a certain percentage, bond prices fluctuate inversely. For bonds with fixed coupons and maturity periods, these changes can be approximated via convexity formulas. Bonds with higher coupons, like Bond K, are less sensitive compared to lower coupon bonds such as Bond J. Calculating the percentage change involves assessing duration and convexity or applying simplified percentage change formulas derived from duration estimates.

Current Yield, YTM, and Effective Annual Yield

The current yield offers a snapshot of the annual coupon payment relative to the market price. The YTM, however, incorporates the present value of all future cash flows, providing a more comprehensive yield measure. The effective annual yield adjusts the semiannual YTM to an annualized basis, accounting for compounding. Together, these metrics enable investors to compare bonds with different coupon rates, maturities, and payment frequencies effectively.

Estimating Remaining Maturity and Holding Period Yield

The relationship between current yield, YTM, and maturity reveals how bond prices and coupon rates interact over time. Maturity can be inferred once the current yield and price are known, assuming the bond’s cash flow pattern. The holding period yield (HPY) considers the actual returns achieved when selling a bond before maturity, combining capital gains or losses with accrued interest. Changes in YTM over time influence bond prices, impacting the realized return on the investment.

Valuation of Complex Bonds

Valuing bonds with irregular cash flows, such as Bond M's delayed payments and phased coupon payments, involves discounting each cash flow individually. Bond N, with no coupons, is simply discounted at the market rate to find its present value. These calculations often employ the time value of money principles, summing discounted cash flows to find the current market price. Accurate valuation requires detailed cash flow schedules and precise discounting techniques.

Conclusion

The comprehensive analysis of bond yields, interest rates, and valuation methods underscores the importance of understanding fundamental financial principles. Whether assessing the impact of interest rate changes, calculating yields, or valuing complex cash flow structures, these concepts enable investors to make informed decisions that optimize return and manage risk. As financial markets evolve, mastery of these tools remains crucial in navigating fixed-income securities effectively.

References

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  • Investopedia. (2023). Yield to Maturity (YTM). https://www.investopedia.com/terms/y/ytm.asp
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  • Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
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