Personal Finance

# what is the present value of a \$7000/yr annuity?

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• Mar 17th, 2014 9:31 pm
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[OP]
Jan 14, 2009
1072 posts

## what is the present value of a \$7000/yr annuity?

It is adjusted for inflation. The rule of thumb used to be multiply by 10 but that was when interest rates were 10%. Real interest rates have fallen so much I have no idea what to use as discount rate.
15 replies
Feb 26, 2008
1662 posts
Not enough information. How old is the annuity recipient, what is the recipient's gender, who is the payor (guarantor) of the annuity?

As a starting point, you can look at published annuity rates to get an idea:

http://www.morningstar.ca/globalhome/ma ... tab=invest

So, this provides a valuation of an non-inflation indexed annuity to a certain demographic, with a certain life expectancy by a large, credit-worthy Canadian life insurer. Then you can adjust upward or downward based on your demographic advantage or disadvantage, and based on the risk of your payor.
[OP]
Jan 14, 2009
1072 posts
Real return on 30yr govt bonds is 1% so is discount rate 1% since payments are inflation adjusted and 30 yrs and infinity are similar for these pv calculations. I'm assuming I am immortal. Pv seems to be \$700k but intuition says \$140k. Forgot the formula for pv.
Deal Expert
Mar 25, 2005
21114 posts
freeonboard wrote:
Mar 15th, 2014 5:29 pm
Real return on 30yr govt bonds is 1% so is discount rate 1% since payments are inflation adjusted and 30 yrs and infinity are similar for these pv calculations. I'm assuming I am immortal. Pv seems to be \$700k but intuition says \$140k. Forgot the formula for pv.
Then calculate it as a perpetuity.
[OP]
Jan 14, 2009
1072 posts
Kasakato wrote:
Mar 15th, 2014 5:31 pm
Then calculate it as a perpetuity.
Too lazy. Just tell me. Or google it. Use 1% discount rate .thx.
[OP]
Jan 14, 2009
1072 posts
Urgh. Did it myself. \$700k.

\$180k for 30 years so infinity means more with lower rates and maybe taking inflation out of the situation affects things to. I did not include inflation component in discount rate because payments adjusted for inflation.
Feb 26, 2008
1662 posts
freeonboard wrote:
Mar 15th, 2014 5:29 pm
Real return on 30yr govt bonds is 1% so is discount rate 1% since payments are inflation adjusted and 30 yrs and infinity are similar for these pv calculations. I'm assuming I am immortal. Pv seems to be \$700k but intuition says \$140k. Forgot the formula for pv.

So, do you have a sovereign guarantee of your annuity? If not, then you cannot use a Government of Canada real return rate.
[OP]
Jan 14, 2009
1072 posts
kneevase wrote:
Mar 15th, 2014 10:46 pm
So, do you have a sovereign guarantee of your annuity? If not, then you cannot use a Government of Canada real return rate.
30 yr rrb rate is pretty good starting point. If the annuity only has 50% chance of being paid that would knock 50% off present value. Trying to find a discount rate to reflect risk of annuity would be too complex. This is a guessing game anyway
Sep 23, 2009
4148 posts
Perpetuity?

What Bank is offering that?

Here is a Calculator from RBC Insurance: http://www.rbcinsurance.com/annuities/p ... lator.html

As I understand ....

- Single Life Annuity is paid out for the life of the recipient
- Joint Life Annuity is paid out for the live of the designated recipients (Husband and wife)
- Term Certain Annuity is paid for a set amount of time.

Note that you can set how long the guarantee is for. Obviously one with a longer guarantee will cost more.

As an example, I choose a Non-Registered, Single Life Annuity with a payout of \$7,000 per year, 0 years guaranteed, for a male 56 year old, living in Ontario and was told the cost was:

\$121,784.57

I also chose a Non-Registered, Single Life Annuity with a payout of \$7,000 per year, 25 years guaranteed, for a male 56 year old, living in Ontario and was told the cost was:

\$131,713.79

I also chose a Non-Registered, Term Certain Annuity with a payout of \$7,000 per year, 25 years in length, living in Ontario and was told the cost was:

\$110,318.89

As you can see, a plan with a higher guarantee of payments costs more.

I have no affiliation with RBC Insurance and I don't know if there mortality rates are better or worse than other insurers.

All that I know is that my Grandfather purchased a Term Certain Annuity (he told us it was because he calculated this as being the best option) and has outlived what he expected to.
Sep 23, 2009
4148 posts
I don't know if RBC offers an inflation protected annuity, but I know that they exist.

Anyways, the calculator I found didn't mention it, so I am not sure that this would be an inflation protected annuity or not. I am thinking not, anyways the next steps are yours.

There probably is someone who can better help you out that posts here.
Feb 26, 2008
1662 posts
freeonboard wrote:
Mar 15th, 2014 11:50 pm
30 yr rrb rate is pretty good starting point. If the annuity only has 50% chance of being paid that would knock 50% off present value. Trying to find a discount rate to reflect risk of annuity would be too complex. This is a guessing game anyway

Well, if your starting point was a 30 year rrb, you could always look around for a typical corporate spread for a nominal 30 year bond, and simply tack it on. That would give you a 30 year real return corporate bond. And then, you would need to to a little bit a witch-craft to add on a few more basis points to recognize the dubious nature of payments farther into the future (ie, years 30-50).

Right now, a typical 15+ year corporate bond spread is about 200bps ( http://research.stlouisfed.org/fred2/gr ... LC8A0C15PY, ). Since you are trying to price a perpetuity and the outer years get increasingly dubious with a non-sovereign payor (ie, insolvency risk is applied for the entire investment horizon), I'd probably add yet another 100bps.

So, we have the 100bps RRB + 200bps credit risk spread + 100bps long maturity premium for an real interest rate of about 4%. You can logic check this by tacking on 175 or 200 bps for inflation, and you should be near a long term corporate bond rate....

Going back to your question of valuation, if your annual \$7k is truly inflation adjusted, and if it's truly perpetual, and if you believe the interest rate methodology that I have suggested, then the value of your annuity is roughly \$175k.
Member
Nov 8, 2010
238 posts
kneevase wrote:
Mar 16th, 2014 9:10 am

Going back to your question of valuation, if your annual \$7k is truly inflation adjusted, and if it's truly perpetual, and if you believe the interest rate methodology that I have suggested, then the value of your annuity is roughly \$175k.
Intriguing. Any chance there is an available calculator that would assist someone a little less versed to demonstrate (and re-create) these results? (I want to run some different numbers)

I ask as I have been trying to find a way to find a present day value for my DBP.
Feb 26, 2008
1662 posts
SustainablePF wrote:
Mar 17th, 2014 8:23 pm
Intriguing. Any chance there is an available calculator that would assist someone a little less versed to demonstrate (and re-create) these results? (I want to run some different numbers)

I ask as I have been trying to find a way to find a present day value for my DBP.

I'm afraid that I do not know of an online calculator for annuities. Calculating the value of a perpetuity is relatively easy...referring to a lifeco for an annuity is relatively easy, but calculating the present value of a specific annuity for a specific person is not easy.
Banned
Feb 15, 2008
26318 posts
Calgary
One thing one has to take into account when doing this calculation is the risk of the payer/issuer of the 'annuity'.

For instance, if the 'annuity' is an indexed government pension, and the assumption made that the government won't default on it, then you would need to use the risk-free rate as applicable to long-term RRB's, to calculate such. In conjunction with a mortality table that accurately reflects the expected lifespan of a government employee.

If said 'annuity' comes from the private sector, then using rates applicable to long-term corporate bonds would be more realistic.
TodayHello wrote:
Oct 16th, 2012 9:06 pm
...The Banks are smarter than you - they have floors full of people whose job it is to read Mark77 posts...
Member
Nov 8, 2010
238 posts
Mark77 wrote:
Mar 17th, 2014 9:07 pm
One thing one has to take into account when doing this calculation is the risk of the payer/issuer of the 'annuity'.

For instance, if the 'annuity' is an indexed government pension, and the assumption made that the government won't default on it, then you would need to use the risk-free rate as applicable to long-term RRB's, to calculate such. In conjunction with a mortality table that accurately reflects the expected lifespan of a government employee.

If said 'annuity' comes from the private sector, then using rates applicable to long-term corporate bonds would be more realistic.