 # PV of uneven CF

There are cash flows of \$100 in year 1, \$200 in year 2, \$300 in year 3, and an assumed interest rate of 10%. Calculate the present value of these uneven CF? My answer: 2nd reset enter 1N 10 I/Y 2nd K = 100 +/- FV CPT PV STO 1 2N 200+/- FV CPT PV STO + 1 3N 300 +/- FV CPT PV STO + 1 RCL 1 Result: 481.59 Are there another more quickly and less confusing way of calculating the above kind of exercise? Pls show me some better solution? Your comments are appreciated.

It would be easier with a BAII Plus (simple or professional): CF0=1 CF1=100, F1=1 CF2=200, F2=1 CF3=300, F3=1, Hit NPV, insert I=10, that would give you NPV=481.5928

dude, learn how to use your calculator , w/o it you will have read hard time in the exam

level1_dec Wrote: ------------------------------------------------------- > dude, learn how to use your calculator , w/o it > you will have read hard time in the exam Sure, bad delivery, but i couldnt agree more. Learning the calculator is the easiest way to knockout some easy, to mildly difficult questions in a time where every second counts. I didint even memorize the depreciation or bond calculation equations because i could simply punch those numbers in. If you have a BA2 Plus these are some of the keys youre going to want to learn how to use: CF, NPV,IRR,TVM keys,DATA,STAT,BOND,DEPR and ICONV. Everything else should be pretty simple. I think a key that i used to overlook alot was the STO (store) and RCL (recall) keys. Being able to keep adding on without having to keep rewriting everything was so key sometimes.

Thank you very much for your comments. I am trying to use button on calculator and getting some problems with it. Sorry for trouble you with one more exercise on PV of annuity as following: A 10-year annuity pays 900 usd per year, with payments made at the end of each year. The first 900 usd will be paid 5 years from now. If the APR is 8% and interest is compounded quarterly, what is the PV of annuity? I don’t know how to solve monthly PMT while the exercise gives annually PMT of 900 usd. Pls help! Thanks alot!

EAR = (1+.08/4)^4-1 = 8.2432% = i/y pmt = -900 fv = 0 n = 10 cpt pv = 5973.38 Discount this back 5 years: 5973.38/(1.082432)^5 = 4019.91 And yes, I agree with the others when I say you should learn your calculator. Spend a night and go through the calculator book and keep it with you until you are comfortable doing anything the cfa exam requires.

EAR = (1+.08/4)^4-1 = 8.2432 pmt = 900 n =10 FV = 13187 now calculate PV based on this FV… with n =14 PV = 4020

I understand the calculations, but why do you need to use the effective annual interest rate in the second question?

mburfien Wrote: ------------------------------------------------------- > I understand the calculations, but why do you need > to use the effective annual interest rate in the > second question? The interest given is the annual rate but since it is compounded quarterly and the payments are annual you need to use the EAR to keep the time periods consistent.

because it’s the effective annual interest rate. it’s the actual interest you’d be earning with quarterly compounding for one year. you’re not earning 8%. you’re earning 2% for the first quarter, then the 2nd quarter you earn another 2% + the interest on the interest you earned in the 1st quarter. if it was annual compounding, you’d use 8%, but since it’s quarterly, you get more interest.

Thu Thuy Wrote: ------------------------------------------------------- > A 10-year annuity pays 900 usd per year, with > payments made at the end of each year. The first > 900 usd will be paid 5 years from now. If the APR > is 8% and interest is compounded quarterly, what > is the PV of annuity? A simple approach that i like to take with these problems is to visualize a timeline. Of course, now i dont have to draw it out anymore and could see the line in my head but this procedure should help: So lets dissect the problem piece by piece. We have a 10 year annuity, and payments are made at the end of each year. but this will start in 5 years. so its really a 15 year time line total. This is a two part problem. 1st part. In 5 years we need to know the PV of this annuity. so to accomplish this you simply: [2nd clear tvm] N=10 (10 payments, always payments) [2nd][I/Y] —> set P/Y to 1 (meaning one payment per year) and set C/Y to 4 (meaning this thing compounds 4 times a year) with this you can ignore any conversions thus: I/Y: 8.0% PMT: -900 (meaning its a cash inflow to you, this will make PV positive, not that important) FV=0 [CPT]PV-> 5973.380 Topher and i already have the same answer. but ill explain the rest right now. In 5 years this annuity is worth 5973.380. But you want to know the value THIS year. 2nd part. FV= -5973.380 PMT=0 N=5 I/Y= stays at 8% if the 2nd functions are C/Y=4 and PMT= 1 CPT PV= 4019.914

Quick explanation of the rate used, and what the calculator thinks and knows. I didint bother having to convert the APR into EAR because the calculator does this for me. Now its important to understand which rate youre getting, but if they give you an annualized rate, you can just plug it into the I/Y as long as you let the calculator know how many payments will be made per year and how many times its compounded. This makes mortgage problems sooo much easier. 12 pmts, compounds 12 times. but for a 30 year mortgage N is still 360 pmts. Know that feature in your calculator. But also know THIS feature. [2nd][ICONV] In this problem Topher converted his apr to an ear, thats cool, know that formula yes, but he couldve also simply: [2nd][ICONV] NOM=8 C/Y=4 CPT EFF= 8.243 (you can also get APRs from EARs in this fashion as well)

Sorry to dig up an old(ish) thread but I wanted to point out that if you use EMRA32’s method (which is awesome - I didn’t know about the C/Y function) make sure you change C/Y back to 1 before you forget. It DOES NOT resest when you hit CLR TVM or CLR WORK…similar to remembering to put the calc back in END mode after calcing an annuity due.

KrukVT Wrote: ------------------------------------------------------- > Sorry to dig up an old(ish) thread but I wanted to > point out that if you use EMRA32’s method (which > is awesome - I didn’t know about the C/Y function) > make sure you change C/Y back to 1 before you > forget. It DOES NOT resest when you hit CLR TVM > or CLR WORK…similar to remembering to put the > calc back in END mode after calcing an annuity > due. Heh, anything that brings attention to my greatness im okay with. However, KrukVT is right… i almost botched a simple bond calculation on test day because i forgot to change P/Y to 2 and C/Y to 2 as well. Luckily the answer i kept getting wasnt even one of the available choices so it was clearly something with me. I fixed it tho 5 seconds before end time.

As an alternate method (once you’ve calculated the EAR), you could use the cash flow register - CF 1 is 0 with a frequency of 4 (the first 4 years have a \$0 CF), and CF2 is \$900 with a frequency of 10. Then calculate NPV. In problems like this, ALWAYS draw a time line. first - it helps.

topher Wrote: ------------------------------------------------------- > EAR = (1+.08/4)^4-1 = 8.2432% = i/y > > pmt = -900 > fv = 0 > n = 10 > > cpt pv = 5973.38 > > Discount this back 5 years: > > 5973.38/(1.082432)^5 = 4019.91 > Should the second part be discounted back 4 years since the first part is the PV of an ordinary annuity ?

i think gugu is right…i was also getting confused…since the first cash flow of 900 is available 5 years from now…the PV of 5973.38 will be for the beginning of the 4th year (unless beg is used in BA2 plus which gives 6465.78)…once you discount 5973.38 for 4 years you will get 4351.28 ( same if you discount 6565.78)…i think this might be the right approcah…anyone???

Sorry i was being lazy and didint feel like responding. To gugu and weirdo: im not researching it enough but im going to go ahead and say my original answer was rushed and that you guys are correct until proven guilty. Heres some evidence that supports your comments: On page 193 of Vol1 we have an exact problem to this one. The first part was right, however, the PV we obtained of that 10 year annuity was in the perspective of t=4, which means that we would need to discount it by 4 not 5. In the perspective of t=4 because a PV at t=5 of 5973.380 is an ordinary annuity problem at t=4 with the payment of 5973 happening at year 5. I will go ahead and edit my previous post to avoid confusion. Good work boys.

Topher and i already have the same answer. but ill explain the rest right now. In 5 years this annuity is worth 5973.380. But you want to know the value THIS year. 2nd part. FV= -5973.380 PMT=0 N=4 I/Y= stays at 8% if the 2nd functions are C/Y=4 and PMT= 1 CPT PV= 4351.28 (took answer from weirdo, cant find my calc)