# Why factor in inflation?



## sucka (Mar 28, 2011)

Hi, new to the site here. I'm 35, married with two kids and recently have gotten somewhat paranoid about my post work life. I have no mortgage, a paid off investment property and a healthy amount of savings in RRSP and elsewhere. I plan on retiring much before 65, as i'd like to be able to still do things when i retire. So, this is why i'm slightly unsure about my financial well being when i'm say, 50 or so, when i do plan to retire. 

I often see inflation being factored into people's calculations and often this leads to confusion and what not. When i do my projections, I choose to leave inflation out of the picture, opting to go for a value in today's dollars. I mean, why guess inflation when you can just leave it out altogether? 
Would that make more sense or am i making a mistake? My assumption is that your return will factor in inflation anyways, hence my calculations use a real return ( i normally use 2-3% to be conservative) As long as you're not locked in long term, or taking undue risk, wouldn't your returns be more or less instep with inflation. Would this approach not only be less confusing, but also if it's in present value, 1 Million dollars 20 years from now, is a more meaningful number than say, 3 Million dollars 20 years out including inflation. I know i'm being long winded here, but isn't it easier to just look at it like this. If I were to retire today (at age 55), is 1M enough?


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## steve41 (Apr 18, 2009)

A financial plan should include non investment items, which all have inflation aspects.... income tax (the brackets are indexed to the cpi), CPP and OAS income are likewise indexed, and your after tax income (lifestyle needs, the amount you spend on beer&groceries)... all of these have a major inflation component. I don't see how you can ignore it.


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## sucka (Mar 28, 2011)

steve41 said:


> A financial plan should include non investment items, which all have inflation aspects.... income tax (the brackets are indexed to the cpi), CPP and OAS income are likewise indexed, and your after tax income (lifestyle needs, the amount you spend on beer&groceries)... all of these have a major inflation component. I don't see how you can ignore it.


Becuase on both sides of the equation you have the same component. Doing the math would suggest you can cancel both sides out. On the left side you have your assets and income sources which grow at rate X. This rate, X, is correlated to the estimated rate of inflation. If inflation was 8%, X might be 11%. If inflation was 3%, return might be 5%. So, loosely, one can intuitively posit that investors require they be compensated for inflation when they buy debt. 
On the other side of the equation, you have your costs, which also grows at a particular rate of inflation This inflation rate should be the same on both sides of the equation, hence, i don't see why you can't eliminate from both sides. 

You still come to the same conclusions at the end of the day (i think), just inflated dollars on both sides. But why not have the financial industry go with one convention to avoid confusion?


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## sucka (Mar 28, 2011)

steve41 said:


> A financial plan should include non investment items, which all have inflation aspects.... income tax (the brackets are indexed to the cpi), CPP and OAS income are likewise indexed, and your after tax income (lifestyle needs, the amount you spend on beer&groceries)... all of these have a major inflation component. I don't see how you can ignore it.



Becuase you're grossing up both sides of the equation with the same number.
Left side is your assets and income sources which grow at a rate X. X includes inflation becuase as a lender of money, you at least want to be compensated for expected inflation. 
Right side is your cost of living + left over equity (so you have a basic balance sheet going), which also grows at a particular rate of inflation. this inflation should be the same for both sides of the equation, so math dictates that you can simply cancel the two out. 

Now, if i'm right, both ways of quoting the estimate is the same, but why muddy the water with inflation if real numbers are easier to relate to?


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## brad (May 22, 2009)

The only value for inflation that you can be certain is wrong is 0, and that's the value you're using. 

To get a sense for what inflation can do for prices 15-20 years into the future, take a look at some old catalogues and newspapers from 15-20 years ago and compare prices of goods. Go back and look at car prices from 1991, for example, and compare to car prices today. Inflation will make a difference in terms of your ability to afford the things you need, and you need to factor it into the expenses side of the equation to come up with a reasonably accurate guess of how much will be "enough" for you to live on in your retirement years.


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## olivaw (Nov 21, 2010)

Inflation will obviously have an impact on what you can buy later in life, but the OP did say that anticipated returns are pegged at inflation plus 3% and that seems reasonable for rough calculations. In my own calculations, I peg inflation at 2% and ROI at 5% which is pretty much like saying that I am planning on earning inflation plus 3%.

As an aside, my favorite calculation is retirement sustainability quotient (RSQ) which I learned about from MoneyGal's book. The calculator doesn't require me to choose a rate of inflation. (I do not know the math behind the calculator)


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## north49th (Mar 8, 2011)

sucka,

I agree with previous posters.

If you'd like to see the historic effects of "official" inflation from the BoC, try out their calculator at: http://www.bankofcanada.ca/en/rates/inflation_calc.html

FWIW


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## CanadianCapitalist (Mar 31, 2009)

OP did not say he is assuming no inflation. He is simply running his numbers with real, inflation-adjusted returns. That's what I personally do. I assume a real return from stocks of 3% and from bonds of 2%. Or you could assume an inflation rate of 2% and nominal returns of 5% from stocks and 4% from bonds. It's just six of one or half a dozen of the other.


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## Sampson (Apr 3, 2009)

Wow, 5% nominal ROR?

Just a wee bit conservative?  I see an early retirement for you CC.


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## Square Root (Jan 30, 2010)

I think the problem with Sucka's approach is it is too simplistic Ie inflation affects various asset classes and income streams in very different ways. Pension, equities, fixed income, cash, are all effected differently. One size would not fit all. Also, people have found that one's own inflation rate(depending on what you buy) can be quite different from the overall CPI.


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## steve41 (Apr 18, 2009)

RRIFmetic treats inflation in this way.... there is the inflation which the govt reports.... it effects how the tax brackets are indexed, the indexing of CPP, OAS, etc... and your own personal inflation rate, the increase in consumption which you personally experience. They needn't be the same.


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## andrewf (Mar 1, 2010)

It's not unreasonable to make real return assumptions instead of trying to guess inflation. But that also requires that your portfolio performance is independent of inflation. For instance, not having a pile of cash stuffed under your mattress.


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## kcowan (Jul 1, 2010)

I agree with Steve. I use a personal inflation rate of 4%/year even though income is indexed at CPI. This prevents big surprises in 10 years. Plus ignoring it can create major dislocations. Cars and houses have increased faster than 2% a year. So have medical and pharmacy costs. So has energy and food.


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## MoneyGal (Apr 24, 2009)

Yes, SquareRoot; but unless you are actually calculating differing rates of inflation for all these expense and return categories, applying an (identical) "inflation rate" to both sides of the ledger is, as Sucka says, mathematically equivalent. 

If you use real returns and estimate your expenses in real (today's) dollars, you are already adjusting for inflation. 

In PYNE our advice was to "think in real terms" (i.e., expect inflation) and "invest in products which are linked to inflation [directly, i.e., RRBs; and indirectly, i.e., equities]."

The bigger issue with inflation and the idea of a "personal inflation rate" is that people will underestimate the extent to which the CPI rate will not apply to their personal situation. And the cure for that is not to assume a higher inflation rate - it is to save more relative to your needs.


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## MoneyGal (Apr 24, 2009)

Wow, lots of responses in the time it took me to type this out. AndrewF, my comment about RRBs is intended to respond to the need to have your portfolio not linked to inflation. Make sense?


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## steve41 (Apr 18, 2009)

To further complicate things, I contend that inflation doesn't track the same as interest.

If you have capital invested at a guaranteed 3%, it will track an exponentially increasing 3% trajectory.... that's the nature of compounding.

On the other hand, 3% inflation doesn't compound, it follows a straight line trajectory with a constant slope of 3%.

In the short term, this won't make much difference, however over a 20-40 plus year projection, this can make a major difference.


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## andrewf (Mar 1, 2010)

Inflation most definitely compounds. Otherwise, 10% inflation off of 1910 levels would result in essentially zero inflation now.


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## steve41 (Apr 18, 2009)

huh? Look at the consumer price index starting back 30 years or so, when the govt started to control inflation (i.e. after the big OPEC inflation scare) There is no way you can fit an exponential curve to that series. At best you can fit a straight line. (not a horizontal line, a straight line)


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## andrewf (Mar 1, 2010)

Oh, well, that's because they changed policy part way through the series. Inflation targeting was put in place in the early 90s and didn't have full effect on inflation until ~1994. The inflation target is trying to increase prices by 2% year over year. Assuming it does this perfectly with no errors, the price level in x years will be 1.02^x times the current price level. If the errors aren't biased to the high or low side, you'd expect to get more or less to the same place.


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## CanadianCapitalist (Mar 31, 2009)

steve41 said:


> To further complicate things, I contend that inflation doesn't track the same as interest.
> 
> If you have capital invested at a guaranteed 3%, it will track an exponentially increasing 3% trajectory.... that's the nature of compounding.
> 
> ...


Huh? Of course, inflation compounds. Every time you see a price increase, it is an increase from the current level. The price increase after that would be an increase on the increased level. If that isn't compounding, I don't know what is.


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## steve41 (Apr 18, 2009)

Again, look at the cpi curve starting back 30 years. That curve does not have an exponential/compound bone in its body. I am the first to admit that a lot of people like to think the cpi compounds, so you are not alone. There is a school of thought which determines the inflation rate as the slope of the cpi curve and that the cpi curve is linear. While I allow my users to chose, I personally believe the cpi is straight. For a better explanation, take a number and subject it to a compounding 3% cpi over 40-50 years, show that to an economist and get him to rationalize the huge (wacky) numbers that are projected. Good luck.

I look at inflation and investment growth as very distinctly different.

Put a laptop and a tin of coffee in a vault and open it after a year. The values of those two commodities will be subject to droughts, labour disruptions, technological advances, commodity shortages/surpluses....

Put $100 in a bank term deposit at 2%, and it will be worth $1.02 The coffee and the laptop will have a completely indeterminate, possibly even a lesser, value.

This is my (albeit naive) take on inflation. BTW.... you are in the majority as far as a compounding inflation rate, mine is a minority opinion.


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## Square Root (Jan 30, 2010)

MG: I agree the best solution to inflation is to save more or spend less than originally planned. inflation is uncertain and simple modelling shortcuts are fine in the short term but inflation and returns are not perfectly correlated so over a 30-40 year period( hopefully my retirement) I think I need to "pad the plan " to cover this risk.


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## andrewf (Mar 1, 2010)

Yikes steve. Let me just say that the entirety of mainstream economics is not in your corner.

I'll just say that when you zoom in on an exponential curve, it looks straight, especially if the base is small (ie, 1.02).

So if we zoom out a bit, here what things look like. A price level chart for Sweden 1830-2010








source

Canada would be similar, but I can't find a chart. I think an exponential function would fit that better than a linear one.


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## andrewf (Mar 1, 2010)

And you claim that using exponential functions leads to crazy price increases. 50 years at 2% linear inflation would double prices if inflation were linear. If it were exponential and compounded at a rate of 2%, prices would increase by 169%, between double and triple. So, not far off. Moreover, if inflation is linear, as you suggest, over fifty years the inflation rate would be declining down to 1% yoy in year fifty. As time marches forward, it would asymptotically approach 0% year over year.


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## steve41 (Apr 18, 2009)

Prior to the 1970/80s, the consumer price index was simply reported.... it just happened. Since then (the big runaway inflation scare), governments have consciously tried to control inflation (by controlling interest rates primarily). I am referring to the cpi curve subsequent to 1980. If you can fit an exponentially increasing curve to that time series best of British luck.


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## Potato (Apr 3, 2009)

steve41 said:


> I am referring to the cpi curve subsequent to 1980. If you can fit an exponentially increasing curve to that time series best of British luck.



Huh? For small percent increases it's tough to see the difference between an exponential and a linear curve, especially with some noise in the data, but all logic suggests that inflation is exponential. 

Let's say from 1985 (since the early 80's still had some high inflation), the Bank of Canada says that inflation made $1 in 1985 about $1.90 in 2011, or about 2.5% per year. But that bounced around from -1% to +5.5% over that time.

You could get from $1 to $1.90 with a smooth exponential at 2.5%, or a constant increase of 3.5 cents (1985 dollars). Interestingly, the linear fit does look to fit pretty good, especially since it so happens that by the mid-2000s, 3.5 1985 cents is about 2 cents of a 2000's dollar, so the percentage inflation has come down along with the reported inflation rate.

But, should the slightly better fit of that linear trend change our minds on the fundamental exponential nature of inflation, or is it just a distraction caused by the changing inflation rate as it came down through the 80's?

What if we just look at the period from 1992-2010, when inflation looked to hover around 2% with some noise, rather than decrease over time (as the effective percentage does with the linear fit)? Then $1 in 1992 goes to $1.39 in 2010. This is a shorter time-base, so it will be hard to see the difference between exponential and linear, but have a look. 

I can't say that in any of these cases the linear curve fits the data much better than the exponential one, certainly not so much better as to question the very nature of inflation and to affect how I plan for the future. Over these timescales/rates the noise in the data is larger than the difference between the two methods of curve-fitting, so I'd rather go with the one that makes more theoretical sense.


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## steve41 (Apr 18, 2009)

As I have said before, most would agree with you. I don't. My take is that inflation is the slope of the cpi trajectory. A 2% inflation scenario going forward over many, many decades is best approximated for planning purposes by a linear curve with a 2% slope, not a compound one. 1+.02*n rather than (1+.02)^n

The reason we like the latter representation is that it is easier to build a formula for mathematically forecasting investment growth adjusted for inflation.


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## steve41 (Apr 18, 2009)

Here are two identical plans... a 25 year old earning $55000, retiring at 65, inflation 3%, nominal rate 4%, dying broke at 95. In one, inflation is treated as compound, in the other, it is treated as a straight line. The plans are quite different.

Compound cpi
Straightline cpi

Pick your poison.


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## steve41 (Apr 18, 2009)

One interesting outcome of the two runs (one assuming 3% straightline inflation and one assuming 3% compounding) is that the answer to the _'how much do I need to retire'_ question gives two radically different results $1.9M in one case and $1.1M in the other case.

This is for 2 identical assumptions, 5% rate, same salary, retirement ages..... the only difference is that in one case we treat inflation as having a linear 3% trajectory and in the other we treat it as 3% compounding. 

Food for thought.


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## Maybe Later (Feb 19, 2011)

CanadianCapitalist said:


> Huh? Of course, inflation compounds. Every time you see a price increase, it is an increase from the current level. The price increase after that would be an increase on the increased level. If that isn't compounding, I don't know what is.


Precisely. Which is why the concept of real returns works.


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## steve41 (Apr 18, 2009)

Maybe Later said:


> Precisely. Which is why the concept of real returns works.


 It is a "concept" only because there is an army of spreadsheet toilers out there who were raised on the mathematical formula of 'real returns'. It makes forecasting very straightforward.... the formula is a pretty simple function, only slightly more intricate than the simple time value of money math. As soon as you try to represent inflation as a straight line or define it as the (constant) slope of the consumer price index, it becomes real tricky to solve with simple spreadsheet math.

Granted, for short time frames (20 years, 2%) the two concepts are quite close, but for long term financial forecasting (50-70 years at 3%), the error gets pretty significant as the above 2 projections show.


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## Financial Cents (Jul 22, 2010)

@steve41 - nice work. 

I've learned factoring in inflation, into your retirement planning (and investment strategies) is a must. 

The real concern I have is, are we going to deal with only 3% inflation going-forward prior to my retirement in another 25 years (my generation (30-something now))???


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## MoneyGal (Apr 24, 2009)

steve41 said:


> It makes forecasting very straightforward.... the formula is a pretty simple function, only slightly more intricate than the simple time value of money math. As soon as you try to represent inflation as a straight line or define it as the (constant) slope of the consumer price index, it becomes real tricky to solve with simple spreadsheet math.
> 
> Granted, for short time frames (20 years, 2%) the two concepts are quite close, but for long term financial forecasting (50-70 years at 3%), the error gets pretty significant as the above 2 projections show.


Hmmm. So how does your straight-line projection of everyone dying at age 95 square with that? Why is a straight-line projection of inflation unacceptable but a terminal age of 95 for the entire population acceptable? Just curious. I may be misunderstanding how your software works, though.


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## steve41 (Apr 18, 2009)

Once more.... here are two identical plans... a 25 year old earning $55000, retiring at 65, inflation 3%, nominal rate 4%, dying broke at 95. In one, inflation is treated as a compound phenomenon, in the other, it is treated as linear. 

Compound cpi
Straightline cpi

They track quite differently.


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## andrewf (Mar 1, 2010)

I think no one is denying that there is a difference between assuming linear vs. exponential. My question at least is why assuming linear is reasonable, especially over longer time frames. Because a loaf of bread rose in price by a ten of a cent per year in 1903 doesn't mean it will continue to rise by a tenth of a cent per year in 2011.


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## steve41 (Apr 18, 2009)

I (and a decided minority) am saying that the cost of living doesn't behave the same way that financial entities (GICs, stocks...) do. The cpi is a defined as the price of a basket of goods and services which fluctuates completely differently than interest rates.... the price of coffee, orange juice, computers..... vary all over the map depending on technology, labor productivity, weather, public taste.... They seem to be completely different in structure. That said, I allow the user to set whether or not he wants to treat inflation as compounding or straightline. Most choose compounding, however I do have die hard 'straightline' advocates.

Whenever I run a projection, I choose compound inflation, just to avoid the controversy, although my heart says otherwise.


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## I'm Howard (Oct 13, 2010)

Retired people are not impacted by inflation the same way younger working people are.

One tank of gas a month, not a week, haven't bought a suit in years,a nd a carton of milk lasts a week not a day.


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## MoneyGal (Apr 24, 2009)

I'll just leave this here: 

http://www.qwema.ca/index.php/video-library/your-personal-inflation-rate/


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## steve41 (Apr 18, 2009)

The only time this bears noting is when the "how much do I need?" question comes up.

If that 25 yo, $55K salaried guy asked the question... how much do I need to accumulate for retirement, then if you belong to the "inflation compounds" school, the answer would be $1.87M, if you took the heretical 'straightline' approach, the answer would be $1.1M. That's a considerable difference.


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## andrewf (Mar 1, 2010)

But one is right, and one is wrong, no?


Your model assumes constant consumption, too, for that matter. Many people choose to consume less in retirement.


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## MoneyGal (Apr 24, 2009)

They consume less, but the things they do consume are typically subject to a higher rate of inflation than the average. Take a look at the CPI-E in the U.S. for empirical proof...it has been higher *every year* for the past 25 years than the generic rate (known as the CPI-W, for Workers, in the U.S.)

Last year I ran some numbers for the Canadian scenario (book research) and the pattern seems to hold in Canada as well.


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## steve41 (Apr 18, 2009)

MoneyGal said:


> Hmmm. So how does your straight-line projection of everyone dying at age 95 square with that? Why is a straight-line projection of inflation unacceptable but a terminal age of 95 for the entire population acceptable? Just curious. I may be misunderstanding how your software works, though.


 Who says my die-broke at 95 projection is cast in stone? You can choose any die broke age.... 120 if you choose.

And it needn't be a die-broke metric. You can specify an estate.... "I want my estate to net $500K (in today's $) at age 100." I choose 95 because it seems to be what my users choose.


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## MoneyGal (Apr 24, 2009)

OK, but haven't you chosen 95 for every single plan you've posted here? The probability of dying at exactly age 95 is actually really low.


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## steve41 (Apr 18, 2009)

MoneyGal said:


> OK, but haven't you chosen 95 for every single plan you've posted here? The probability of dying at exactly age 95 is actually really low.


 If you examine those plans, you will see a single "N" or "S" in the age column. These represent life expectancies for each individual (nonsmoking/smoking) based on their current age and sex.

95 isn't a life expectancy, it is simply a most optimistic guess a person would have..... "in the best of all worlds, what is the maximum age I could expect to achieve?" Users pick anything ranging from 80 to 100 depending how lucky/healthy they feel. (and possibly what age their parents made it out to)


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## MoneyGal (Apr 24, 2009)

And the probability of dying at the age of your life expectancy is also pretty low (but not as low as 95). 

I just don't understand why you would argue that inflation is unknown and hard to predict and you provide detailed ways of modelling different inflation outcomes when the planning horizon - which is an order of magnitude, if not several orders of magnitude more important than the impact of inflation on a retirement income plan - is left to 3 data points: an age the user picks or age 95, and a non-smoking and a smoking life expectancy. [shrug] It is a mystery.


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## steve41 (Apr 18, 2009)

The user, once he picks various parameters, retirement age, runout age(90-95-100), interest rate, inflation rate, province, can create a projection which can stand up to full scrutiny/accuracy. Most programs will fail the accuracy test, especially income tax accuracy. The appeal is that my users (planners) don't get calls from confused clients who can't verify the numbers (especially tax). The normal planning approach is to choose various rate (hi/lo/med) estimates in order to cover off uncertainty. (or MC the plan) 

When a planner puts out a plan which approximates basic rules such as income tax, he loses credibility. It is as simple as that.

The inflation assumption, die broke age, estate goals, along with all the other non-investment entities such as loans, cpp/oas, realestate strategies, RESPs, life insurance, annuities, future windfalls, aftertax income profile.... these are all identified by the planner and his client and may get changed as the plan is fine tuned and/or revised each year.


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## sucka (Mar 28, 2011)

This is getting all confusing to me. 

Instead can we look at backwards? Just start at the retirement age now and calculate what you need to live on and then work out what that would take (amount X) today to generate this income. So far, no inflation is in the picture. 

From there I can take X, and do a present value annuity (or whatever function that's appropriate), using a real return as the basis of growth. Wouldn't this give me what i need to save annually to get to X? I'm assuming for simplicity my pay increase will just keep pace with inflation, so i don't need to take that into account. I mean, if i know what I need to save annually, and make start at today the base year, I know what % of income in need to sock away. 10 years from food might cost 25% more, but i'm also making 25% more through wage increases.
Following years, I'll take the same percentage and apply to my income for the actual amount saved. For analysis as of today, everything is based on Base Year. I don't need to care what inflation might be.


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## steve41 (Apr 18, 2009)

sucka said:


> This is getting all confusing to me.
> 
> Instead can we look at backwards? Just start at the retirement age now and calculate what you need to live on and then work out what that would take (amount X) today to generate this income. So far, no inflation is in the picture.
> 
> ...


 Of course there are all kinds of rules of thumb, approximations, etc. If you want to take the effect of CPP/OAS/pension, income tax (where the tax brackets are indexed to inflation), etc, then differentiating inflation and nominal rates is perhaps a better way to go. It depends on how accurate/inclusive you want to get.


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