Talk:Time value of money/Archives/2012

This is an archive of past discussions about Time value of money. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Annuity Formula Derivations

Further to my observation below, research enlightens me that the financial industry allows for payments at the end of year, so earning no interest in Year 1, while another version will allow for payments at the start. I think that this should be made clear in Example 5 and that the stated formula should be multiplied by (1+r) to give this result. 82.3.28.212 14:04, 19 September 2007 (UTC) Hi, I do not understand Example 5 on Saving $1000 per year for 20 years at 7% - compound interest, I presume, as I calculate the total to be $43,865.18 based on $1070 at the end of Year1, $2214.90 Year 2, etc. The example gives the total as $40,995 - I get $39,995 at the end of Year 19 - Where am I going wrong? Thanks 82.3.28.212 15:52, 18 September 2007 (UTC) Can someone please add the mathematical derivation of the FV_annuity formula from the regular/lump sum FV formula? (Same for the PV formulas). Thanks.

I put the derivation of the PV annuity formula, but think you meant something else. If I understand the question properly, to calculate the future value of an annuity, calculate the present value. Then calculate the future value of that present value. I may put up an example.--Gregalton 20:32, 20 November 2006 (UTC)

Removed the numismatic notice - Time Value of Money has little or nothing to do with the physical manifestation of money. Gary 19:08, 31 July 2006 (UTC)

Putting the text Numismaticnotice here so the bot will not tag it again. Ingrid 17:02, 1 August 2006 (UTC)

Revert to previous version, Sept 8, 2006

Your changes were not beneficial. You took away the simple references that the old version had to the formulas. If you want to make a change, do not remove the listings of the various formulas like you did. (This person did not sign)

My version did NOT remove the listings of formulas. Nor did it remove the references to the formulas. I guess you did not bother to spend much time reading it. It was only posted for a few hours before you threw it out. Other viewers should look at the version from Sept 8, 2006 @18.35 Retail Investor 01:24, 9 September 2006 (UTC)

You did not respond saying what exactly I deleted, so I have reverted the page a second time. Retail Investor 20:45, 12 September 2006 (UTC)

P/E calculations should not be here

I personally think the section on P/E should be pasted at the P/E page, not here. I added its mention at the very top so you could make that into a link if you like.Retail Investor 19:22, 23 November 2006 (UTC)

Thanks for the comments. I have made some changes to this section (that I think got removed or denatured by other edits) to make it more clear why it is here. I still think it is relevant to include on this page, and hopefully the new text will help to establish this. I have frequently encountered the statement that "real world" perpetuities do not exist, but lots of real world cases are essentially perpetuities - P/Es being a case that is frequently encountered by e.g. financial people and retail investors. Although it may be useful to include on the P/E page, I also think it is useful to underline that most investment analysis is underpinned by TVM.--Gregalton 22:06, 23 November 2006 (UTC)

An additional point: someone reverted the text that bonds with bullet payments can be rolled over, and therefore can be modelled as perpetuities. While this is strictly feasible, it seems pointless (we already know how to calculate a bullet-payment bond with considerable accuracy, why duplicate?; to answer my own question, it's a useful shortcut for long maturity securities, but the existence of a shortcut is a different point). It also ignores rollover risk, etc (how much can the new bond place interest at? A bond that is fixed at $x per year forever may have a substantially different value than a floating rate note). For these reasons, I've tried to rephrase to say that lots of "perpetual" investments exist that are not notes, like real estate. --Gregalton 22:06, 23 November 2006 (UTC)

Rate of return / discount rate

Some text on the choice of appropriate rate of return has been duplicated through edits. Personal opinion, I think it should go in the top section; grateful other views. It is a frequent problem for those new to TMV to understand what rate should be used, it is central to understanding the issue, and the effect on final results dramatic. That said, if it seems esoteric or technical to some perhaps it should be placed further down.--Gregalton 22:14, 23 November 2006 (UTC)

I deleted the resulting duplicate paragraphs. I left it in the section on "how to do the calculation" and left the top "conceptual". Even though it is important, it is no more so than the other variables. Personally I most often end up solving for the return variable.Retail Investor 18:29, 25 November 2006 (UTC)

Fair enough, I think it reads well. Thanks for the input. I think, however, that the discussion of the Gordon growth model would best go in the section on P/E, not in the formula introduction to growing perpetuities. If I remember correctly, the distinction about the gordon model is dividends vs earnings as "cashflows" (to investors); the underlying math is the same. I am not aware of any other mathematical model for valuing growing perpetuities - there are different models for dealing with uncertainty, and ones where the uncertainty is corrected for by using different models entirely (like "multiple soup"). But where the annuity rate and growth rate are known, this is pretty much the formula; if there are other theories that question the math, I'm not aware (or far more likely, I've forgotten;) Best regards.--Gregalton 19:00, 25 November 2006 (UTC)

My objective was to put up a big red flag about using this calc. In addition to the Div/Earnings distinction, there is the requirement about the discount being greater than the growth (which was in the section I overwrote). But of even greater importance, from my POV, is the probable misunderstanding of how long perpetuity really is. Since most people understand that $100 in 60 years is only worth $1 today, assuming an 8% discount, they will think that any perpetuity over 60 years can be ignored. But for this equation to be true, it often requires hundreds of years of payments. At the 60 year cut off the PV can be only half as much. Couple that issue with the requirement to correctly predict the growth rate over that period, with GREAT exactitude. I put these warnings on the Gordon Model page. I believe the correct calculation has NEXT year's payment as the numerator (*(1+g), but that is not really going to make a difference.Retail Investor 18:02, 28 November 2006 (UTC)

I have moved the comments on the Gordon model to the P/E section. I grant the objections, but think it more appropriately goes here. Contrary to the way it read, there really isn't "another model" for perpetually growing annuities, to the extent they exist - there are modifications/qualifications to account for the fact that few exist in pure, unrisky form. Put differently, if a true perpetuity with a fixed growth rate exists, this is the way it is valued, there is pretty much no debate about that. To deal with your (quite appropriate) comments that they rarely exist, I've qualified the text above quite explicitly. —The preceding unsigned comment was added by Gregalton (talk • contribs) 13:19, 3 December 2006 (UTC).

annuity derivation - new version

This may be a personal issue, but I find the updated derivation of the annuity formula (dated today) much less easy to read for non-specialists. I'll admit to bias, I drafted much of the previous version. Any other opinions?--Gregalton 13:49, 12 December 2006 (UTC)

Compound yield vs simple interest rate

There seems to be some inconsistency among the various Wiki finance articles on the use of Time Value of Money and the meaning of Time Value of Money. Finance textbooks (such as Barron's Finance) include compounding/reinvestment in their sections on the Time Value of Money, but it seems to me that increasing the amount of money invested by reinvesting interest is an investment decision based primarily on the simple interest rate. The factors that affect the Time Value of Money -- inflation, risk and preference for liquidity -- determine the simple interest rate.

From a conceptual perspective it makes no difference if the interest earned in a compounding period is paid out or reinvested. It is assumed that the return on this original income is the same in either circumstance. Your choice (if you have it) to reinvest, or take out and invest elsewhere has nothing to do the concept of time-value-of-money. You are simply optimizing your returns.Retail Investor 02:23, 18 January 2007 (UTC)

In the Wiki article on Future Value, there's an explanation of the difference between Future Value without compounding and Future Value with compounding. As best I understand it, the Time Value of Money determines the simple interest rate, not the compound yield. Future Value tables give the compound yield for $1 after n periods for various simple interest rates. Compound yield assumes reinvestment of interest in the investment instrument.

You are misunderstanding the difference between simple and compound. When the compounding period is one year, they are the same, because the point of differentiating them is to ensure we can translate one to another. Think of them as being different languages to measure the same thing. The 'thing' (interest) doesn't change. But they use different words (measures of %) to express the same thing.Retail Investor 02:23, 18 January 2007 (UTC)

Is there something we can do here in Wiki to help people understand the various uses of Time Value of Money and Future Value? If the meaning of Future Value and the Time Value of Money now assume reinvestment of returns, should we state that explicitly? 64.181.91.66 17:57, 17 January 2007 (UTC)

Look at compound interest for some examples of real life uses. Retail Investor 02:23, 18 January 2007 (UTC)

Are you saying that you consider simple interest equivalent to compound interest? Or are you saying that describing simple interest is no longer pertinent from a historical, mathematical or cultural perspective? I don't understand your comments above.

I'm sorry but I can't figure out how you reached those conclusions from what I said. I don't agree with any of those statements. Retail Investor 23:35, 21 January 2007 (UTC)

PVGA is here could someone please ad th FVGA

Assuming you mean future value of a growing annuity: take the same formula for PVGA; multiply it by (1+i)^t, where i is the interest rate and t the number of years in the future. (Assuming annual compound interest).--Gregalton 16:12, 2 February 2007 (UTC)

Financial Planning

This section is dedicated to the use of TVM in regards to financial planning for the financial consultant/planner. I strongly believe that in order to compare current situations in regards to current and future obligations, it is usefull to reduce all assets, liabilities, income, and expenses to a common denominator; present value. I would like to standardize the evaluation of current financial situations in a manner that will permit all aspects of a financial situation to be balanced against each other.

I will share my views and ideas in hope of colaborating on this project to bring a method of evaluation that will help better present financial consequences of decisions.

I look forward to seeing this topic expand.

Best Regards

Michel McMahon 22:37, 15 August 2007 (UTC)

Benchmark - Expected rate of return

To be completed...

Assets

Assets are economic entities that give rise to future economic benefit and is controlled by the entity as a result of past transaction or other events. It is probable that the future economic benefit will eventuate and the amount of asset can be measured with reliability from source document which makes it representationally faithful. Examples include cash, equipment, buildings, and land.

The accounting equation relates assets, liabilities, and owner's equity:

{\mbox{Assets}}={\mbox{Liabilities}}+\mathrm {Owners'\ Equity} ,

Michel McMahon 23:16, 15 August 2007 (UTC)

Liabilities

Company's obligations

Income

To be completed...

Expenses

To be completed...

Limitations

The expected rate of return on assets can change due to changes in ratio of assets owned.
- However, it can be said that a properly balanced portfolio of assets which is maintained in a way that no asset is provided the liberty to become out of ratio will provide a controlled amount of risk and a realistic rate of return. It is important to estabish a realistic rate of return as all aspects of the financial situation will be weighed against this benchmark.

Calculators and Software

To be completed...

Calculating annuity of FV or PV

This article contains the formulae for 'Present value of an annuity' and 'Future value of an annuity.' It does not, however, contain the formula for the reverse of these operations. I.e., calculating the annuity knowing either the FV or PV, n, and i. 66.94.95.194 20:45, 18 September 2007 (UTC)

i vs. r

If I recall correctly, convention is to use i for the rate and n for the periods when doing discrete period interest calculations, and use r for the rate and t for the time (starting at 0) for continuously compounded situations. -- Avi 21:36, 22 October 2007 (UTC)

PVA is there, but would someone please add "PVFA"?

The article seems to give description and examples for PVA i.e. Present Value Of An Annuity, which maybe could be called

PVCA i.e. Present Value Of A Currently-paying Annuity.

But maybe the article does not give description or examples for what could be called

PVFA i.e. Present Value Of A Future-commencing Annuity

(and such PVFA situations seem extremely common).

(I already did a medium amount of unsuccessful browsing and searching for such PVFA examples in the References, the External Links, and on the Internet.) Bo99 (talk) 16:13, 8 October 2009 (UTC)