For winners of the California SuperLotto Plus the choice is between a lump sum a

Question

For winners of the California SuperLotto Plus the choice is between a lump sum and annual pay- ments that increase from 2.5% for the first year, to 2.7% for the second year, and then increasing by .1% per year to 5.1% for the 26th payment. The lump sum is equal to the net proceeds of bonds pur- chased to fund the 26 payments. This is estimated at 45% to 55% of the lump sum amount. At what interest rate is the present worth of the two pay- ment plans equivalent if the lump sum is 45%? If it is 55%?

Explanation / Answer

Year Option 1 Option 2 0 -45% -55% 1 2.50% 2.50% 2 2.70% 2.70% 3 2.80% 2.80% 4 2.90% 2.90% 5 3.00% 3.00% 6 3.10% 3.10% 7 3.20% 3.20% 8 3.30% 3.30% 9 3.40% 3.40% 10 3.50% 3.50% 11 3.60% 3.60% 12 3.70% 3.70% 13 3.80% 3.80% 14 3.90% 3.90% 15 4.00% 4.00% 16 4.10% 4.10% 17 4.20% 4.20% 18 4.30% 4.30% 19 4.40% 4.40% 20 4.50% 4.50% 21 4.60% 4.60% 22 4.70% 4.70% 23 4.80% 4.80% 24 4.90% 4.90% 25 5.00% 5.00% 26 5.10% 5.10% Ans 6.17% 4.43% IRR(B1:B27) IRR(C1:C27) Note: as per the requirement there is two options available lumpsum or installments and we have to determine the rate which will equate lumpsum payment and installment payment discounted at that rate, and that rate can only be determined by IRR Calculation under which both option would have equal value.

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