Final answer:
To determine the best option for receiving the lottery winnings, we need to calculate the present value of each option and compare them. The best option is the second option, which is receiving $10 million today.
Step-by-step explanation:
To determine the best option for receiving the lottery winnings, we need to calculate the present value of each option and compare them. We will use the formula for calculating the present value of an annuity to determine the present value of the first option, which is receiving $1.25 million per year for the next 10 years.
The present value of the first option can be calculated as follows:
PV = CF * (1 - (1 + r)^(-n)) / r
PV = 1.25 * (1 - (1 + 0.1)^(-10)) / 0.1
PV = 1.25 * (1 - 0.386) / 0.1
PV = 1.25 * 0.614 / 0.1
PV = 0.76625 / 0.1
PV = $7.6625 million
Therefore, the present value of the first option is $7.6625 million.
Now, let's calculate the present value of the second option, which is receiving $10 million today.
Since you can expect to earn an annual return of 10 percent on investments, the present value of the second option can be calculated as follows:
PV = CF / (1 + r)^n
PV = 10 / (1 + 0.1)^0
PV = 10 / 1
PV = $10 million
Therefore, the present value of the second option is $10 million.
Finally, let's calculate the present value of the third option, which is receiving $4 million today and $1 million for each of the next eight years.
The present value of the third option can be calculated as follows:
PV = CF / (1 + r)^n
PV = 4 / (1 + 0.1)^0 + 1 / (1 + 0.1)^1 + 1 / (1 + 0.1)^2 + ... + 1 / (1 + 0.1)^8
PV = 4 / 1 + 1 / 1.1 + 1 / 1.21 + ... + 1 / 2.59
PV = $13.2536 million
Therefore, the present value of the third option is $13.2536 million.
Based on these calculations, the best option for receiving the lottery winnings is the second option, which is receiving $10 million today. This option has the highest present value of $10 million, compared to the present values of $7.6625 million for the first option and $13.2536 million for the third option.