Is this correct? Why or why not? A local government is about to run...
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Is this correct? Why or why not?
A local government is about to run a lottery but does not want to be involved in the payoff if a winner picks an annuity payoff. The government contracts with a trust to pay the lump-sum payout to the trust and have the trust (probably a local bank) pay the annual payments. The first winner of the lottery chooses the annuity and will receive $150,000 a year for the next 25 years. The local government will give the trust $2,000,000 to pay for this annuity. What investment rate must the trust earn to break even on this arrangement?
Present Value = CF * [(1 - (1 + r) ^ -n) / r]
Where: CF is the cash flow per period ($150,000), r is the investment rate (unknown), n is the number of periods (25 years). r = [1 - (CF / Present Value)] ^ (-1/n) - 1
Given CF = $150,000 and the initial investment of $2,000,000, we can calculate the investment rate:
Present Value = $150,000 * [(1 - (1 + r) ^ -25) / r] $2,000,000 = $150,000 * [(1 - (1 + r) ^ -25) / r] r 0.0611
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