Cash payment before tax=181,500,000(.5)=90,750,000
With total tax rate of .28+.042=.322,
Cash payment after tax=90,750,000-90,750,000(.322)=61,528,500
Find the present value of the annuity payment and compare it with 61,528,500.
Annual payment before tax=181,500,000/26=6,980,769.23
Annual payment after tax=6,980,769.23-6,980,769.23(.322)=4,732,961.54
So, find the present value of the annuity which has 26 payments of 4,732,961.54 at 5% interest:
So the annuity option is better since it has a higher present value than the cash payment.
In terms of after tax present value, each cash prize is worth 61,528,500, and two prizes are worth 2(61,528,500)=123,057,000. So, 363,000,000 is for sure an exaggeration.
He should find investment opportunities that yield higher than 5% rate of return. The present value of the annuity calculated in question 1 is based on a discount rate of 5%. However, if Larry invests the annual cash flows at higher than 5% rate, his net present value will be higher than 68,037,199.16.
Because they assume they can make a higher rate of return than 5%, and also there is no liquidity risk (no one knows what will happen in the next 26 years).
With the same net present value, to make the annuity option more attractive, they may increase the annual payments and reduce the number of years.