Crissie just won the lottery , and she must choose between three award options.
ID: 2663063 • Letter: C
Question
Crissie just won the lottery , and she must choose between three award options. She can elect to receive a lump sum today $61 million, to receive 10 end-of-year payments of $9.5 million, or to receive 30 end-of-year payments of $5.5 million.a. If she thinks she can earn 7% annually, which should she choose?
b. If she thinks she can earn 8% annually, which should she choose?
c. If she thinks she can earn 9% annually, which should she choose?
d. Explain how interest rates influence the optimal choice.
Explanation / Answer
a) If she thinks she can earn 7%, then the third option is the best one. The third option will make you to receive a lump sum of $68,249,726 today. Calculating the present value of annuity: Step1: Go to excel and click "insert" to insert the function. Step2: Select the "PV" function as we are finding the present value of annuity in this case. Step3: Enter the values as Rate = 7%; Nper = 30; PMT = -5500000 Step4: click "OK" to get the desired value. The value comes to "$68,249,726" b) The present value of second option comes to "$63,745,773" The present value of third option comes to "$61,917,808" Here, we will choose the second option as he can receive a lump sum of $63,745,773 which is more than the other two options at 8% annual rate. c) The present value of second option comes to "$60,967,748" The present value of third option comes to "$56,505,097" Here, we will choose the first option as he can receive a lump sum of $61,000,000 which is more than the other two options at 8% annual rate. d) As the interest rate increases, the present value of annuity decreases.
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