Question

1. The state lottery claims that its grand prize is $2 million. The lucky winner will receive $200,000 upon presentation of the winning ticket plus $200,000 at the end of each year for the next 19 years. Assume your own discount rate.

a-Why isn't this really a million-dollar prize? (5 Points)

b-What would it actually be worth in dollars to you? (5 Points)

c-What would the 20 yearly payments need to be for the present value of the lottery to be $2 million? Hint: The first step is to determine what type of an annuity the lottery represents. (10 Points)

Answer 1

Question (a)

The lottery claims of giving $2 million is not correct due to the concept of Time Value of Money. The money in hand today is more valuable than money in the future. Therefore, the yearly payments of $200,000 will mean less to the investor in present value. The Present Value will be arrived at by discounting the cash flows with an appropriate discount rate. The discount rate generally comprises of

· Real Risk-Free Rate

· Inflation Premium

· Default Risk Premium

· Liquidity Premium

· Maturity Premium

For the question, let us assume a discount rate of 10%

Question (b)

For this purpose, the present value of annuity must be used. The annuity is annuity due as the winning prize is to be received at the presentation of the ticket and then end of each year. This means that cash flows occur at starting of Year 0, Year 1 and so on

PV of annuity formula will be used.

PV = 200000 * 8.51* 1.1

PV = 1,872,984 which is less than 2,000,000

Question (c )

Here, Present Value is given, and A must be found

Rearranging the above formula

A = 2,000,000 / (8.51*1.1)

A = 213,652