31. You win the lottery. You can get a lump sum of $25,000,000 or receive $2,000
ID: 2621429 • Letter: 3
Question
31. You win the lottery. You can get a lump sum of $25,000,000 or receive $2,000,000 a year (at the end of each year) for 20 years. You expect to receive interest at 5% (ignore taxes) over the next 20 years.
a. Do you take the lump sum of $25,000,000 or the annuity of $2,000,000?
b. Change the facts. The annuity is paid at the beginning of each year instead of at the end. Now, do you take the lump sum of $25,000,000 or the annuity of $2,000,000?
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Explanation / Answer
a)
Present value of annuity = 2,000,000*(P/A, 5%, 20) = 2,000,000*12.4622 = $24,924,400 < $25 millions
Since this amount is less than lump sum amount of $25,000,000, taking lump sum of $25 millions will be profitable.
b)
Since annuity starts from t=0 in this case,
Present value of annuity will get multiplied by factor of (1.05)
Now Present value of annuity = 24924400*(1.05) = $26,170,620 > $25 millions
This amount is more than lump sum amount we will get so taking annuity will be benificial
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Financial calculators have option to enter if PMT payments are at the end of year or beginning of year
After computations are made,
Lump Sum Annuity
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Lump Sum Annuity
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Lump Sum Annuity
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25,000,000 ?? (to be determined)FV =
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0 2,000,000 (at the END)n =
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- 5%Lump Sum Annuity
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- 5%Related Questions
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