Suppose you win a small lottery and have the choice of two ways to be paid: You

Question

Suppose you win a small lottery and have the choice of two ways to be paid: You can accept the money in a lump sum or in a series of payments over time. If you pick the lump sum, you get $2,700 today. If you pick payments over time, you get three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. At an interest rate of 10% per year, the winner would be better off accepting the___since it has the greater present value. At an interest rate of 12% per year, the winner would be better off accepting___since it has the greater present value. Years after you win the lottery, a friend in another country calls to ask your advice. By wild coincidence, she has just won another lottery with the same payout schemes. She must make a quick decision about whether to collect her money under the lump sum or the payments over time. What is the best advice to give your friend? The lump sum is always better. The payments over time are always better. It will depend on the interest rate; advise her to get a calculator. None of these answers is good advice.

Explanation / Answer

FIRST WE WILL CALCULATE PRESENT VALUE UNDER BOTH THE INTEREST RATE

PV FACTOR @10% FOR ONE YEAR IS 0.9091 AND FOR SECOND YEAR IT IS 0.8264

ON CALCULATING = 1000 + [1000* 0.9091] + [1000 * 0.8264] = 1000 + 909.1 + 826.4 = 2735.5

NOW FOR 12% RATE WE WILL CALCULATE THE PRESENT VALUE.

PV FACTOR @12% FOR ONE YEAR IS 0.8929 AND FOR SECOND YEAR IT IS 0.7972

ON CALCULATING = 1000 + [1000* 0.8929] + [1000 * 0.7972] = 1000 + 892.9 + 797.2 = 2690.1

WE SEE THAT IN CASE OF 10% THE PAYOUT IS MORE THAN 2700 IN PRESENT VALUE TERMS. SO IT WOULD BE BETTER TO ACCEPT THREE PAYMENTS OF 1000 @10% SINCE THEY HAVE GREATER PRESENT VALUE.

WE SEE THAT IN CASE OF 12% THE PAYOUT IS LESS THAN 2700 IN PRESENT VALUE TERMS. SO IT WOULD BE BETTER TO ACCEPT LUMP SUM PAYMENTS OF 2700 @12% SINCE IT HAS GREATER PRESENT VALUE.

NOW COMING TO THE FRIEND, SINCE THERE ARE NO INTEREST RATES GIVEN SO IT WILL DEPEND ON THE INTEREST RATE, ADVISE HER TO GET A CALCULATOR.

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