Question

has government attempted to manage this relationship? 15 2. You win a lottery and are offered a one time lump sum payment of $650,000 (NOW) or five (5) payments of $200,000 - one per year. What is the lottery payment plan implied rate of time preference (approximation is ok)? If you decide to take the lump sum, is your time higher or lower than the lottery payment plan's time preference? How would your expectations of future inflation/deflation effect your decision on choosing lump sum versus annuity? Show the table of your annuity payment calculations.

need help

Answer 1

The lottery has value of $650000 lump sum payment or $200000 per year for 5 years.

a) We will find the interest rate which will equate the values of these two cash flows.
=RATE(5,200000,-650000)
= 0.1632 or 16.32%

b) The option of lump sum is preferred when time period is longer because the discounting of the cash flow will yield lower amount as a present worth of that cash flow.

c) An inflation has a net effect of decreasing the value of money. A higher rate of inflation will decrease the future value of cash flow and they will be worth less. If the inflation rate is higher then lump sum option is more beneficial.
Deflation is the opposite of the inflation and in that case annuity payment will be more preferable.

d) Annuity payments needs to be discounted to get the present worth of the cash flow.
PW = Cash Flow / (1+Discount Rate) ^ Duration

If the rate is 15%
200000 / (1.15 ^ 1) = 173913.04
200000 / (1.15 ^ 2) = 151228.73

We can create a table here

Year	Cash Flow	PW @ 10%	PW @ 15%	PW @ 20%
1	200000	181818.18	173913.04	166666.67
2	200000	165289.26	151228.73	138888.89
3	200000	150262.96	131503.25	115740.74
4	200000	136602.69	114350.65	96450.62
5	200000	124184.26	99435.35	80375.51
NPW		758157.35	670431.02	598122.43

We can observe that NPW is higher than lump sum amount if we assume 10% discount rate but it will be lower if the discounting rate is 20%.