Question

Your friend won a lottery! However, the winner was not knowledgeable in finance but was aware that you are a student of finance at USQ. He did not want to share his secret with anyone in the neighbourhood except you of course. He was given a choice between accepting a lump sum of $200,000,000 or an immediate payment of $20,000,000 now and a further $20,000,000 every year for the next 10 years (making 11 payments of $20,000,000) at a time when the alternative investment rate was 6% per annum.

His concern was that he will be getting either $220,000,000 in eleven payments or $200,000,000 upfront. He wants to know which option is truly better. Since he heard about time value of money and annuities, he thought he should check with you which option is more valuable for him. What would be your recommendation for your friend?

Answer 1

Choice 1 : lump sum amount = $ 200000000

Choice 2 : getting eleven payments of $ 20000000 each year starting immediately

PV of Annuity Due:
Annuity Due is series of cash flows that are deposited / withdrawn at regular intervals for specific period of time from today

PV of Annuity Due = Cash Flow + [ Cash Flow * [ 1 - [(1+r)^-(n-1)]] /r ]
r - Int rate per period = 6 % or 0.06
n - No. of periods = 11

Particulars	Amount
Cash Flow	$ 20,000,000.00
Int Rate	6.000%
Periods	11

PV of Annuity Due = [ Cash Flow + Cash Flow * [ 1 - [(1+r)^-(n-1)]] / r ]
= [ $ 20000000 + $ 20000000 * [ 1 - [(1+0.06)^-10] ] / 0.06 ]
= [ $ 20000000 + $ 20000000 * [ 1 - [(1.06)^-10] ] / 0.06 ]
= [ $ 20000000 + $ 20000000 * [ 1 - [0.5584] ] / 0.06 ]
= [ $ 20000000 + $ 20000000 * [0.4416] ] / 0.06 ]
= [ $ 20000000 + $ 147201741.03 ]
= $ 167201741.03

Present value of choice 2 i.e present value of getting eleven payments of $ 20000000 each year starting immediately is $ 167201741.03

if you choose choice 2 you will loose $ 32798258.97 ($ 200000000 - $ 167201741.03)

Choice 1 is better than choice 2 .