A state lottery makes the following announcement: \"Frederick Carbuncle has just

Question

A state lottery makes the following announcement: "Frederick Carbuncle has just won $100 million! We'll pay Frederick $10 million each year for the next 10 years!" a. Has Frederick really won $100 million? Explain. b. Many state lotteries allow winners to choose a single payment instead of a series of annual payments. "We'll offer you the present value of your annual payments, Frederick," the lottery commissioner says. "And because we're feeling generous, we'll use a really high interest rate when we calculate how much that prize will be. Congratulations, Fred!" Comment on the generosity of the lottery commissioner.

Explanation / Answer

a.) It seemed that the state lottery had paid Frederick $100 million. But in actual, the total amount is not equal to $100 million because of the concept time value of money. $10 million dollars received today is not equal to $10 million dollars received after 1 year and so on in financial management terms. $10 million dollars received 1 year later is less than $10 million dollars received today. It is because, if the amount is received today, we will invest that amount in some place and would atleast get interest on such amount. Thus, such interest is lost for 1 year, if the amount is received after 1 year. Hence, the amount recived today is more than the amount received after 1 year.

Therfore, Frederick has not really won $100 million, since amount is paid as $10 million each year for 10 years.

b.) The amount to be received after 1 year can be converted into its equivalent amount today by discounting the amount with the interest rate (discounting rate). Higher the interest rate, lesser the amount to be receive today. Here, state lottery has offered to pay present value of annual payments as on today and use a high interest rate to convert those annual payments into present value. Usage of high interest rate results in lower present value of annual payments. Thus, the amount receivable by Frederick is lower because of the generosity of the state lottery.

Therefore, the lottery commissioner is not generous in using high interest rate to convert annual payments into present value.

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