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In: Finance

Group 1: You won $5,000,000 in the Massachusetts Lottery's Halloween Bonanza game. It pays out 10...

Group 1: You won $5,000,000 in the Massachusetts Lottery's Halloween Bonanza game. It pays out 10 years from now. How much is it worth today?

Group 2: You won a similar prize, but it pays out $500,0000/yr for the next 10 years.

Group 3: You won a prize that pays out $600,000/yr for the next 15 years.

Groups, what is your prize worth today assuming a 2% interest rate? Which prize would you rather receive assuming it is taxable at a 55% tax rate? Please explain your answer with all calculations.

Expert Solution

Group 1

Present value factor of 10 years at 2% = 1/(1+r)^10 = 1/(1.02)^10 = 0.820348299875155

After tax price received = 5,000,000 * (1-tax rate) = 5,000,000 * (1-55%) = 2250000

Present value of winning = After tax winning * present value factor = 2250000 * 0.820348299875155 = 1845783.67

Group 2

Accumulated present value factor for 10 years = (1- (1+r)^^-n)/r

= (1-(1.02^-10))/.02 = 8.98258500624223

After tax annuity for 10 years = 2250000

Prsent value of annuity = 2250000 * 8.98258500624223 = 20210816.26

Group 3

Annuity present value factor for 15 years = (1-(1.02^-15))/.02 = 12.849263500574

Annuity = 600000

After tax annuity = 600000 * (1-55%) = 270000

Present value of annuity = 270000 * 12.849263500574 = 3469301.15

Summary : present value of prices

Group 1 = 1845783.67

Group 2 = 20210816.26

Group 3 = 3469301.15

From the above present values I would rather have second price.

Note : group 2 price pays $500,0000/yr for the next 10 years, which is very evidently more than other 2, it could have been an confusion, please check if it is actually $500,0000/yr for the next 10 years or $500,000/yr for the next 10 years.

jeff jeffy answered 1 month ago

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