# Commuted value of CPP



## canadian_investor (Jul 4, 2011)

Does CPP plan have commuted value? all other defined plans do. i requested and received the latest benefits statement from CPP but it shows only what my projected benefit is upon retirement if I continue making the same payments.
I know it is not possible to take the commuted value of CPP and leave the plan like it's possible with other employer sponsored plans but it must have a commuted value.
does anyone know?


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## MoneyGal (Apr 24, 2009)

You can calculate the actuarial present value of a future income stream. The value will depend primarily on your gender and on the discount rate you use.


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## kcowan (Jul 1, 2010)

I do that every month for my net present value calculation. It is easier because we are both receiving it so we avoid a step.


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## canadian_investor (Jul 4, 2011)

MoneyGal said:


> You can calculate the actuarial present value of a future income stream.


you mean use the following value from the CPP statement:

_Based on your average earnings since January 1, 1966 or when you reached age 18, if your earnings continue at this level until age 65, you could receive a retirement pension of : *$XXX.XX* per month_

so i should plug in this number into a PV(A) calculator?
or is it better to use PV of growing annuity formula to account for CPI adjustment?
what number to use?


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## MoneyGal (Apr 24, 2009)

Well, it depends on whether you are calculating the PV of the earnings you've accumulated now, or the earnings you project at x point in time. If you are calculating a retirement income stream, you'd probably do PV of the current CPP maximum payments. 

Do you have an actuarial PV calculator available to you?


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## canadian_investor (Jul 4, 2011)

MoneyGal said:


> Well, it depends on whether you are calculating the PV of the earnings you've accumulated now, or the earnings you project at x point in time. If you are calculating a retirement income stream, you'd probably do PV of the current CPP maximum payments.


you pre-empted my next question 

The CPP statement shows what my monthly pension may be at 65 _if current contribution amounts continue until 65_.
But it never is that simple.
contribution amount can (and does) change because of salary changes.
there may be periods of 0 contributions like between jobs or unemployed or whatever.
so one number that I need is what my pension will be (if any at all) if I were to stop all further contributions immediately (i.e. leave the workforce).
is there a way to get that number?
and what is the PV(A) of that pension.

the second thing I need (which was my original question in this thread) : going with CPP's assumption of exact same contributions from now until 65, how to calculate the PV of the number they quoted in the statement.
Let's say that number in my case is $400/month.
How to calculate the PV(A) of that?



> Do you have an actuarial PV calculator available to you?


No, I was going to use any one on the web like this one:
http://financialmentor.com/free-stuff/financial-calculators/present-value-of-annuity-calculator
or this one
http://www.investopedia.com/calculator/AnnuityPV.aspx

is there a problem and do i need a special professional calculator?

thank you.


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## MoneyGal (Apr 24, 2009)

I need to come back to this. The problem with the calculators you are linking is that they are asking for N (number of periods) when you need T (a random variable to represent unknown life expectancy). 

If you could solve this using N, you wouldn't need a pension of any kind, because you'd know your exact date of death and could plan the number of payments necessary (and you might also be a Vulcan).


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## canadian_investor (Jul 4, 2011)

Update on this : I called CPP and they calculated the pension i will receive at 60 or 65 if i stop contributions today.
so I have that number now.
is it possible to calculate the present value of that income stream?
keeping in mind that the income won't start until at least 15 years from now if I take it at 60.
So now i have the payment amount, the interest rate (2%) and the number of periods (I can assume age 95 for this calculations. beyond that what do i care anyway).
is it possible to calculate this and also does it matter that there is a lag of 20 years before the income stream starts?


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## MoneyGal (Apr 24, 2009)

Yes. It is possible to calculate that now. 

If you are going to assume a life expectancy of 95, then go ahead and use a generic PV calculator to calculate the value of a stream of income to be received in the future. 

There are multiple online versions of the calculator you need; here is one:

http://www.investopedia.com/calculator/AnnuityPV.aspx#axzz1Xqs7Gxjl

You can also calculate this in Excel. 

I note that this is *not the same* as the actuarial present value.


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## steve41 (Apr 18, 2009)

Here's another, more meaningful treatment..... say you were 40, earning 65K planning to retire at 65 and live til 95. Based on a market rate of 5% and inflation of 2%, CPP represents an increased lifestyle (beer&groceries) of $3283 annually for the remainder of your life (40-95)

This value will change as individual circumstances (salary, market, age.... etc) change. It is an interesting stat nonetheless.


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## canadian_investor (Jul 4, 2011)

MoneyGal said:


> I note that this is *not the same* as the actuarial present value.


thanks MoneyGal.
by actuarial present value, you don't mean the commuted value or do you?

commuted value just takes into account prevailing interest rates vs. a full blown actuarial assessment involving longevity probabilites, interest rates and the nominal present value?

i'm sorry if I don't understand the deeper difference between commuted value and actuarial present value.

and the PV calculators that we have been talking about just provides the nominal present value aka commuted value?


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## MoneyGal (Apr 24, 2009)

What I said was that calculating the present value of your expected CPP payments out to your age 95 is not the same as the actuarial present value. 

APV is usually the same as commuted value. The reason you would use the phrase "commuted value" is that there is a value to commute - i.e., you are leaving a pension plan. With CPP, there's no opportunity to get a commuted value - there's just the actuarial present value, which is the PV accounting for a random variable, which is your expected lifespan. 

When you assume a defined lifespan (whether age 65 or 95 or any particular age) you have removed the random factor from the calculation, hence you are no longer calculating an actuarial present value. 

Clear as mud?


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## steve41 (Apr 18, 2009)

Once again.... who cares about the PV of your CPP stream, or the actuarial value. It isn't as if the tooth fairy is going to magically appear and write you a check on your 65th birthday. A far more informative number is what those CPP checks will deliver -after tax- over your lifetime... in other words, what can you look forward to spend on beer and groceries assuming the CPP was (or was not) in place.

The problem is that this calculation is different for each person, depending on the state (size and type) of all their finances.


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## MoneyGal (Apr 24, 2009)

steve41 said:


> Once again.... who cares about the PV of your CPP stream, or the actuarial value.


I do. 

I understand that you think this is a calculation that has little or no value, and I'm not going to try to convince you otherwise, although I can think of multiple applications for this little piece of knowledge. 

But whether or not you personally think it is valuable to understand that a future stream of income that has a random aspect also has a present value, I don't understand why you would be so dismissive of another point of view. 

I understand your point of view - I think - but I'm not going to dismiss it as useless.  How does that help the free flow of ideas and information here? (Especially as I was directly answering the OP's question?!)


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## canadian_investor (Jul 4, 2011)

MoneyGal said:


> When you assume a defined lifespan (whether age 65 or 95 or any particular age) you have removed the random factor from the calculation, hence you are no longer calculating an actuarial present value.
> 
> Clear as mud?


it actually is, surprisingly 
thank you.

@steve41, i understand what you are saying.
PV of pension is not meaningful from a Main-Street person's point of view.

however, to calculate what you are referring to involves several assumptions too far out in the future.
such as province of residence, tax brackets prevailing at that time, OAS/GIS clawback laws (they _will _change, trust me), inflation and so on.
and not least of all, the life span.

you are almost facing a monte carlo situation.


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## sags (May 15, 2010)

With the CPP having a spousal benefit, wouldn't the longevity of the spouse, and the amount of spousal benefit, also be a consideration in the calculations?


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## MoneyGal (Apr 24, 2009)

The spousal benefit also has an APV.


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## Four Pillars (Apr 5, 2009)

MoneyGal said:


> although I can think of multiple applications for this little piece of knowledge.


I'd be interested in knowing what those applications are.


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## MoneyGal (Apr 24, 2009)

Let's say you wanted to "pensionize" 1/3 of your wealth, to achieve a balance between the sustainability of your retirement income, and leaving a financial legacy at death. 

To achieve this optimal balance, you should add the discounted value of any pension and social security (CPP, OAS, GIS) benefits to arrive at a mark-to-market “value” of the retirement nest egg - and only one-third of this broadly defined nest egg should be annuitized. 

Alternately, if the discounted value of these benefits is more than twice your liquid investable net worth at retirement, you already have all the annuitized income you need - you have satisfied the quota. 

The POV I'm working from is, what is the optimal amount to allocate to annuities? (And once you have allocated an optimal amount to annuities, how should you invest your remaining wealth?) The main paper where this is explore in some detail is here: http://www.ifid.ca/pdf_workingpapers/Spending_Retirement_Vulcan_14MAR2010.pdf

and it takes into account annuitization, spending rates, and asset allocation in the non-annuitized portion. 

The "man on the street" may not have an interest in knowing the APV of pension entitlements - but the question of how is optimal to annuitize is subject to mathematical exploration, and that's part of what I'm doing here.


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## steve41 (Apr 18, 2009)

canadian_investor said:


> however, to calculate what you are referring to involves several assumptions too far out in the future.
> such as province of residence, tax brackets prevailing at that time, OAS/GIS clawback laws (they _will _change, trust me), inflation and so on.
> and not least of all, the life span.
> 
> you are almost facing a monte carlo situation.


Done.... for a 65 yearold with 500K in his RSP, his die-broke at 95 ATI comes in at $40,010 (AVG) with his full CPP, and $31,940 with no CPP. This is taking into account full taxation with indexed tax brackets (at 2%), living in BC. This is a real life number that everyone can relate to, IMHO.


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## Four Pillars (Apr 5, 2009)

@MoneyGal - thanks - that makes sense.


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