Question

As the winner of the Standup sweepstakes, you are entitled to one of the following prizes:

1. $999,999 payable immediately.
2. $125,000 per year forever (1st payment is a year from today).
3. $185,000 per year for 10 years (1st payment is received immediately).

The stated annual interest rate is 14 percent. Rank the alternatives in order of preference showing work (or relevant inputs to a program) for full credit.    

Answer 1

Option 1: Immediately payment

PV = $ 999,999

Option 2: Perpetuity payment

PV = Periodic payment/Rate of return = $ 125,000/0.14

= $ 892,857.14285714 or $ 892,857.14

Option 3: Annuity payment

PV of annuity due = P + P [1 - (1+r) ^-(n-1)/r)

P = Periodic payment = $ 185,000

r = Rate of return = 0.14

n = Number of periods = 10

PV = $ 185,000 + $ 185,000 x [1 – (1+0.14) ^-(10-1)/0.14]   

    = $ 185,000 + $ 185,000 x [1 – (1.14) ^{- 9}/0.14]   

   = $ 185,000 + $ 185,000 x [(1 – 0.307507942851544)/0.14]   

    = $ 185,000 + $ 185,000 x (0.692492057148456/0.14)

    = $ 185,000 + $ 185,000 x 4.94637183677468

    = $ 185,000 + $ 915,078.789803317

= $ 1,100,078.789803317 or $ 1,100,078.79

Ranking in descending order of present value:

Option	PV	Rank
1	$ 999,999	II
2	$ 892,857.14	III
3	$ 1,100,078.79	I

Option 3^rd, annuity due of 10 periods is preferable as it has highest present value.