Thomas is considering the purchase of two different annuities. The first begins
ID: 2617386 • Letter: T
Question
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 S2,500 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 S5 ,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? 17. Jennifer is trying to save $2,500 for a trip to Hawaii. She plans to invest S100 each month in a fund that earns 6.5% per year. How long will she have to save before she can afford to go to Hawaii? 18.Explanation / Answer
(17) Before proceeding to solve and analyze Thomas' situation one must recognize that the discount rate for the annuities is 4 % per annum up to the end of Year 9 and increases to 9 % per annum beginning from the end of Year 10.
Annuity 1: Thomas pays $ 5000 to buy the annuity which pays $ 1000 beginning from the end of year 3 and continues for 5 years.
PV of Annuity at end of Year 2 = 1000 x (1/0.04) x [1-{1/(1.04)^(5)}] = $ 4451.82
PV of Annuity at present = 4451.82 / (1.04)^(2) = $ 4115.96
Net Value = 4115.96 - 5000 = - $ 884.04
Annuity 2: Thomas pays $ 5000 today to purchase the annuity which pays him $ 2500 beginning from the end of Year 10 and goes on for 7 years. The discount rate in this case is partially 9 % as his discount rate increases to 9 % after the end of Year 9.
PV of Annuity at the end of Year 9 = 2500 x (1/0.09) x [1-{1/(1.09)^(7)}] = $ 12582.38
PV of Annuity at present = 12582.38 / (1.04)^(9) = $ 8840.21 (note that the discount rate becomes 4 % for year 9 and before)
Net Value = 8840.21 - 5000 = $ 3840.21
Hence, the annuity 2 is better for Thomas as the same provides him with a positive net value.
NOTE: Please raise a separate query for the solution to the second unrelated question.
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