Question

Congratulations, you have won the California State Lottery. Lottery officials are giving you a choice of payment options. You will need to choose from one of the following streams. Assume at 5% interest rate for all scenarios.

Option 1	Immediate payment of $1,000,000
Option 2	10 annual installments of $120,000
Option 3	$2,650,000 paid at the end of 20 years
Option 4	20 annual installments of $80,000
Option 5	5 annual installments of $100,000 plus a lump sum of $750,000 at the end of 5 years

Consider these options without referencing the calculation methods presented in the Chapter 12 Appendix.

Which options will result in receiving the most cash? Which option do you think you should choose and why? Which will be the least favorable option and why?

Answer 1

Solution:

We have to calculate present value of cash flows for each option in order to identify which option will result in receiving of most cash

Option 1: Immediate payment of $1,000,000

Present value of cash flows = Cash flow * PV factor at interest rate at period of cash flow

= $1,000,000*1 = $1,000,000

Option 2: 10 annual installment of of $120,000 each

Present value of cash flows = $120,000 * cumulative PV factor at 5% for 10 periods

= $120,000 * 7.721735 = $926,608.19

Option 3: $2,650,000 at end of 20 years

Present value of cash flows = $2,650,000 * PV factor at 5% for 20th period

= $2,650,000 * 0.376889 = $998,757.13

Option 4: 20 annual installment of $80,000 each

Present value of cash flows = $80,000 * cumulative PV factor at 5% for 20 periods

= $80,000 * 12.46221 = $996,976.83

Option 5: 5 annual installments of $100,000 plus a lump sum of $750,000 at the end of 5 years

Present value of cash flows = $100,000 * cumulative PV factor at 5% for 5 periods + $750,000 * PV factor for 5% at 5th period

= $100,000 * 4.329477 + $750,000 * 0.783526 = $1,020,592.29

Hence option 5 will result in receiving the most cash as present value is higher among all options i.e. $1,020,592.29. I will choose option 5 as it resulting in higher cash in present value terms.

The least favorable option is Option 2 as it resluting into lowest cash flows in present value terms i.e. $926,608.19