Question

1. Arthur Flack just won the lottery! He has 3 options to collect his prize
   1. Option 1: A one-time single payment of $250,000 today
   2. Option 2: An ordinary annuity of $30,000 for the next 10 years
   3. Option 3: A mixed stream of payments corresponding to the table below

End of year	Cash flows (option 3)
1	$120,000
2	$100,000
3	$60,000

Arthur can earn 8% interest on any of his investments. Which is the best alternative for Arthur? Explain.

Answer 1

The NPV of the first option wil be $ 250,000 since the same is received today.

The NPV of the second option is computed as follows:

= Future value / (1 + r)ⁿ

= $ 30,000 / 1.08¹ + $ 30,000 / 1.08² + $ 30,000 / 1.08³ + $ 30,000 / 1.08⁴ + $ 30,000 / 1.08⁵ + $ 30,000 / 1.08⁶ + $ 30,000 / 1.08⁷ + $ 30,000 / 1.08⁸ + $ 30,000 / 1.08⁹ + $ 30,000 / 1.08¹⁰

= $ 201,302.44 Approximately

The NPV of the third option is computed as follows:

= Future value / (1 + r)ⁿ

= $ 120,000 / 1.08 + $ 100,000 / 1.08² + $ 60,000 / 1.08³

= $ 244,474.93 Approximately

Since the present value of the first option is the greatest among all the three options, hence option 1 is the best option for Arthur Flack.

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