Question

You just won the lottery! You can elect to receive your prize in one of four ways: a) $1,000,000 now b) $1,400,000 at the end of five years e) $75,000 per year in perpetuity, with payments made at the end of each year (so your first payment comes one year from today) d) $150,000 per year for the next ten years, with payments made at the end of each year (so your first payment comes one year from today) Suppose the annual interest rate is 5% with certainty and in perpetuity. Calculate the present value of each of the four payment options (i.e., in today's dollars). Rank for four options from most to least valuable.

Answer 1

Receiving Options

a) $1,000,000 NOW. So PW will be remains same.

b) $1,400,000 at the end of 5 years. Interest = 5%

PW = $1,400,000 (1 + 0.05) ^{– 5} = $1,096,936.6

c) $75,000 per year in perpetuity (n=infinity)

PW = A/interest

PW = $75,000/0.05 = $1,500,000

d) $150,000 per year for 10 years

PW = $150,000 (P/A, 5%, 10)

PW = $150,000 (7.72173) = $1,158,259.5

Ranking from most to least

c) PW = $1,500,000

d) PW = $1,158,259.5

b) PW = $1,096,936.6

a) PW = $1,000,000