Question

1. Suppose you win the lottery and you have the choice of a selecting the following options:

a/ $400 million in 10 equal payments starting today or;

b/ $300 million today or;

c/ $25 million per year starting at the end of year 5 forever

If the interest rate is 6%, which option is the best option? (the option that will have the highest present value).

Answer 1

Interest Rate = 6%

Option 1:

10 equal annual payment of $40 million beginning today

Present Value = $40 million * PVAD of$1 (6%, 10)
Present Value = $40 million * 1.06 * (1 - (1/1.06)^10) / 0.06
Present Value = $40 million * 7.8017
Present Value = $312.07 million

Option 2:

$300 million today

Present Value = $300 million

Option 3:

Perpetuity of $25 million with first payment at the end of year 5

Value of Perpetuity at the end of year 4 = $25 million / 0.06
Value of Perpetuity at the end of year 4 = $416.667 million

Present Value = $416.667 million / 1.06^4
Present Value = $330.04 million

So, Option 3 is the best option as its present value is highest.

answered by: anonymous