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 Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance

 May 11th, 2011, 05:25 AM #1 Newbie   Joined: May 2011 Posts: 3 Thanks: 0 Present value Hi pals, I wonder the formula i use to calculate the present value can be applied in this way, originally formula is: NPV=CF/(1+i)^t CF=cashflow i= annual interest rate t= number of years. In term of year(s), straightly apply the formula with no doubts. However, i hav d question on calculating the present value in month(s) or day(s) basis. For example, A debtor amounting USD3,000 and the invoice dated 20 Mar 2009. Said, i wan to know the present value of the debts as at 31 December 2010 and 12 May 2011. the interest is 5% p.a., and the expected recovery date is 12 May 2011. So, here is how I tackle the formula,----------------------------------------------------------- 20 Mar 2009 till 31 December 2010 got the total of 651days. so as at 31 December 2010, the NPV=USD3,000/(1+(5%/365))^651=USD2744.06 and, 20 Mar 2009 till 12 May 2011 got the total of 783days. so upon the collection, the NPV=USD3,000/(1+(5%/365))^783=USD2694.89 ------------------------------------------------------------------------------------------------------- from the results which mean the longer I collect the debts, my money value would be decreasing instead of face value collected, rite? also am i correct in daily-lised the interest rate and power the days for applying the formula, as my friends argue with me the formula should be applied in this way,: NPV=USD3,000/(1+5%)^(651/365)=USD2749.97 NPV=USD3,000/(1+5%)^(783/365)=USD2701.89 pls comment any conceptual errors~~ May 11th, 2011, 11:10 PM #2 Senior Member   Joined: Apr 2011 From: USA Posts: 782 Thanks: 1 Re: Present value The equation you're using is for a present value, not a net present value. (NPV = net present value and means something different, though present values are involved.) So call it PV rather than NPV, because what you're doing here isn't a NPV and isn't related to it. That said, you're applying the equation in the wrong place. If the 3000 is on May 20, 2009 and you're finding the value in 2010 and 2011, then you're solving for a future value, not a present value. The 3000 is already the present value. This is the equation for future value: Where i = interest per compounding period and n = number of compounding periods. I see various letters used, though t usually stands for "time" and you need "periods," which aren't the same thing. You did this correctly when you plugged in, but you stated it incorrectly. (Might want to watch that since someone who doesn't know these equations would get confused.) The equation you've got is simply this equation, but solving for PV instead of FV (which can be done with a bit of algebra instead of twisting the equation all around). Mathematically what you did was correct. Your friend is wrong. In other words, the way you changed it to daily was done correctly. Since i actually stands for interest per compounding period, you would divide the annual amount by 365 days. And since n is the number of periods, then the exponent is the total number of days. However... you need to be solving for future value, not present value. Present is now, this is something that grows into a bigger future value. You're confused over your answers being smaller, because a present value would be smaller than future. But 2010 and 2011 are the future of 2009. Use the equation I have above and you should get it. But... do you want daily compounding? This would be a funny thing to compound daily. If you were using it just as an example of how to get daily, then that would be OK, but in reality, an invoice would not likely compound daily, but annually. May 16th, 2011, 06:58 AM #3 Newbie   Joined: May 2011 Posts: 3 Thanks: 0 Re: Present value Thanks for clarify me Erimess! ============================= Another scenario here wish to be clarified:- --------------------------------------------------------------------------------- Scenario A : calculating the fair value and provide impairment loss --------------------------------------------------------------------------------- Invoice date @20-Mar-10 USD3,000.00 Book value @31-Dec-10 USD3,000.00 Collection date @17-May-11 USD3,160.00 (incl.interest) Days due from 20-Mar-10 to 31-Dec-10 is 286 days, where from 20-Mar-10 to 17-May-11 is 423 days. interest rate is 5%p.a. --------------------------------------------------------------------------------- On reporting date@31-Dec-10, I use future expected receipts to calculate the fair value on 31-Dec-10. My question is : which days due would be more logic to applied on 31-Dec-10? I go for 286 days as I only need to report on that date value; however, my friends argue due to using expected collection date to calculate the fair value, it would be more logic to apply the equation by 423 days. Fair value = USD3,160.00/(1+(5%/365))^286=USD3,038.60 OR Fair value = USD3,160.00/(1+(5%/365))^423=USD2,982.11 So, here come with two results:- in my opinion, no impairment need to be made on the reporting date (31-Dec-10), as fair value is greater than book value, so treat the book value as fair. when coming to reporting date (31-Dec-11) no impairment need to be reviewed as the debts was settled. On the side of my friend, impairment of USD 17.89 need to be provided on reporting date (31-Dec-10), the account entrys would be: DR impairment loss CR provision of impairment loss Upon receipts, would reverse the entries. Again, please comment which is more viable on practicing or we got the conceptual errors? May 16th, 2011, 10:42 PM #4 Senior Member   Joined: Apr 2011 From: USA Posts: 782 Thanks: 1 Re: Present value Hi again. First, you're welcome. Now as to this new stuff... I'm not terribly familiar with the concept of reporting a note payable at fair value. With some exceptions that have existed for as long as I can remember, this fair value thing is fairly new in the U.S., it's mostly an option, and I am not very familiar with it and don't really use it. I just went to some reference material and can't even find anything about this for a note payable. I did find something for bonds payable, which can be much longer term and therefore more susceptible to value changes over the years. I would not think an approximate 14-month note payable would change in value all that much. It's "long term" by definition, but in actuality is fairly short-term. But... based on what I saw of the bonds, here are some thoughts I can give you. One, the bonds use the time left on them, not any time that has already gone by. If a bond from 2009 were sold in 2010, the present value would be figured as of the selling date, relative to the future. That is, how many years would be left on the bond, and nothing to do with what time had already passed. Relate this to your note and that would be the 137 days that are left as of 31 Dec 10. Before I even read over the bond stuff, I was thinking you would use the time left and not any time gone by. As for the rest of it, I'm not sure. I'm not understanding why you're compounding daily. You would compound in the same manner that the note actually does. Since I get the impression you are following something not in the U.S., perhaps that is common where you are. It's not common here so I'm just not wrapping my head around that. Was the $160 of interest at maturity calculated on a daily-compounding basis? Would it be typical in the market for this type of note to compound daily? The other question in my mind is whether you need to account for the interest that would be accrued as of the end of 2010. That is, the 3160 includes all of the interest, but 286 days of it should be accrued. I don't have an answer to how that affects it, simply because I'm not familiar with the fair value rules as applied to a note. I do know if you use the 137 days that are left, and use the 3160, you would end up with a present value that doesn't make any sense. If this were a bond, we would only use the interest that would be paid from the day of re-valuation to maturity, and not the interest that came prior. (In fact, the amortized part of any discount/premium would have to be accounted for as well, but that's a complication a note payable shouldn't have to get into.) I don't know the original rate of the note, so I just approximated that about$110 would be accrued as of the end of 2010. Doing a present value of what is left, I came up with a present value of approximately \$3107. That's about the same as it would be if you simply accrued the interest as of that date, so I don't comprehend the reasoning behind doing this at all. This leads me to wonder: is this for a class? Or is this related to a real company, in which case I would just drop it. Or are you just making up examples to use to practice the concept? In the end, I just don't know the rules for this, since it's a new idea here, and I never learned it. And, international rules can differ from U.S. rules. Everything I've said above is an educated guess based on my knowledge about present values, and from I read about re-valuing bonds, which are also liabilities but they work differently. Perhaps that information will help, and perhaps someone else more familiar with this will come along. May 19th, 2011, 05:07 AM #5 Newbie   Joined: May 2011 Posts: 3 Thanks: 0 Re: Present value Ya, i'm just making up the example for comment to know whether i'm misunderstanding the concept or the theory...shame Anyway thank u for your helps!  May 19th, 2011, 09:39 PM   #6
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Re: Present value

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 Originally Posted by gouhayashi Ya, i'm just making up the example for comment to know whether i'm misunderstanding the concept or the theory...shame No shame. If it's just an example to see how the math works out, then it doesn't need to be realistic.

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