Question

Print 6. Listed below are three lottery payout options. (Click the icon to view the lottery payout options.) Rather than compare the payout options at their present values, compare the payout options at their future value ten years from now. a. Using a 6% interest rate, what is the future value of each payout option? b. Rank your preference of payout options. c. Does computing the future value rather than the present value of the options change your preference of payout options? Explain. 2(Click the icon to view the future value factor table.) 3(Click the icon to view the future value annuity factor table.) 4(Click the icon to view the present value factor table.) 5(Click the icon to view the present value annuity factor table.) a. Using a 6% interest rate, what is the future value of each payout option? Compute the future value of each payout option. (Round your answers to the nearest whole dollar.) Future value Option 1: Option 2 Option 3 = b. Rank your preference among payout options. most preferable next preferable least preferable c. Does computing the future value rather than the present value of the options change your preference between payout options? Explain. -, as long as we convert each payment option to its value (5) - using the same interest rate. The preference among the options (6) - we compare We can make a valid comparison between the payout options (4) – the options at their present values or at their future values. Valid comparisons can be made among options at any point in time, as long as we convert (7) cash flows to (8) point in time using (9) - interest rate.

Answer 1

6)

a)

Computation of future value of each option;

Option 1- $ 995000 now  

Interest rate = 6%

Future value = Amount * Future value factor at 6% for 10th year

                   = $ 995000 * 1.791 = $ 1782045

Option 2 - $ 150000 at the end of each year for next 10 years

Future value = Amount * Future value annuity factor at 6% for 10 years

               = $ 150000 * 13.181 = $ 1977150

Option 3 - $ 1750000 ten years from now

Future value of the amount that is going to get in the 10th year will be same as of that amount. The amount will get only in 10th year, so its value will be same.

Future value of each payout option
Options	Future value
Option 1	$ 1782045
Option 2	$ 1977150
Option 3	$ 1750000

b)

Future value of option 2 is higher among the options. So it will be most preferable. And option 1 have the 2nd highest value, so it will be next preferable option. Option 3 have lowest future value, so it will be least preferable.

Ranking of preferences among payout options;

1) Option 2    Most preferable

2) Option 1    Next preferable

3) Option 3    Least preferable

c)

Present value of each options;

Option 1: $ 995000 now

The present value of $ 1 for today will be 1. So the present value of any amount that is getting today will the amount itself.

Present value = $ 995000

Option 2: $ 150000 at the end of each year for next 10 years

Present value = Amount * present value annuity factor at 6% for 10 years

            = $ 150000 * 7.360 = $ 1104000

Option 3: $ 1750000 ten years from now

Present value = Amount * Present value factor for 10th year at 6% rate

             = $ 1750000 * 0.558 = $ 976500

Ranking of the options based on present values;

1. Option 2 , Present value = $ 1104000    - Most preferable

2. Option 1, Present value = $ 995000      - Next preferable

3. Option 3, Present value = $ 976500      - Least preferable

* We can make a valid comparison between the payout options at any point in time, as long as we convert each payment option to its value at the same point in time using the same interest rate. The preference among the options is the same regardless of whether we compare the options at their present values or at their future values.

Valid comparison can be made among options at any point in time, as long as we convert all cash flows to the same point in time using the same interest rate.