# annuity problem

i got this on Shweser book 1 page 130 problem no.13 An investor will recieve an annuity of \$4,000 a year for ten years. The first payment is to be received five years from today . at 9% discount rate , this annuity’s worth today is closest to: A. \$16,684 B. \$18,186 C. \$25,671 D. 4,0000 i solved the first part to get a PV of a ten year annuity which resulted in PV of 5,670.63 , the problem with me that i dont understand why would i disoucnt it back as the answer states for 4 years , not 5 years ? since the payment will be recieved on year 5 , then what i thought about is to discount it back till t=0 which is five years ? , can anyone explain why sould i use 4 years not 5 ?

Begining of year 5 means end of year 4

but the problem didnt state begining or ending ? , i still cant figure it out

here’s what i would do. solve for the PV of an annuity DUE… beg period CF’s n = 10 i = 9 pmt = 4,000 pv = x then take the PV number and discount if for 5 years n = 5 i = 9 pmt = 0 FV = x PV = z z should be your answer OR treat it as a capital budgeting problem and find the NPV

nutshell Wrote: ------------------------------------------------------- > but the problem didnt state begining or ending ? , > i still cant figure it out 5 years from today…it means begining

ic , thanks alot guys

Nutshell, I understand your confusion about how many periods elapse from for the second part of the problem. As a few people pointed out the end of period 4 is the same as the start of period 5. If you look at a timeline this may be easier to see: End/Begin {…[…[…[…[…[ 0 1 2 3 4 5 Don’t know if the timeline will post the way I typed it. Anyway, I try and remember that an annuity payment (unless it is annunity due) always comes at the end of the period -which is the same as the begining of the next period. In this case a payment at beginning of period 5 would require the annunity to started at the begining of period 4. Also, I check my answer by clearing the TVM data and putting the PV I think is right, the interest rate and period to see if the FV matches what the first part of the problem requires. If not, i can change the period to see if that makes the problem fit the value I found in the first part of the problem. Not a prefered method, but it helps me keep on track. Good luck - please add any comments or corrections.

los_cfa08 , ur clarification helped me alot , thanks for dropping by

The other way to solve this would be to calculate the annuity as an annuity due, then discount it bac 5 years. Gives the same answer, reflects the way the question was asked a little more accurately.

as a tip, i’d recommend to ALWAYS draw out a timeline… you make less errors this way, plus it helps you understand the more complicated questions

I think this question is kinda ambiguous… For me I’d also have discounted it by 5 years and getting A as the asnwer! I don’t see how 5 yrs from today=beginning. Seriously.

I asked this very same question 2 weeks ago on AF. Pity they didnt ask anything like it in the exam!

Yeah. Nothing near this. But I do remember having an annuity question in the PM session for 2121.

Don’t quite understand why 5 years from today = BEG. If it said 1 year from today you need to discount it back 1 period right? 2 years from today, discount back 2 periods. So on. It’s nasty little tricks like this that can mean the difference between pass/fail, even if you know your material they can still f*rk you up on the day.

After you find out the present value of the annuity which comes out to be around \$25670, you need to discount it. Either you can discount it with 9% for 5 years using the begining method or for four yeas using the end method. i’d suggest you do a simple calculation: 25670* (1/1.09)^4 = 18185

ptan54 Wrote: ------------------------------------------------------- > Don’t quite understand why 5 years from today = > BEG. > > If it said 1 year from today you need to discount > it back 1 period right? > > 2 years from today, discount back 2 periods. So > on. > > It’s nasty little tricks like this that can mean > the difference between pass/fail, even if you know > your material they can still f*rk you up on the > day. Absolutely agreed. There is no indication as to whether it is the beginning or the end of the period. What I was thinking was, say this is the end of 2007. 5 years on it’ll be the end of 2012…Seriously…the question really isn’t clear. 5 years from today does not really tell you anything.

hey hydrogen again ! If its mentioned that its 5 years from today then it means that its begining of the year . imagine. todays 1st jan 2007 and u get the first payment on 1st jan 2012. you will obviously discount it for 4 years (or take it as begining) because you’ll be discounting only for 2008, 2009, 2010, 2011.

the question is very straight forward… you just have to remember what the cash flows of an ordinary annuity look like, compared to an annuity due… ordinary annuity - first cash flow is at the END of the first period annuity due - first cash flow is at the BEGINNING of the first period (ie. today) first payment is received 5 years from today, so the timeline is: 4k 4k … |____|____|____|____|____|____|____… Po Pd now, Po is the price of an ordinary annuity… Pd is the price of an annuity due… SO, if you find the price of Po, you can see from the timeline that it must be discounted back for 4 years… BUT if you find the price of Pd, it must be discounted back 5 years…

^oops, that looks terrible… hopefully this is better: …4k… 4k …etc |____|____|____|____|____|____|____… …Po… Pd

Hmmm. This seems totally off from whatt I have been learning throughout in Finance and my Financial Math class, which specify clearly whether it is an annuity due or an annuity immediate, though not outright, but it is very obvious. Bleah. Oh well. But my take on this is 5 yrs from today, today can either be at the end of the year or at the beginning of the year. Bluey I get the diagram. But the problem here is whether it is an annuity due or an annuity immediate.