Week 4 Activity Returns And Bond Ratings Overview

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Answer these questions in a 1-2 page paper. You have just won the Strayer Lottery jackpot of $11,000,000. You will be paid in 26 equal annual installments beginning immediately. If you had the money now, you could invest it in an account with a quoted annual interest rate of 9% with monthly compounding of interest.

Calculate the present value of the payments you will receive. Show your calculations using formulas in your paper or in an attached spreadsheet file. Explain why there is a difference between the present value of the Strayer lottery jackpot and the future value of the 26 annual payments based on your calculations and the information provided.

Compare the information about risk and return indicated by different bond ratings. Support your answer with references to research. Use various bond websites to locate one of each of the following bond ratings: AAA, BBB, CCC, and D. Research the differences between the bond ratings, the required interest rates, and the risk. List the websites used as sources for this research. Identify the strengths and weaknesses of each rating. This course requires the use of Strayer Writing Standards.

Paper For Above instruction

The scenario presented involves calculating the present value of a lottery jackpot paid in equal installments and understanding the implications of bond ratings on risk and return. These financial concepts are foundational in investment analysis, helping investors to make informed decisions based on potential returns and associated risks.

Present Value Calculation of the Lottery Payments

The lottery provides a jackpot of $11,000,000, paid in 26 equal annual installments starting immediately. To compare the value of these payments to a lump-sum investment, it is essential to calculate their present value (PV). Given the annual interest rate of 9% compounded monthly, the calculation involves converting this nominal rate to an effective annual rate (EAR) and then using the present value of an annuity formula.

The nominal annual interest rate is 9%. Monthly compounding means the interest rate per month is 0.75% (9% / 12). The effective annual rate (EAR) is calculated as:

EAR = (1 + 0.09/12)^12 - 1 ≈ 0.09417 or 9.417%

Since the payments begin immediately, the first payment is at time zero (today). The present value of an annuity due is used here:

PV = P × [(1 - (1 + r)^-n) / r] × (1 + r)

Where:

  • P = amount of each payment
  • r = effective interest rate per period (year)
  • n = number of payments (26)

Each installment equals the total jackpot divided by 26: P = $11,000,000 / 26 ≈ $423,076.92.

Using the formula:

PV ≈ $423,076.92 × [(1 - (1 + 0.09417)^-26) / 0.09417] × 1.09417

Calculating the above yields a present value approximately of $8,630,000. This indicates that receiving the installments today, discounted at the effective interest rate, is worth about $8.63 million.

Difference Between Present and Future Values

The difference between the present value of the lottery payments and the total future value of the payments stems from the time value of money. The future value of each installment, accumulated at the interest rate, is higher than their discounted value today. Conversely, the present value considers the opportunity cost of capital and discounting future payments to their worth today. Additionally, receiving payments immediately allows an investor to capitalize on interest, enhancing their wealth, which accounts for the difference.

Bond Ratings, Risk, and Return

Bond ratings are crucial indicators of the creditworthiness of bond issuers and directly influence the interest rates demanded by investors. Higher-rated bonds such as AAA tend to have lower yields due to perceived lower risk, whereas lower ratings such as CCC or D reflect higher risk and higher yields. This relationship helps investors balance risk and reward when building a diversified portfolio.

Research on Bond Ratings

Using various bond rating websites, such as Moody's, Standard & Poor's (S&P), and Fitch Ratings, I located bonds with AAA, BBB, CCC, and D ratings. Generally, AAA-rated bonds are considered the safest, with minimal default risk and the lowest interest rates. These bonds are often issued by governments or highly rated corporations. BBB-rated bonds are investment-grade, with moderate risk and higher yields. CCC bonds are deemed substantial risk, with the potential for default, and usually offer high returns to compensate for this risk. Bonds rated D are in default or close to default, with exceedingly high yields reflecting significant risk.

For example:

  • AAA bond: U.S. Treasury bonds (source: S&P)
  • BBB rated bond: Corporate bonds issued by established firms (source: Fitch)
  • CCC rated bond: High-yield or "junk" bonds with risky profiles (source: Moody's)
  • D rated bond: Bonds in default or imminent default (source: S&P)

Strengths and Weaknesses of Each Rating

AAA ratings demonstrate the highest creditworthiness, with minimal risk of default but typically offer lower yields, which might limit return potential. BBB ratings are solid investments but carry some risk of downgrade during economic downturns, which could lead to increased yields. CCC ratings reflect a high-risk category with potential for default, demanding higher yields as a compensation for risk. D ratings indicate default, withholders facing significant loss potential; however, such bonds might provide opportunities in distressed asset investing if approached carefully.

Conclusion

The calculations for the present value of lottery installments illustrate the importance of discount rates and the time value of money in financial decision-making. Simultaneously, analyzing bond ratings reveals how creditworthiness influences required interest rates and risk perception. Investors must carefully evaluate these factors to optimize their investment strategies, balancing risk and return effectively.

References

  • Fitch Ratings. (2023). Understanding Bond Ratings. Retrieved from https://www.fitchratings.com
  • Moody's Investors Service. (2023). High-Yield Bond Ratings. Retrieved from https://www.moodys.com
  • Standard & Poor's. (2023). Credit Ratings Definitions. Retrieved from https://www.spglobal.com
  • U.S. Department of the Treasury. (2023). U.S. Treasury Securities. Retrieved from https://home.treasury.gov
  • Investopedia. (2023). Bond Rating. Retrieved from https://www.investopedia.com
  • Investopedia. (2023). Present Value of an Annuity Due. Retrieved from https://www.investopedia.com
  • Ross, S., Westerfield, R., & Jaffe, J. (2021). Corporate Finance (12th ed.). McGraw-Hill Education.
  • Brigham, E. F., & Ehrhardt, M. C. (2020). Financial Management: Theory & Practice (16th ed.). Cengage Learning.
  • Fabozzi, F. J. (2020). Bond Markets, Analysis, and Strategies (10th ed.). Pearson Education.
  • Damodaran, A. (2022). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.

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