Value of an annuity versus a single amount Personal Finance Problem Assume that
ID: 2732827 • Letter: V
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Value of an annuity versus a single amount Personal Finance Problem Assume that you just won the state lottery. Your prize can be taken either in the form of $79,000 at the end of each of the next 30 years (that is, $2,370,000 over 30 years) or as a single amount of $979,000 paid immediately. If you expect to be able to earn 7% annually on your investments over the next 30 years, ignoring taxes and other considerations, which alternative should you take? Why? Would your decision in change if you could earn 9% rather than 7% on your investments over the next 30 years? Why? On a strictly economic basis, at approximately what earnings rate would you be indifferent between the two plans? To decide which alternative to take, you need to compare the values of these alternatives. Although the total nominal dollar amount of the annuity is much larger than the single payment, the former is not necessarily a better choice due to the different timing of cash flows. A way to make a meaningful comparison of the two alternatives is to compare their present values. If you take the prize as an annuity, the present value of the 30-year ordinary annuity is s. (Round to the nearest cent.) If you take the prize as a single amount, the present value of the lump sum is s. (Round to the nearest dollar.) Which alternative should be chosen? (Select the best answer below.) Lump sum, because the present value is greater. Annual payments, because the present value is greater. If you earned 9% rather than 7% on your investments, the present value of the 30-year ordinary annuity is s. (Round to the nearest cent.) Which alternative should be chosen? (Select the best answer below.) Annual payments, because the present value is greater. Lump sum, because the present value is greater. On a strictly economic basis, the rate at which you would be indifferent between the two plans is %. (Round to two decimal places.)Explanation / Answer
A PRESENT VALUE OF ANNUITY ANNUITY AMOUNT 79000 PERIOD 30 YEARS RATE 7% USING PRESENT VALUE FUNCTION WE CAN FIND OUT THE PRESENT VALUE $980,314.25 PRESENT VALUE OF ANNUITY 980314.25 VALUE OF LUMP SUM PAYMENT 979000 OPTION WITH 79000 ANNUITY WOULD BE PREFERRED DIFFERENCE IN VALUE AT LOWER RATE 1314.25 B PRESENT VALUE OF ANNUITY ANNUITY AMOUNT 79000 PERIOD 30 YEARS RATE 9% USING PRESENT VALUE FUNCTION WE CAN FIND OUT THE PRESENT VALUE $811,618.67 PRESENT VALUE OF ANNUITY 811618.67 VALUE OF LUMP SUM PAYMENT 979000 DIFFERENCE IN VALUE AT HIGHER RATE -167381.3 OPTION WITH LUMP SUM PAYMENT WOULD BE PREFERRED C- INDIFFERENCE RATE LOWER RATE + (DIFFERENCE IN VALUE AT LOWER RATE )/ (DIFFERENCE IN VALUE AT LOWERRATE - DIFFERENCE IN VALUE @HIGHER RATE)*DIFFERENCE IN RATES LOWER RATE (DIFFERENCE IN VALUE AT LOWER NPV / DIFFERENCE IN VALUE AT LOWER RATE - HIIGHER RATE DIFFERENCE IN VALUE DIFFERENCE IN RATES 7 0.007791 2 INDIFFERENCE RATE 7.015581321 PERCENT
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