Q23E Congratulations! You have won a ... [FREE SOLUTION]

Chapter 26: Q23E (page 1469)

Congratulations! You have won a state lottery. The state lottery offers you the following (after-tax) payout options:
Option #1: $12,000,000 after five years
Option #2: $2,150,000 per year for five years
Option #3: $10,000,000 after three years
Assuming you can earn 6% on your funds, which option would you prefer?

Short Answer

Expert verified

Option #2 would be preferable.

Step by step solution

Meaning of Lottery

A lottery could be a kind of gaming in which members buy numbered tickets. The numbers on tickets are picked, and those with particular numbers on their tickets win a prize.

Analyzing the various option

Option #1

$\begin{array}{rcl} P r e s e n t v a l u e & = & A m o u n t r e c c e i v a b l e a t t h e e n d o f 5 t h y e a r 脳 P V F @ 6 %, 5 y e a r \\ = & $ 12, 000, 000 脳 0.747 \\ = & $ 8, 964, 000 \end{array}$

Option #2

$\begin{array}{rcl} P r e s e n t v a l u e & = & A m o u n t r e c c e i v a b l e a t t h e e n d o f 1 s t t o 5 t h y e a r 脳 P V F @ 6 %, 5 y e a r \\ = & $ 2, 150, 000 脳 4.212 \\ = & $ 9, 055, 800 \end{array}$

Option #3

$\begin{array}{rcl} P r e s e n t v a l u e & = & A m o u n t r e c e i v a b l e a t t h e e n d o f 3 r d y e a r 脳 P V F @ 6 %, 3 y e a r \\ = & $ 10, 000, 000 脳 0.840 \\ = & $ 8, 400, 000 \end{array}$

Option #2 depicts more present value as compared to the other option. So, option #2 will be preferable.

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Year	Plan Alpha	Plan Beta
1	\(1,600,000	\)1,600,000
2	\(1,600,000	2,200,000
3	\)1,600,000	2,800,000
4	\(1,600,000	2,200,000
5	\)1,600,000	1,600,000
6	\(1,600,000	1,500,000
7	\)1,600,000	1,300,000
8	\(1,600,000	1,100,000
9	\)1,600,000	900,000
10	\(1,600,000	800,000
Total	\)16,000,000	\(16,000,000

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Short Answer

Step by step solution

Meaning of Lottery

Analyzing the various option

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