Mary just won the lottery, and she must choose between two options. She can elect to receive a lump sum payment of $70 million today or she can elect to receive 30 end-of-the-year payments of $5.5 million. If the appropriate discount rate is 7%, which option should she choose? The lump sum of $70 million. The 30 year annuity because its present value is $8,013,394.14. The 30 year annuity because its present value is $68,249,726.51. The 30 year annuity because its present value is $165,000,000.

Question

Paxton Jacobs

Business

8 June, 17:53

Mary just won the lottery, and she must choose between two options. She can elect to receive a lump sum payment of $70 million today or she can elect to receive 30 end-of-the-year payments of $5.5 million. If the appropriate discount rate is 7%, which option should she choose? The lump sum of $70 million. The 30 year annuity because its present value is $8,013,394.14. The 30 year annuity because its present value is $68,249,726.51. The 30 year annuity because its present value is $165,000,000.

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Answers (1)

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Sidney Atkinson · Answer 1

Lump sum of $70 million

Explanation:

We must calculate the present value of the 30 yearly payments of $5.5 million so that we can compare what option is best for Mary.

We can use an excel spreadsheet to determine the present value of the 30 year annuity using the PV function:

n = 30 r = 7% payment = 5.5

The present value of the annuity = PV (7%,30,5.5) = $68.25

Since the lump sum is larger than the present value of the annuity $70 million > $68.25 million), then Mary should choose to receive the lump sum.