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A fifteen year annuity of $300 starting at T3. Interest rate 6%. Find a present value.
I have taken approach explained by Mr.Moffat in chapter7, example 5:
Year
1-18 18 y.annuity AF=(1-1.06^(-18))/0.06=10.828
1-3 3 y. annuity AF=(1-1.06^(-3))/0.06=2.673
4-18 PV= $300x (10.828-2.673)= 2446.5In Kaplan book they have different approach & the answer completely different
300 x 9.712 ( AF for 15 years @ 6%)= 2913.6
PV = 2913.6 x 0.890 (PF 2 years @ 6%)= 2593.1I am really confused. The approach in Kaplan does not make a sense for me. Why do they take 15 years annuity when the cashflow is coming up untill 18 years. Why do they time it with a present value table?
Which approach should I use in exam? Can I use the first approach? It make more sense for me & no confusion with years. I am only concerned that my answers are different…maybe I do something wrong?
Thank you very much for your help!There are two different ways of getting the same answer.
However you have made a mistake!
If the first receipt is at time 3, and there are 15 receipts, then the last receipt is at time 17.
So……you need to calculate the annuity factor for 17 years (this would be the total for time 1 to 17). The you need to subtract the annuity factor for 2 years (the total for time 1 and time 2).
If you subtract the second figure from the first then you will be left with the total from 3 to 17.The only problem with doing that in this question is that it does mean that you have to calculate the 17 year annuity factor using the formula, because the tables only go to 15 years.
So….the other way of doing it is to take the 15 year annuity factor (from the tables) because there are 15 years. However just multiplying by the annuity factor would only give the present value if the first receipt was in 1 years time. In fact the first receipt is in 3 years time (which is 2 years later – 3 years instead of in 1 year).
So you then multiply by the ordinary discount factor for 2 years because it starts 2 years later.Both ways will give the same answer. If you repeat the way you were doing it, but using 17 years less 2 years, then you will get the same answer at Kaplan (maybe a very tiny bit different because of roundings – but roundings do not lose marks in the exam).
So……you can do it whichever way you find more sensible. They both give the same answer.
Mr. Moffat,
Your answer was comprehensive & clear. I understood what was wrong, I was counting 18 years because I thought I have to count T0 as well… Hope I will not confuse with “years” in the middle of the exam :).
Thank you very much!Thanks – I was having exactly the same problem and your explanation not only really helped me, but I think that your way makes more sense to me.
Thanks
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