Question

A relative has just won a state lottery paying $20 million in installments of $1 million per year for twenty years. Your relative states that she is 20 million richer. Is she correct? Create a simple example for two years to illustrate your position

Answer 1

She amount by which she will become richer would be equals to the present value of future stream of payments/revenues.

Here she will not become richer by $ 20 millions because the present value of those 20 installments of $1 million each is lesser than the $20 million.

Eg. If she will receive $1 million for the next 2 years & let rate of interest = 10%,

Then the present value of this 2 year stream of payments would be :

P = 1* (1/1.1)¹ + 1* (1/1.1)² = 0.91 + 0.83 = 1.74.

Hence the present value of receiving $1 million for the next 2 years is $1.74 million which is lesser than $2 million. Similary the present value of those 20 installments of $1 million each would be lesser than $20 million.