Question

You have won the NY State Lottery. The prize is $100,000,000, which is determined by 20 annual payments of $5,000,000. You can either accept the 20 annual payments of $5,000,000 or take an upfront, pre tax payment of $60,000,000. Either decision entails paying taxes of 40% when you receive the money and we assume that the tax rate will not change in the future. What would you do and why? On an after tax basis in today’s dollars, how much richer are you now?Answers must include an analysis using PV and IRR. RISK ASSESSMENT - appropriate discount rates US Government 2% NY State/City 4% Venezuela15% Restaurants30% You can collaborate but you must individually write and submit your own analysis.

Answer 1

Answer:

The annual payment have a better present value. It is $40,770,979 to $36,000,000.

After tax-basis we are $40,770,979 more richier

IRR for the prize 5.45%

Explanation:

we will use the NY state discount rate:

60,000,000 x (1- 40%) = 36,000,000 after-tax

second option:

5,000,000 x (1-40%) = 3,000,000 after-tax

we calculate the present value of a 20 year annuity for 5,000,000 dollars with a 4% discount rate.

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 3,000,000

time 20

rate 0.04

$3000000 \times \frac{1-(1+0.04)^{-20} }{0.04} = PV$

PV $40,770,979.0349

As this option is better than the upfront payment, it is better to take the annual payment.

We can determinate the real rate of return

We consider 60,000,000 upfront against 20 payment of 5,000,000 the rate will be calcualte with goal seek excel tool or trial and error manually:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 5,000,000

time 20

PV $60,000,000.0000

$5000000 \times \frac{1-(1+r)^{-20} }{r} = PV$

rate = 0.05450114 = 5.45%

notice: that with this rate if we apply the tax rate we got the same rate:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 3,000,000

time 20

PV $36,000,000.0000

$5000000 \times \frac{1-(1+r)^{-20} }{r} = PV$

rate = 0.05450114 = 5.45%