### Author Topic: Determining the Value of a Future Cash Flow  (Read 3567 times)

#### Yankuba

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•     • Posts: 1357
• Location: Long Island, NY ##### Determining the Value of a Future Cash Flow
« on: July 28, 2015, 05:44:51 PM »
Hello - how do I calculate the 2015 value of a \$50k (annual) pension that begins paying out in 2026 and lasts let's say 38 years? What discount rate should I use? Thank you Mustachians!

#### Glenstache

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• Target FI date 2027 (maybe?) ##### Re: Determining the Value of a Future Cash Flow
« Reply #1 on: July 28, 2015, 05:51:34 PM »
Most of the future value of money calculations I've worked with are based on T-bill rates, though they are designed to be conservative. Question is if 50K will be what is written on those checks or if it will be adjusted for inflation. If so, you should see the pension fine print on how inflation is calculated.

#### MDM

• Walrus Stache
•       • Posts: 9246 ##### Re: Determining the Value of a Future Cash Flow
« Reply #2 on: July 28, 2015, 06:07:34 PM »
The math part is reasonably straightforward.
First calculate the Future Value of \$50K/yr with return "r" lasting 38 years.  This gives the amount you would have in your account at the end of that time.
Then you need to calculate the Present Value of that Future Value.  In your case, you have to discount the FV by 38+11=49 years, at some discount rate "i".

The hard parts are picking what to use for "r" and "i" - so you ask a good question.  You might want "r" to represent the return you can expect on investing that money (assuming you will invest it), and "i" to be the inflation rate that gives you an idea of how much that result will buy in today's dollars.

A couple of defensible numbers, off the top of my head, are 8% for a long term return and 3% for inflation.

Depending on whether you assume the \$50K is invested at the start or end of the year, the final answer would be ~\$2.6-\$2.8 million using the numbers above.

E.g., using Excel functions:
FV(8%,38,-50000,0,1) = \$11,897,061
PV(3%,49,0,-11897061) = \$2,795,218

#### beltim

• Magnum Stache
•      • Posts: 2823 ##### Re: Determining the Value of a Future Cash Flow
« Reply #3 on: July 28, 2015, 06:53:10 PM »
E.g., using Excel functions:
FV(8%,38,-50000,0,1) = \$11,897,061
PV(3%,49,0,-11897061) = \$2,795,218

That number doesn't pass the sniff test.  \$2.8 million would provide \$112,000 per year using the 4% rule, with at least a 90% chance of paying out more than 30 years, and that's inflation-adjusted.  It makes no sense that the present value of a pension that pays out \$50,000 a year, that doesn't start for 11 years, to be so much.

I think you're using the FV function incorrectly.

#### MDM

• Walrus Stache
•       • Posts: 9246 ##### Re: Determining the Value of a Future Cash Flow
« Reply #4 on: July 28, 2015, 06:54:49 PM »
E.g., using Excel functions:
FV(8%,38,-50000,0,1) = \$11,897,061
PV(3%,49,0,-11897061) = \$2,795,218

That number doesn't pass the sniff test.  \$2.8 million would provide \$112,000 per year using the 4% rule, with at least a 90% chance of paying out more than 30 years, and that's inflation-adjusted.  It makes no sense that the present value of a pension that pays out \$50,000 a year, that doesn't start for 11 years, to be so much.

I think you're using the FV function incorrectly.

Calculations above assumed complete investment of each year's \$50K.  The other extreme is complete spending of each year's \$50K.  In that case, there are no returns and one "merely" needs to pick a discount rate.
First, calculate the Present Value of 38 years of \$50K/yr at discount rate "i".
Then, discount that result by dividing the PV by (1+i)^11 to bring it all the way back to today.

Alternatively, calculate the Net Present Value of 11 years of \$0 followed by 38 years of \$50K.

E.g., using Excel functions:
PV(3%,38,-50000,0) = \$1,124,623
1124623/(1+0.03)^11 = \$812,452
or
NPV(3%,some range with 11 zeros followed by 38 values of 50000) = \$812,452

#### Another Reader

• Magnum Stache
•      • Posts: 4835 ##### Re: Determining the Value of a Future Cash Flow
« Reply #5 on: July 28, 2015, 06:55:17 PM »
The math part is reasonably straightforward.
First calculate the Future Value of \$50K/yr with return "r" lasting 38 years.  This gives the amount you would have in your account at the end of that time.
Then you need to calculate the Present Value of that Future Value.  In your case, you have to discount the FV by 38+11=49 years, at some discount rate "i".

The hard parts are picking what to use for "r" and "i" - so you ask a good question.  You might want "r" to represent the return you can expect on investing that money (assuming you will invest it), and "i" to be the inflation rate that gives you an idea of how much that result will buy in today's dollars.

A couple of defensible numbers, off the top of my head, are 8% for a long term return and 3% for inflation.

Depending on whether you assume the \$50K is invested at the start or end of the year, the final answer would be ~\$2.6-\$2.8 million using the numbers above.

E.g., using Excel functions:
FV(8%,38,-50000,0,1) = \$11,897,061
PV(3%,49,0,-11897061) = \$2,795,218

The OP is looking for the present worth of a future stream of income payments.  Computing the future worth at the anticipated investment rate of return and then discounting it back at the rate of inflation does not accomplish that objective.

The problem is how long will you receive the income stream (i.e. when will you die), is the pension COLA'd, and what's an appropriate discount rate.  Nords had a couple of good articles on this as it applies to military pensions over at his blog and it's been discussed on several threads over at early-retirement.org.

The discount rate should consider the risk of the pension.  If it's a military or federal pension or a fully funded state or local government pension, the risk component should be lower than if you work for the City of Detroit or a shaky corporation.

I collect two fairly solid pensions and in the future I will collect Social Security.  I am closer to collecting Social Security than the OP is to collecting the pension.  All three are weakly COLA'd in my opinion, so I use 2 percent for the COLA on all three.  I used a termination year based on my anticipated life expectancy tempered by my family history.  I was conservative in the choice of discount rate, adding a risk premium of three percent to an estimated 3 percent risk free return over 20 plus years.  That's a little better than a WAG, but not perfect.  The total discount rate I used was 6 percent.  You can make an argument that the present worth of the lump sum at the time the pension starts should only be discounted by the anticipated rate of inflation, but my view is the risk premium should apply during the deferral period.

#### beltim

• Magnum Stache
•      • Posts: 2823 ##### Re: Determining the Value of a Future Cash Flow
« Reply #6 on: July 28, 2015, 07:04:02 PM »
Calculations above assumed complete investment of each year's \$50K.

That's not what the OP asked for, hence my confusion.

Quote
The other extreme is complete spending of each year's \$50K.  In that case, there are no returns and one "merely" needs to pick a discount rate.
First, calculate the Present Value of 38 years of \$50K/yr at discount rate "i".
Then, discount that result by dividing the PV by (1+i)^11 to bring it all the way back to today.

Alternatively, calculate the Net Present Value of 11 years of \$0 followed by 38 years of \$50K.

E.g., using Excel functions:
PV(3%,38,-50000,0) = \$1,124,623
1124623/(1+0.03)^11 = \$812,452
or
NPV(3%,some range with 11 zeros followed by 38 values of 50000) = \$812,452

That's much more reasonable.

#### Yankuba

• Handlebar Stache
•     • Posts: 1357
• Location: Long Island, NY ##### Re: Determining the Value of a Future Cash Flow
« Reply #7 on: July 28, 2015, 07:04:52 PM »
An online calculator says the 38 payments of \$50k (using a three percent rate) starting today is worth \$1.1mil - so then I need to discount that for 11 years at a rate of six percent (what I think returns will be) and I get \$816k. I think that sounds right. Thanks everyone!

#### MDM

• Walrus Stache
•       • Posts: 9246 ##### Re: Determining the Value of a Future Cash Flow
« Reply #8 on: July 28, 2015, 07:09:28 PM »
The OP is looking for the present worth of a future stream of income payments.  Computing the future worth at the anticipated investment rate of return and then discounting it back at the rate of inflation does not accomplish that objective.

Yes, specifying what is done with each year's \$50K (invest all, spend all, spend some and invest the rest in some constant or linearly- or exponentially-increasing fashion, etc.) is one part of the puzzle: see reply #4 for "the other" extreme.

Another big part of the puzzle is "what will one do with the calculated number?"  Knowing that would bound much of the speculation we could otherwise do.

#### MDM

• Walrus Stache
•       • Posts: 9246 ##### Re: Determining the Value of a Future Cash Flow
« Reply #9 on: July 28, 2015, 07:19:17 PM »
An online calculator says the 38 payments of \$50k (using a three percent rate) starting today is worth \$1.1mil - so then I need to discount that for 11 years at a rate of six percent (what I think returns will be) and I get \$816k. I think that sounds right. Thanks everyone!

Yankuba, if you don't mind, what are you going to do with this number?  Would anything change if the answer had been twice that?  ...half that?

In any case, good luck with whatever you do!

#### Yankuba

• Handlebar Stache
•     • Posts: 1357
• Location: Long Island, NY ##### Re: Determining the Value of a Future Cash Flow
« Reply #10 on: July 28, 2015, 07:28:41 PM »
An online calculator says the 38 payments of \$50k (using a three percent rate) starting today is worth \$1.1mil - so then I need to discount that for 11 years at a rate of six percent (what I think returns will be) and I get \$816k. I think that sounds right. Thanks everyone!

Yankuba, if you don't mind, what are you going to do with this number?  Would anything change if the answer had been twice that?  ...half that?

In any case, good luck with whatever you do!

A friend at work took a job in the private sector and we were trying to figure out how he could construct an annuity that would match the pension he would have otherwise received.

#### MDM

• Walrus Stache
•       • Posts: 9246 ##### Re: Determining the Value of a Future Cash Flow
« Reply #11 on: July 28, 2015, 08:01:40 PM »
A friend at work took a job in the private sector and we were trying to figure out how he could construct an annuity that would match the pension he would have otherwise received.

Ok.  In that case, one still needs to know if the \$50K is constant, has a COLA, is in present dollars, future dollars, etc.

Assuming \$50K in 2026 dollars, no COLA, 6% nominal returns, and a 38 year payout that depletes all funds:
- a \$414,500 lump sum now will grow to ~\$787K in 11 years, and \$50K/yr can be withdrawn each year for the next 38 years.

Assuming \$50K in 2026 dollars, 3% COLA, 6% nominal returns, and a 38 year payout that depletes all funds:
- a \$618,100 lump sum now will grow to ~\$787K in 11 years, and \$50K/yr (increasing by 3% annually) can be withdrawn each year for the next 38 years.

A COLA can be very valuable.

And the numbers above assume constant 6% returns.  As the Trinity study et al. indicate, assuming constant returns is optimistic.  But we're just playing "what if?" here....

#### tooqk4u22

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•     • Posts: 2195 ##### Re: Determining the Value of a Future Cash Flow
« Reply #12 on: July 30, 2015, 02:42:18 PM »
As you can see there are a lot of ways to slice and dice this.....I will try a simple one MMM style.

\$50k in today's dollars assuming 3% inflation over 11 years would equal 36k - apply the 4% rule and you would need the equivalent of \$903k today.

#### NorCal

• Pencil Stache
•    • Posts: 660 ##### Re: Determining the Value of a Future Cash Flow
« Reply #13 on: July 30, 2015, 03:14:58 PM »
The NPV function in Excel is the appropriate way to get there.  Use \$0 for all the years until the pension starts paying out.

To be technically accurate, your discount rate should be your personal discount rate.  If I was using a 4% SWR in retirement, this is what I would use for my real discount rate.

You can add in inflation assumptions if you want the nominal value (which may be valuable as well). 