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Thomas is considering the purchase of two different annuities. The first begins in three years and...

Thomas is considering the purchase of two different annuities. The first begins in three years and pays $1,000 per year for five years. The second begins in 10 years and pays $2,500 per year for seven years. Thomas is currently very risk-averse as he has a young family and little income, and thus his current opportunity cost of capital is 4%. In nine years, Thomas expects to be more financially secure and his cost of capital will increase to 9% from then on. If each annuity costs $5,000 today, which annuity (or annuities), if any, should Thomas purchase? How much value will Thomas realize from his purchase(s), if he makes any purchases? Show work

Answer: He should purchase the second annuity; he will realize $3,840.21 in value

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Answer #1
Annuity-1
Year 0 1 2 3 4 5 6 7 8
Payment 1000 1000 1000 1000 1000
Rate 0.04 $4,451.82
Cost of annuity 5,000.00
NPV -1,042.35 Using NPV to find present value of annuity at year 3 using 4% rate, and discounting back the PV at year 3 to today at 4% rate
Annuity-2
Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Payment 2500 2500 2500 2500 2500 2500 2500
Rate 9% 12,582.38
Cost of annuity 5,000.00
NPV 3,840.21 Using NPV to find present value of annuity at year 9 using 9% rate, and discounting back the PV at year 9 to today at 4% rate
So he should go for Annuity 2 as NPV is positive with value 3840.21
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