Question

Your have won the lottery and you will receive $50,000 a year for the next 20 years. Based on this information, is the present value of your lottery winnings more than $1,000,000, less than $1,000,000, or equal to $1,000,000? Why?

Answer 1

The present value of lottery winnings will be less than $ 1,000,000 as described below.

First of all we shall compute the winning price of lottery as follows:

= $ 50,000 each year x 20 years

= $ 1,000,000

Now when we compute the present value, we always take the discounted value of the future cash flows, which in this case are $ 50,000 a year and as a result the sum of discounted values will always be lower than that of $ 1,000,000.

For example present value of $ 50,000 to be received in 1 year at a discount rate of 10% is computed as follows:

= $ 50,000 / 1.10

= $ 45,454.55 Approximately

As can be seen we have discounted the future cash flow and as a result the present value is lower than $ 50,000

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