Marge Simons won a $15 million lottery and elected to receive her winnings in 30
ID: 2464486 • Letter: M
Question
Marge Simons won a $15 million lottery and elected to receive her winnings in 30 equal installments. After receiving the first 10 installments, Marge and her husband divorced, and the remaining 20 payments became part of the property settlement. The judge who presided over the divorce proceedings awarded one-half interest in the future lottery payments to Marge and the other half to her ex-husband.
Following the divorce, Marge decided to sell her interest in the 20 remaining lottery payments to raise the cash needed to open a flower store. An investor has offered Marge $2,128,400.
Required
What discount rate did the investor use in calculating the purchase price?
If Marge can invest the money she gets at 8%, which is the better option, keeping the annuity or accepting the investor's offer? Why?
What needs might Marge have that would make the investor's offer the preferable option, no matter what the interest rate (within reason)?
(a)What discount rate did the investor use in calculating the purchase price?
Explanation / Answer
(a) The annuity payments are 15000000/30 = $500,000. 50% of it $250,000 is each ones share.
The PV of the annuity is what is offered by the investor.
Hence, 2128400 = 250,000*PVIFA(i,20)
8.5136 = PVIFA(i,20)
From the interest factor tables for ordinary annuity, the factor of 8.5136 is for 10%.
Hence, the rate used by the investor to calculate the purchase price = 10%.
(b) The PV of the annuity at 8% = 250000*9.8181 = $24,54,525.
Since the PV of the annuity at 8% is greater than the money offered by the investor, the annuity is preferable.
(c) Marge's need for cash to open the flower store would make the investor's offer the preferable option.