I have one finane question, anyone can help me????

2008-05-06 9:26 pm

Jane & John have just won the Big Game jackpot
lottery with a published face value of $30
million . The winnings can be paid in two ways:
as an ordinary annuity or in a one lump- sum/
cash option. Jane & John are excited by the win
but when they discuss the options with their
financial adviser they realize that if they
select the cash option, they will receive
immediately 45% of the published face value or
alternatively they can choose to receive a 25
year annuity so that it sums to $30 million.

1) Are the lottery organisers justified in
advertising a prize of $30 million? Explain?

2) Jane & John select the cash option plan,
Justify with calculations their selection and the
assumptions that they are making.

回答 (1)

用戶22404

2008-05-07 1:10 am

✔ 最佳答案

1)The lottery organisers are not justified as they do not consider the TIME VALUE of money. It is because the sum of all annual payments equal the $30 million, the claimed amount of prize, however, if they are discounted to present value, the sum of prize is less than 30 million. 2) The value of cash option =$30million*45%=$13.5million which can be obtained at PRESENT. The annual payment is $30million/25 = $1.2million. According to the annuity table, the sum of present value of the 25 annual payments of $1.2million, if the interest rate is 6%, equals $13.55036million. However, if the interest rate is 7%, then the sum of all 25 annual payments equals $12.46933 million. Therefore, they must assume that their annual return of investment on the lump-sum $13.5milliom must be at least reached 6% and they don't want to take the DEFAULT RISK of the lottery organisers for 25 years.

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