question archive A lottery claims its grand prize is $25 million, payable over five years at $5,000,000 per year

A lottery claims its grand prize is $25 million, payable over five years at $5,000,000 per year

Subject:FinancePrice:2.86 Bought9

A lottery claims its grand prize is $25 million, payable over five years at $5,000,000 per year. If the first payment is made immediately, and the next 4 payments at the end of year 1, year 2, year 3 and year 4, what is this grand prize really worth? Use an interest rate of 8%.

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Answer:

Here to calculate real worth of these future cash flow from lottery claims we need to calculate present value of all these cash flow.

The formula of calculating PV (present value) of Future value (FV) cash flow is,

PV = FV / (1+r)^n

PV = Present value

FV =Future value

r =interest rate

n= time

So PV of all cash flow of this lottery is,

PV = $ 5,000,000 / (1+8%)^0 + $ 5,000,000 / (1+8%)^1 + $ 5,000,000 / (1+8%)^2 +$ 5,000,000 / (1+8%)^3 +$ 5,000,000 / (1+8%)^4

= $ 5,000,000 + $ 4,629,629.63 + $ 4,286,694.10 + $ 3,969,161.21 + $ 3,675,149.26

= 21,560,634.20

This is real value of $ 25 million today at 8%.