Question

In: Finance

Rita Gonzales won the $62 million lottery. She is to receive $1.9 million a year for...

Rita Gonzales won the $62 million lottery. She is to receive $1.9 million a year for the next 25 years plus an additional lump sum payment of $14.5 million after 25 years. The discount rate is 13 percent. What is the current value of her winnings? Use Appendix B and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods.(Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Solutions

Expert Solution

Answer:

Person RG won a lottery $62 million. She will be paid with yearly payments. Thus, payment for one year is $1.9 million for the next 25 years. The lump sum amount of $14.5 million will be paid in year 25. The applicable discount rate is 13%.

Current value of the winnings of person RG is the present value of the payments that can be received by her in the future. Hence, sum of the present value of annuity and present value of the single payment in year 25 is the current value of the winnings.

First, calculate the present value of annuity using the following equation:

here,

Present value of annuity

Annuity amount

Interest rate/Discount rate

Number of periods

Substitute $1.9 million for annuity amount, 0.13 for discount rate, and 25 for number of periods in the equation of present value of annuity:

Therefore, the present value of annuity is $14.0630666 million.

Now, calculate the present value of the lump sum payment in last year using the present value equation:

here,

Present value

Future value

Interest rate

Number of periods

Substitute $14.5 million for future value, 0.13 for discount rate, and 25 for number of periods in the equation of present value:

hence, the present value of the lump sum payment is $0.682964 million.

Now, calculate the current value of the winnings:

Current value of winnings = PV of annuity + PV of lump sum payment

= $14.0630666 million + $0.682964 million

= $14.7460306 million

Therefore, the current value of the winnings is $14.7460306 million

jeff jeffy answered 1 year ago

Next > < Previous

Related Solutions

Rita Gonzales won the $65 million lottery. She is to receive $3 million a year for...

Rita Gonzales won the $65 million lottery. She is to receive $3 million a year for the next 20 years plus an additional lump sum payment of $5 million after 20 years. The discount rate is 6 percent. What is the current value of her winnings? Use Appendix B and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods.(Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Rita Gonzales won the $38 million lottery. She is to receive $1.1 million a year for...

Rita Gonzales won the $38 million lottery. She is to receive $1.1 million a year for the next 25 years plus an additional lump sum payment of $10.5 million after 25 years. The discount rate is 12 percent. What is the current value of her winnings?

Rita Gonzales won the $44 million lottery. She is to receive $1.3 million a year for...

Rita Gonzales won the $44 million lottery. She is to receive $1.3 million a year for the next 25 years plus an additional lump sum payment of $11.5 million after 25 years. The discount rate is 18 percent.

Alysha has just won a lottery. She will receive a payment of $8,000 at the end...

Alysha has just won a lottery. She will receive a payment of $8,000 at the end of each year for 9 years. As an alternative, she can choose an immediate payment of $55,000. A. Which alternative should she pick if the interest rate is 4 percent: make a payment at the end of each year or an immediate payment? (choose) B. What would the interest rate have to be for Alysha to be indifferent about the two alternatives? (Round answer...

Alysha has just won a lottery. She will receive a payment of$8,000 at the end...

Alysha has just won a lottery. She will receive a payment of $8,000 at the end of each year for 9 years. As an alternative, she can choose an immediate payment of $55,000.A. Which alternative should she pick if the interest rate is 4 percent: make a payment at the end of each year or an immediate payment? (choose)B. What would the interest rate have to be for Alysha to be indifferent about the two alternatives? (Round answer to 4...

You have just won the lottery and will receive $500,000 in one year. You will receive...

You have just won the lottery and will receive $500,000 in one year. You will receive payments for 25 years, and the payments will increase 4 percent per year. If the appropriate discount rate is 11 percent, what is the present value of your winnings? 5,511,586 $29,258,112 $36,804 $29,258,112 $5,741,235

You have just won the lottery and will receive $1,500,000 in one year. You will receive...

You have just won the lottery and will receive $1,500,000 in one year. You will receive payments for 30 years, and the payments will increase by 2.5 percent per year. If the appropriate discount rate is 7 percent, what is the present value of your winnings?

You have just won the lottery and will receive $610,000 in one year. You will receive...

You have just won the lottery and will receive $610,000 in one year. You will receive payments for 19 years, which will increase 5 percent per year. The appropriate discount rate is 12 percent. Required: What is the present value of your winnings?

You have just won the lottery and will receive a lump sum payment of $22.53 million...

You have just won the lottery and will receive a lump sum payment of $22.53 million after taxes. Instead of immediately spending your money, you plan to deposit all of the money into an account that will earn 4.81 percent. If you make equal annual withdrawals for the next 25 years, how much can you withdraw each year starting exactly one year from now? Fancy Cat Products has a project that will cost $250,100 today and will generate monthly cash...

You recently won $80 million in lottery. You will receive 20 payments of $4 million per...

You recently won $80 million in lottery. You will receive 20 payments of $4 million per year (starting from today). If the interest rate is 6.5%, what is your lottery payment worth today?

Subjects