Question

You have just won the lottery. You will receive $2,000,000 today and then receive 40 payments of $750,000. These payments will start one year from now and will be paid every six months. A representative from TheExpert Investment has offered to purchase all the payments from you for $17 million. The appropriate discount rate is 9 percent APR compounded daily. Assume there are 12 months in a year, each with 30 days.

a)What is the effective six month rate? Show your work.

b)What is the PV of the lottery

c)Should you take the offer?

Answer 1

Part (a)

Total number of days in a year = N = 30 days x 12 months = 360

If R is 9 percent APR compounded daily and r is the effective 6 month rate then,

(1 + r)2 = (1 + R/N)N = (1 + 9% / 360)360

Hence, the effective 6 month rate, r = [(1 + 9% / 360)360]1/2 - 1 = (1 + 9%/360)180 - 1 = 4.6022%

Part (b)

PV of n = 40 number of annuities, A = 750,000 at the end of 6 months from now (so that the first annuity is still 6 months = 1 period away) = PVA = A/r x [1 - (1 + r)-n] = 750,000 / 4.6022% x [1 - (1 + 4.6022%)-40] = $13,602,152.32

Hence, PV of the lottery = C0 + PV of PVA = C0 + PVA / (1 + r) = 2,000,000 + 13,602,152.32 / (1 + 4.6022%) = $15,003,696.50 = $15,003,696 (if you need to round it off to the nearest dollar)

Part (c)

Offered price = $ 17 million > PV of the lottery.

Hence, you should take the offer.