Value of an annuity versus a single amount Personal Finance Problem Assume that
ID: 1172440 • 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 efther in the form of $34,000 at the end of each of the next 25 years (that is, $850,000 over 25 years) or as a single amount of $545,000 paid immediately atf you exped to be able to t. Would your decision in part a change if you could earn g% rather than 7% on your nvestments over he next 25 years? why? eam 7% arnuary on your investments over the next 25 years ignoring taxes and other considerations, which a ternative should you take? why? c. On a strictly economic basis, at approximately what earnings rate would you be indifferent between the two plans? a. To decide which alternative to take, you need to compare the values of these aternatives. Athough 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 fows A way to make a meaningful comparison of the two afternatives is to compare ther present values If you take the prize as an annuity, the present value of the 25-year ordinary annuity isRound to the nearest cent) if you take the prize as a single amount, the present value of the Aump sum is (Round to the nearest doar Which aternative should be chosen? (Select the best answer below) Lump sum because the present value is greater Annual payments, because the present value is greater OExplanation / Answer
a)let us find the present value in both cases and whichever is higher we need to choose it
34000 for next 25 years
use pv formuale in excel:pv(rate,nper,pmt,fv,type)
=pv(7%,25,34000,0)=396221.83
other option is to receive 545000 now
we should take amount 545000 now since this is higher than other option
25 year annuity it is 396221.83
lump sum it is 545000
choose lump sum because the present value is gretaer
b)=pv(9%,25,34000,0)=333967.71
25 year annuity it is 333967.71
lump sum it is 545000
choose lump sum because the present value is gretaer
c)use rate formuale in excel
=rate(nper,pmt,pv,fv,type)
=rate(25,-340000,545000,0,0)
=3.76%
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