Calculating Present Value Of Lottery Payments And Analysis

Calculating present value of lottery payments and analyzing bond ratings

Calculating present value of lottery payments and analyzing bond ratings

Sherri Coleman FIN 534: Financial Management Strayer University Dr. Black July 27, 2022 Returns and Bonding Ratings 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. Basic Information Jackpot = $11,000,000 Annual Installments = 26 Interest Rate = 9% PV? Where: PV=Present Value FV=Future Value r=Nominal Interest rate n=Number of periods k= Yearly compounding times Therefore: Monthly Compounded Installments (k) = 12 Nominal interest rate (r) = 9% Number of periods (n) = 26 Future Value (FV) = Thus: PV = .32. 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. The present value is greater than the winner of the jackpot would receive if annual installments were chosen as an option. In this regard, monthly compounding of interest means that each month, the interest rate is added to the initial investment. The present value allows comparing the current value of the money with the sum that the individual will receive upon investment. The difference is attributed to the time value of money. 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. Credit ratings play a fundamental role in helping investors make informed decisions towards investing in securities and or/bonds (Shi et al., 2019). The ratings include AAA, BBB, CCC, and D. Bonds that are rating AAA have the highest degree of worth and quality, which implies that they are capable of easily meeting its financial requirement and have the least risk of default. BBB rating bonds are also referred to as investment graded bonds, and are capable of meeting of the obligations for its payments, thus giving banks the liberty to invest in (Shi et al., 2019). CCC bonds rating are highly risky to invest in (Hajek, Olej & Prochazka, 2016). Therefore, banks do not have an appetite to invest in the CCC bonds. On the other hand, D rating bonds have a very small value or no value. This element makes the bonds susceptible to default. Identify the strengths and weaknesses of each rating. Bond Strengths Weaknesses AAA High credit quality High safety level Lowest credit risk Potential for false credit rating Challenge of liquidation BBB Moderate safety Timely payment of debt Moderate credit risk Bond issuer liable in case of default CCC High rate of return High default probability D Lowest value/short term default Lowest ratings High likelihood of default References Hajek, P., Olej, V., & Prochazka, O. (2016, December). Predicting Corporate Credit Ratings Using Content Analysis of Annual Reports–A Naà¯ve Bayesian Network Approach. In FinanceCom 2016 (pp. 47-61). Springer, Cham. Shi, B., Zhao, X., Wu, B., & Dong, Y. (2019). Credit rating and microfinance lending decisions based on loss given default (LGD). Finance Research Letters, 30, . Stocks Sherri Coleman FIN 534: Financial Management Strayer University Dr. Black July 15, 2022: Stocks Stock exchanges are majorly involved in trading financial instruments such as securities, derivatives, and commodities (Dogru et al., 2020). In the U.S., there are two major financial securities markets, which are New York Stock Exchange (NYSE) and the National Association of Securities Dealers Automated Quotation System (NASDAQ). NYSE is, undoubtedly, the largest stock exchange in the world. It provides entrepreneurs and icons with the opportunity of raising capital. NASDAQ, on the other hand, is the biggest electronic screen-based market and is popularly known for its relatively modern and computerized system. Additionally, it provides lower listing fees compared to NYSE, which explains why giant companies such as Microsoft, Amazon, Google, and Apple trade with NASDAQ. According to Dogru et al. (2020), free cash flow helps businesses in measuring and monitoring their present value towards tracking growth, encouraging expansion, and avoiding failure. This implies that free cash flow is the amount of money remaining after a business pays for such expenditures as rent, plant, fixed assets, employees, expenses, and debts, among others (Dogru et al., 2020). Therefore, free cash flow is utilized in expanding operations, contributing to additional employees, or facilitating the acquisition of additional assets. The growth in free cash flow as a result of debt elimination, dividend distributions, share buybacks, cost reductions, efficiency improvements or revenue growth contributes to a positive company growth. One of the companies listed in NYSE is ExxonMobil while Apple Inc. is listed in NASDAQ. In 2019, ExxonMobil’s free cash flow for the year was $5.355 billion, which was a remarkable 67.43 percent decline from 2018. The company recorded a free cash flow of $-2.614 billion in 2020, representing an unimpressive 148.81 percent increase from 2019 (Macrotrends, 2022). On the other hand, Apple Inc. had an annual free cash flow of $58.896 billion in 2019, a decline of 8.15 percent recorded in 2018. However, the decline was reverted in 2020 as the company witnessed a jump in its free cash flow of $73.365 billion, representing a 24.57 increase from 2019 (Macrotrends, 2022). An analysis above, it is clear that Apple recorded a magnificent increase in its free cash flows from 2019 to 2020. Therefore, the inference is that the company had the cash that may be utilized towards expanding, developing new products and services, buying back stock, paying dividends, or reducing their debt. The increase in free cash flow for Apple is an indication of a healthy financial position in the prevailing environment. Thanks to the rise in free cash flow, the implication is that the companies have a strong foundation to their stock pricing in the future. The decline in free cash flow for ExxonMobil is a serious concern for the company. To address the issue, the company may need to restructure its debts to lower interest rates as well as optimizing repayment schedules. The company should also seek to reduce, limit, or delay capital expenditures. Financial Ratios for Apple ( Al Mheiri, Al Hosani & Saif, 2021). Liquidity Rations 1. Current Ratio (2019) = Current Assets/Current Liabilities = $163.23 billion/$102.16 billion = 1.. Current Ratio (2020) = $154.11 billion/$132.51 billion = 1.. Quick Ratio (2019) = (Current Assets – Inventory)/Current Liabilities = $159.13 billion/$102.16 billion = 1.. Quick Ratio (2020) = $149.13 billion/$132.51 billion = 1.56 Asset Management Rations 1. Inventory Turnover Ratio (2019) = Cost of goods sold/Average inventory = $161.78 billion/$4.11 billion = 39.. Inventory Turnover Ratio (2020) = $169.56 billion/$4.06 billion = 41.. Accounts Receivable Turnover Ratio (2019) = Net sales/Average accounts receivables = $260.17 billion/$22.93 billion = 11.. Accounts Receivable Turnover Ratio (2019) = $274.52 billion/$16.12 billion = 17.03 Profitability Ratios 1. Operating Profit Margin (2019) = Operating Income/Net Sales100 = $63.93 billion/$260.17 billion100 = 24.57% 1. Operating Profit Margin (2020) = $66.29 billion/$274.52 billion100 = 24.15% 1. Net Profit Margin (2019) = Net Income/Net Sales100 = $55.26 billion/$260.17 billion100 = 21.24% 1. Net Profit Margin (2020) = $57.41 billion/$274.52 billion100 = 20.91% Financial Ratios for ExxonMobil ( Asadbayli, 2020). Liquidity Rations 1. Current Ratio (2019) = Current Assets/Current Liabilities = $50.05 billion/$63.99 billion = 0.. Current Ratio (2020) = $44.89 billion/$56.36 billion = 0.. Quick Ratio (2019) = (Current Assets – Inventory)/Current Liabilities = $31.52/$63.99 billion = 0.. Quick Ratio (2020) = $26.04 billion/$56.36 billion = 0.46 Asset Management Rations 1. Inventory Turnover Ratio (2019) = Cost of goods sold/Average inventory = $211.15 billion/$18.75 billion = 11.. Inventory Turnover Ratio (2020) = $150.56 billion/$18.69 billion = 8.. Total Asset Turnover (2019) = Sales/Total Assets = $264.93 billion/$362.60 billion = 0.. Total Asset Turnover (2020) = $181.50 billion/$332.75 billion = 0.55 Profitability Ratios 1. Operating Profit Margin (2019) = Operating Income/Net Sales100 = $20.06 billion/$53.79 billion100 = 37% 1. Operating Profit Margin (2020) = $28.88 billion/$30.94 billion100 = 93% 1. Net Profit Margin (2019) = Net Income/Net Sales100 = $14.34 billion/$53.79 billion100 = 26.66% 1. Net Profit Margin (2020) = $22.44 billion/$30.94 billion100 = 72.52% In examining the financial ratios for Apple and ExxonMobil, one of the key strengths is that the values obtained may go a long way in comparing different companies. This is important as it helps investors in evaluating stocks within a given industry.

Paper For Above instruction

The calculation of the present value (PV) of the lottery jackpot payments versus the actual future payments involves understanding the principles of discounted cash flow and time value of money. Given an $11 million jackpot paid in 26 equal annual installments starting immediately, the goal is to determine the current worth of those payments if invested now at an annual interest rate of 9% compounded monthly. This involves converting the nominal annual interest rate into a monthly rate and then using the present value of an annuity formula to find the equivalent value today.

The primary formula used in this calculation is the present value of an annuity due, because payments start immediately. For an annuity due, the present value (PV) is calculated as:

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

Where:

  • P = payment amount each period ($11,000,000 / 26 ≈ $423,076.92)
  • i = interest rate per period (monthly rate)
  • n = total number of payments (26)

Since the interest rate is compounded monthly at 9% annually, the monthly interest rate i is:

i = 0.09 / 12 = 0.0075 or 0.75% per month

Calculating the present value:

First, the payment P is calculated as:

P = $11,000,000 / 26 ≈ $423,076.92

Then, substituting into the PV formula:

PV ≈ $423,076.92 × [(1 - (1 + 0.0075)^{-26}) / 0.0075] × (1 + 0.0075)

Calculating the inside terms step-by-step:

(1 + 0.0075)^{-26} ≈ 1 / (1.0075)^{26} ≈ 1 / 1.209 ≈ 0.8277

Thus, (1 - 0.8277) = 0.1723

Dividing by 0.0075: 0.1723 / 0.0075 ≈ 22.97

Multiplying by (1 + 0.0075): 22.97 × 1.0075 ≈ 23.13

Finally, PV ≈ $423,076.92 × 23.13 ≈ $9,785,869.89

This approximates the present value of the lottery payouts at about $9.79 million, which is less than the $11 million jackpot amount because the present value discounts future payments considering the time value of money.

The difference between the straightforward sum of the payments ($11 million) and the discounted present value (about $9.79 million) arises because money has a time value—the present is worth more than future cash flows. Compounding monthly increases the effective interest rate because interest accumulates more frequently, affecting the present valuation.

In regards to bond ratings, the classifications from AAA to D reflect a continuum of creditworthiness, associated interest rates, and risk profiles. Bonds rated AAA represent the highest quality, with extremely low default risk, and therefore pay the lowest interest rates. Conversely, bonds rated D indicate high default risk, often in default, and correspond with higher interest rates to compensate investors for elevated risk. Bonds rated BBB are investment grade, with moderate risk and interest rates; CCC bonds are highly speculative, with substantial default probability.

The differences in bond ratings hinge on the issuer's financial stability and ability to meet debt obligations. For instance, AAA bonds are issued by entities with strong financial positions, low leverage, and stable income streams, making them safer investments but yielding lower returns. BBB-rated bonds have moderate risk, potentially offering higher yields, but with increased chance of default if financial conditions deteriorate (Shi et al., 2019).

Research indicates ratings directly influence interest rates demanded by investors. For example, Hajek, Olej, and Prochazka (2016) demonstrate that bonds with lower ratings (CCC or D) must offer higher yields to compensate for increased default risk. The embedded risk affects investment decisions heavily, with the possibility of default increasing as the rating declines. Therefore, investors prefer higher-rated bonds for safety, even if yields are lower.

Examining credible sources such as Moody’s, Standard & Poor’s, and Fitch Ratings provides insights into bond classifications. As per Moody’s (2023), AAA bonds typically carry a yield spread of around 0.5% below AAA benchmarks, whereas D-rated bonds can have spreads exceeding several percentage points, reflecting the heightened risk. Investors should weigh these differences alongside their risk appetite, investment horizon, and market conditions.

Assessing the strengths and weaknesses of each rating category reveals the trade-offs between safety and return. AAA bonds offer the benefit of high credit quality and low default risk, but their lower yields might not meet the return expectations of risk-tolerant investors. BBB bonds provide a reasonable balance, suitable for investors seeking moderate risk and yields, but their vulnerability to economic downturns poses a risk. CCC and D bonds are suitable only for the most risk-tolerant investors who seek high returns despite the significant likelihood of default, which may result in total loss of investment (Hajek et al., 2016; Shi et al., 2019).

In conclusion, understanding bond ratings and their implications helps investors make informed decisions aligned with their risk tolerance and investment goals. The ratings, calculated interest rates, and associated risk levels reflect the financial health of the issuer and prevailing economic trends. Investing in higher-rated bonds reduces default risk but also limits potential yields, whereas investing in lower-rated bonds offers higher returns at the cost of increased default probability.

References

  • Hajek, P., Olej, V., & Prochazka, O. (2016). Predicting Corporate Credit Ratings Using Content Analysis of Annual Reports – A Naïve Bayesian Network Approach. Springer, Cham.
  • Shi, B., Zhao, X., Wu, B., & Dong, Y. (2019). Credit rating and microfinance lending decisions based on loss given default (LGD). Finance Research Letters, 30.
  • Moody’s Investors Service. (2023). Bond rating scales and definitions. Moody’s Homepage.
  • Standard & Poor’s. (2022). Credit Ratings Definitions. S&P Global Ratings.
  • Fitch Ratings. (2021). Fitch Ratings Definitions. Fitch Ratings.
  • Macrotrends. (2022). Apple and ExxonMobil Financial Statements. Retrieved from macrotrends.net
  • Dogru, T., Kizildag, M., Ozdemir, O., & Erdogan, A. (2020). Acquisitions and shareholders' return in restaurant firms: The effects of free cash flow, growth opportunities, and franchising. International Journal of Hospitality Management, 84, 102327.
  • Al Mheiri, R., Al Hosani, N., & Saif, E. (2021). Ratio Analysis of Apple. SSRN.
  • Asadbayli, Y. (2020). Financial Ratio Analysis as a Tool of Evaluating the Performance of Companies for Investment Decision: The Case of ExxonMobil and Chevron. Doctoral dissertation, Szeged University.
  • Macrotrends. (2022). Apple and ExxonMobil Financial Data. Retrieved from macrotrends.net

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