Jack just discovered that he holds the winning ticket for the $87 million mega lottery in Missouri. Now he needs to decide which alternative to choose: (1) a $44 million lump-sum payment today or (2) a payment of $2.9 million per year for 30 years; the first payment will be made today. If Jack's opportunity cost is 5 percent, which alternative should he choose?
Present Value of Annuity Due:
Present value of annuity due is given as the sum of the present values of the individual cash flows in an equal periodic series of cash flows from the beginning of a period.
Answer and Explanation:
Jack should choose the option with the higher present value.
For Alternative 1
Present value = $44,000,000.00
For Alternative 2
Present value = Annuity + Annuity * PVAF (r, (n - 1))
PVAF or present value annuity factor is the sum of discounting factors at a given rate r for n number of years.
It can be calculated using the following formula:
- Annuity = $2,900,000.00
- r = 5% = 0.05
- n = 30
So, Present value
= 2,900,000 + 2,900,000 x PVAF (5%,30 years)
= 2,900,000 + 2,900,000 x 15.3725
Jack should choose the second alternative as it gives the higher present value.
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from Business 110: Business MathChapter 8 / Lesson 3