February 26th, 2007MidtermThe Wharton SchoolJeffrey JaffeCorporate Finance (100)Spring, 20071.Net Present ValueThomas James, who just won the Pennsylvania lottery, has hired you as his financial advisor.Tom can take the lottery payout in two ways, a) as a 50 million ($50m) lump sum payment, or b) as anannuity of 30 payments of $5m per payment, with the first payment today and subsequent paymentsat annual intervals.Tom needs to plan for his and his family’s future. Tom tells you he wants to spend $1m per year everyyear for the next 25 years, with the first payment today and the last payment 24 years from today.After that, he expects to spend twelve $2m payments at two-year intervals, with the first payment 25years from today and the last payment 47 years from today.Once these expenses are accounted for, Tom will invest any remaining money in a trust fund for hisyounger brother Bob, which his younger brother will receive on his 21st birthday ten years from today.Tom pays tax at a rate of 40% on all payments he receives. Tom can borrow or lend at a nominal rateof 12%. Assume all cash flows are to be discounted at an annual rate of 12%. Do not tax-adjust thisdiscount rate. All numbers are nominal.Give all your answers to 3 decimal places.(a) What is the present value of his winning ticket after tax for each of the two payment options?Should he take the lump sum or the annuity?(b) What is the present value of Tom’s planned future expenditures?