Assume That You Just Won 35 Million In The Florida Lottery

Assume That You Just Won 35 Million In The Florida Lottery And H

Assume that you just won $35 million in the Florida lottery, and hence the state will pay you 20 annual payments of $1.75 million each beginning immediately. If the rate of return on securities of similar risk to the lottery earnings (e.g., the rate on 20-year U.S. Treasury bonds) is 6 percent, what is the present value of your winnings?

Consider the following investment cash flows: Year Cash Flow 0 $1. a. What is the return expected on this investment measured in dollar terms if the opportunity cost rate is 10 percent? b. Provide an explanation, in economic terms, of your response c. What is the return on this investment measured in percentage terms? d. Should this investment be made? Explain your answer.

Assume that two investments are combined in a portfolio. a. in word, what is the expected rate of return on the portfolio? b. what condition must be present for the portfolio to have lower risk than the weighted average of the two investments? c. is it possible for the portfolio to have lower risk than that of either investment? d. is it possible for the portfolio to be riskless? If so, what condition is necessary to create such a portfolio?

Paper For Above instruction

Winning a substantial sum like $35 million in the Florida Lottery presents a unique financial scenario that requires careful valuation, especially when considering the timing of payments and the relevant rates of return. In this case, the winnings are paid as 20 annual installments of $1.75 million, beginning immediately, which implies the need to calculate their present value using an appropriate discount rate. The rate of return on comparable securities, such as 20-year U.S. Treasury bonds, stands at 6 percent, making it the ideal discount rate for valuation. Therefore, determining the present value involves calculating the present worth of an annuity with an immediate start using the discount rate of 6 percent. This calculation provides a realistic estimation of the current worth of the lottery winnings, considering the time value of money and the risk profile of similar securities.

Specifically, because the payments commence immediately, this scenario involves an annuity due. The present value of an annuity due can be calculated using the formula: PV = C [(1 - (1 + r)^-n)/r] (1 + r), where C is the annual payment, r is the discount rate, and n is the number of payments. Plugging in the values: C = $1.75 million, r = 6%, and n = 20, the calculation becomes PV = $1.75 million [(1 - (1 + 0.06)^-20)/0.06] (1 + 0.06). This computation results in a present value of approximately $24.4 million, reflecting what the winnings are worth today based on the given discount rate.

This valuation underscores the importance of factoring in the timing and risk associated with the payments. The immediate start of payments increases their value since each payment is received sooner, rather than at the end of each period. The use of a 6 percent discount rate aligns with the risk profile of similar investment opportunities, ensuring the valuation reflects market conditions. Investors or recipients of such lottery winnings must understand that the actual worth of future cash flows today can substantially differ depending on the chosen discount rate, emphasizing the significance of market-based rates such as treasury bonds.

When considering another investment scenario involving cash flows and opportunity costs, the expected return measured in dollar terms depends on the initial investment and the subsequent cash flows over a period. For instance, if the initial cash flow is $1, and the opportunity cost rate is 10 percent, the expected dollar return can be computed as the difference between the future value of the investment and the initial amount, scaled by the opportunity cost. Similarly, the return in percentage terms can be derived by dividing the dollar return by the initial investment, illustrating the investment’s profitability. Economic reasoning highlights that a higher expected return indicates more attractiveness, but risk considerations and opportunity costs determine whether the investment is worthwhile.

Finally, in portfolio management, understanding the expected rate of return involves weighting the individual asset returns by their proportions in the portfolio. The risk profile of the combined portfolio depends on the correlation between the assets. When assets are negatively correlated or uncorrelated, the combined risk can be lower than the weighted average risk. For a portfolio to be less risky than either individual investment, diversification benefits must be realized, specifically through assets that do not move in perfect tandem. Achieving a riskless portfolio requires combining assets in proportions that perfectly offset each other’s risks, which is only possible if the assets are perfectly negatively correlated at the right proportions. Such an equilibrium can lead to a portfolio with zero risk, illustrating the fundamental principles of diversification in modern portfolio theory.

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