Question

Value of an annuity versus a single amount 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.

PLEASE SHOW ALL WORK OR EXCEL FUNCTIONS
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

a)

Rate=	5%
Time(n)	25
Amount received annually	40000
PV of the anuity using excel	563757.78	PV(5%,25,40000)

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

b)

Rate=	7%
Time(n)	25
Amount received annually	40000
PV of the anuity using excel	466143.33	PV(7%,25,40000)

Yes the decision would chnage for rate = 7% beacuse PV = 466143.33 which is less than the lump sum of 500,000

c)

Rate using Rate function of excel

6.24%

Rate(25,40000,-500000)

Rate at which he would be indifferent = 6.24%

answered by: anonymous