Bond Valuation Calculations And Related Financial Concepts

Bond valuation calculations and related financial concepts

BBA 3310 Unit VI Assignment Instructions: Enter all answers directly in this worksheet. When finished, save the document using your last name and student ID, and upload it as a .doc, .docx, or .rtf file.

Question 1: Calculate the value of a bond maturing in 12 years with a $1,000 par value, an annual coupon rate of 9 percent, and a market yield to maturity of 12 percent. Round to the nearest cent.

Question 2: Determine the value of Enterprise, Inc. bonds with an 11 percent annual coupon, semiannual interest payments, a 9-year maturity, and a $1,000 par value, given market yields of 14 percent. Find bond values with interest paid semiannually and annually, respectively, rounded to the nearest cent.

Question 3: Find the yield to maturity for a bond priced at $750, with a $1,000 par value, 9 percent annual interest paid semiannually over 20 years. Round to two decimal places.

Question 4: Calculate the yield to maturity for a bond valued at $950, with a $1,000 par value, 14 years to maturity, and an 8 percent annual coupon with semiannual payments. Find the YTM for maturities of 14, 28, and 7 years, respectively, rounded to two decimal places.

Question 5: For a bond issued by Arizona Public Utilities paying $70 in interest, with a $1,000 par, 25-year maturity, and a required yield of 8 percent, determine its value at 8%, 11%, and 7% yields. Also, explain the effect of interest rate changes on bond value, and compare bond prices for 5-year maturities at different yields. Conclude how interest rate risk varies between long-term and short-term bonds.

Question 6: Calculate the growth rate of Pepperdine, Inc., with a 14 percent return on equity and a 55 percent retention ratio. Round to two decimal places.

Question 7: Find the value of NCP’s stock with a last dividend of $1.29, a 6 percent growth rate, and an 8.70 percent required return. Decide whether to invest based on valuation, and compare to current market price.

Question 8: Determine the firm's growth rate with a 22 percent ROE and a 37 percent retention ratio. Explain the effect of increasing retention on stock value, rounded to two decimal places.

Question 9: Using the P/E ratio approach and dividend discount model, calculate the stock value. Conditions: required return 13%, earnings at year-end $8, 40% earnings retention, 15% ROE, and P/E multiple of 8.571. Show both methods with rounded results.

Question 10: Calculate the value of a preferred stock paying an $8 dividend with a 13% required yield. Round to the nearest cent.

Paper For Above instruction

Introduction

Valuation of bonds and stocks are fundamental concepts in corporate finance, enabling investors and firms to make informed decisions regarding investment, issuance, and risk assessment. Understanding bond valuation involves analyzing various factors such as coupon payments, yield to maturity, and maturity period. Similarly, stock valuation connects dividend policies, growth rates, and market multiples to current and future value estimations. This paper explores these aspects through detailed calculations and theoretical explanations, incorporating relevant financial models and empirical data.

Bond Valuation Techniques

The core of bond valuation lies in discounting future cash flows—periodic coupon payments and the face value at maturity—back to their present value using the market’s required rate of return (YTM). For example, in question 1, the bond's projected cash flows include annual coupons of 9% of $1,000 ($90) and the face value of $1,000. Discounting these at a 12% YTM yields a present value of approximately $814.17, illustrating the inverse relationship between YTM and bond price: as yields rise, bond prices fall, reflecting increased required returns by investors.

In question 2, the valuation depends on the payment frequency. Bonds paying interest semiannually effectively halve the period interest rate while doubling the number of periods, influencing the present value calculation. The calculated bond values of $849.11 (semiannual payments) and $851.61 (annual payments) demonstrate minor differences attributable to compounding frequency, consistent with the bond valuation principles discussed in standard finance literature (Ross, Westerfield, & Jaffe, 2013).

Calculating Yield to Maturity (YTM)

YTM is the internal rate of return given the current market price, coupon payments, and face value. In question 3, the calculation involves solving the bond pricing formula for the discount rate, considering 20 years to maturity, semiannual coupons, and market price. The computed YTM of 12.41% aligns with the well-established bond pricing approach, involving iterative or financial calculator techniques (Brealey, Myers, & Allen, 2019).

Similarly, in question 4, the effect of varying maturities on YTM emphasizes that longer-term bonds typically exhibit higher sensitivity to interest rate changes, increasing interest rate risk. The decreasing YTM for longer maturities (8.62%) indicates market adjustments to discount future cash flows at prevailing rates, and shorter maturities (7 years) show slightly higher yields (8.98%) due to the shorter duration’s impact on risk and reinvestment assumptions (Fabozzi, 2021).

Relationship between Bond Price and Yield

Questions 5a-5c explore how yield changes influence bond value. At the coupon rate, bonds typically trade at par ($1,000). When market yields increase beyond the coupon rate, bonds sell at discounts (e.g., $663.13 at 11%), and when yields decrease below, bonds can sell at a premium, approaching face value ($1,000 at 7%). This demonstrates the fundamental inverse relation: as yields rise, bond prices decline, illustrating interest rate risk (Mishkin & Eakins, 2018).

Additional discussions on maturity illustrate that longer-term bonds undergo more significant price fluctuations in response to interest rate changes, hence higher interest rate risk exposure compared to shorter-term bonds, consistent with duration theory.

Retained Earnings and Firm Growth

Retained earnings fuel growth as they are reinvested into the firm's operations. In question 6, Pepperdine, Inc.'s growth rate equals its ROE multiplied by its retention ratio (14% × 55%), resulting in 7.70%. Similarly, in question 8, the growth rate depends on the ROE and retained earnings, and increasing the retention ratio enhances growth, subsequently increasing the stock's intrinsic value. These principles are embedded in the Gordon Growth Model (Berk & DeMarzo, 2020).

Stock Valuation Models

The valuation of stocks can be approached through dividend discount models (DDM) or P/E ratios. In question 7, with a dividend of $1.29 growing at 6% and an 8.70% required return, the DDM formula yields a stock value around $14.50, suggesting whether the stock is undervalued depends on comparison with current market price. The P/E approach, using similar companies' multiples of 8.571, confirms this valuation, highlighting the importance of multiple-based valuation methods.

Questions 9 and 10 extend these concepts by combining P/E ratios with growth assumptions and calculating preferred stock value based on fixed dividends and market yield, respectively. These models are extensively discussed in finance literature, illustrating their utility and limitations.

Conclusion

Comprehensive understanding of bond and stock valuation is vital for effective financial decision-making. Bond prices are sensitive to interest rate changes, with longer maturities exhibiting greater risk. Stock valuation involves growth prospects, dividend policies, and market multiples, underpinning investment strategies. Mastery of these concepts facilitates risk assessment and valuation accuracy, essential skills for finance professionals and investors alike.

References

• Berk, J., & DeMarzo, P. (2020). Fundamentals of Corporate Finance (4th ed.). Pearson.
• Brealey, R. A., Myers, S. C., & Allen, F. (2019). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
• Fabozzi, F. J. (2021). Bond Markets, Analysis, and Strategies (10th ed.). Pearson.
• Mishkin, F. S., & Eakins, S. G. (2018). Financial Markets and Institutions (9th ed.). Pearson.
• Ross, S. A., Westerfield, R. W., & Jaffe, J. (2013). Corporate Finance (10th ed.). McGraw-Hill Education.