Question

You have won the lottery. You will receive $2,590,000 today, and then receive 40 payments of $1,295,000 These payments will start one year from now and will be paid every six months. A representative from Greenleaf Investments has offered to purchase all the payments from you for $25 million. The appropriate discount rate is an APR of 9 percent compounded daily. Assume there are 12 months in a year, each with 30 days.

  

What is the present value of the cash flows from your lottery winnings? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Answer 1

Discount rate per period = r = 6 monthly discount rate = (1 + 9% / 360)¹⁸⁰ - 1 = 4.60%

Hence, first annuity, A = 1,295,000; n = 40

Hence, PV of all the annuities 6 months from now = A / r x [1 - (1 + r)^-n] = 1,295,000 / 4.60% x [1 - (1 + 4.60%)^-40] =  23,486,383.00

Hence, the present value of the cash flows from your lottery winnings = PV today = 2,590,000 + PV of  23,486,383.00 = 2,590,000 + 23,486,383.00 x (1 + 4.60%)^-1 = $  25,043,049.29