Answer to Question #287103 in Finance for Antara

Question

Assume that you just won the state lottery. Your prize can be taken either in the form

of $40,000 at the end of each of the next 25 years (that is, $1,000,000 over 25 years)

or as a single amount of $500,000 paid immediately.

a) If you expect to be able to earn 5% annually on your investments over the next

25 years, ignoring taxes and other considerations, which alternative should

you take? Why?

b) Would your decision in part a) change if you could earn 7% rather than 5% on

your investments over the next 25 years? Why?

c) On a strictly economic basis, at approximately what earnings rate would you

be indifferent between the two plans?

Answer 1

Solution:

a)

A prize of 40,000 should be taken per month rather than the lump sum of 500,000 because the PV of prize money is 563757.78 which is higher than the lump sum amount of 500,000.

PVA25 = ($\frac{40,000}{0.05}$) × [1 - (1 + .05)-25 ]

PVA25 = $800,000 × .704697

PVA25 = $563,758

b) Now Interest

Rate = 7%

Stream 1:

Annual Prize Money = $40000

Period = 2 Years = 25 months

Present Value of Annuity = $40000*[1-$\frac{\frac{1}{(1+0.07)^{25}}}{0.07}$ = $466143.33

Stream 2: Single amount of $500,000 paid immediately. Stream 2 amount is more than the stream 1 amount. So, it is viable to take a single amount in this case.