Question

You win a scratch off lottery ticket that promises to pay an initial payment of 10,000 next year and grow at a rate of 2% forever. If the discount rate is 5%, what is the present value of the lottery ticket?

Answer 1

Answer:

$PW=\frac{10,000}{0.05-0.02}\\ PW=\ 333,333.333$

Present value of lottery= $333,333.333

Explanation:

Given Data:

Initial Payment=$10,000

Rate at which payment grow=2%=0.02

Discount Rate=5%=0.05

Required:

Present value of lottery=?

Solution:

$PW=\frac{Initial\ Payment}{r-g}$

where:

r is the discount rate

g is the growth rate

$PW=\frac{10,000}{0.05-0.02}\\ PW=\ 333,333.333$

Present value of lottery= $333,333.333