Question

Using Present Value Concepts for Decision Making

You have just won the state lottery and have two choices for collecting your winnings. You can collect $105,000 today or receive $20,700 at the end of each year for the next seven years. A financial analyst has told you that you can earn 9% on your investments.
Required:
1. Calculate the present value of both the options (FV of $1, PV of $1, FVA of $1, and PVA of $1).
2. Which alternative should you select?

Answer 1

1. Option 1: Present value of cash winnings collected today = $105,000 * 1 = $105,000

Option 2: Present value of annual cash collections = $20,700 * 5.033 = $104,183

2. Option 1 should be selected.

Step-by-step explanation:

a) Data and Calculations:

Cash winnings collected today = $105,000

Annual cash collection = $20,700

Discount factor = 9%

Period of annual cash flows = 7 years

Present Value Annuity Factor at 9% for 7 years = 5.033

Present value of cash winnings collected today = $105,000 * 1 = $105,000

Present value of annual cash collections = $20,700 * 5.033 = $104,183

NPV = ($817)

b) Option 1 is worth more in present value terms than option 2. The present value consideration is all about taking into account the time value of money. Using a present value annuity factor of 5.033, the annual cash inflows are determined to their present value to be $104,183. This is less than the $105,000 cash collected today in bulk.