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.
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 3,000,000
time 20
rate 0.04
[tex]3000000 \times \frac{1-(1+0.04)^{-20} }{0.04} = PV\\[/tex]
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:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 5,000,000
time 20
PV $60,000,000.0000
[tex]5000000 \times \frac{1-(1+r)^{-20} }{r} = PV\\[/tex]
rate = 0.05450114 = 5.45%
notice: that with this rate if we apply the tax rate we got the same rate:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 3,000,000
time 20
PV $36,000,000.0000
[tex]5000000 \times \frac{1-(1+r)^{-20} }{r} = PV\\[/tex]
rate = 0.05450114 = 5.45%
