Present marginal value of pension or Social Security

[forummm]

I'm trying to figure out what the marginal benefit to me is of working another year or taking another job. Salary is easy. Pensions and Social Security are a little more complicated.

Let's make the math easy. Using the SS formula, if I'm 37 and I work another year making $100k then at 67 I get another $1000/year (in 2016 dollars) in SS.  Let's say I expect to live until 87. What is the marginal benefit to me today of this increased SS payment? I did some spreadsheeting and it seems like the NPV (using the 30-year Treasury rate of 2.5%) of this future stream of payments is about $7k--which is about the amount of employee SS tax on that income. Does that sound right?

Similarly for a pension that 1) starts at 67, 2) is not adjusted for inflation until 67, and 3) pays out an additional $1000 per year for working at a $100k income for a year. Again let's say I expect to live until 87. If I add in an expected inflation rate of 2% to the 2.5% Treasury rate I get an NPV of about $3500. Does that sound right?

[beltim]

Yes, that's about what I get.  I'd use a slightly different methodology to get pretty similar figures.

[Systems101]

Let's start with one thing that impacts the entire OP: I don't understand why you discounted the SS dollars. 

The instant you say the future benefit of SS is $1000 in present (2016) dollars, to my mind, you have the answer: You don't need to discount it for inflation. 
If the present day $1000 (estimated future value of $2,098 when you are 67) continues to be indexed to inflation until you are 87, then the 2016 dollar value remains $1K per year.
Thus the sum of 20 years (87-67 = 20) is $20K in 2016 dollars.

Why did you discount it by the treasury rate?  What does that discount represent?

[forummm]

Let's start with one thing that impacts the entire OP: I don't understand why you discounted the SS dollars. 

The instant you say the future benefit of SS is $1000 in present (2016) dollars, to my mind, you have the answer: You don't need to discount it for inflation. 
If the present day $1000 (estimated future value of $2,098 when you are 67) continues to be indexed to inflation until you are 87, then the 2016 dollar value remains $1K per year.
Thus the sum of 20 years (87-67 = 20) is $20K in 2016 dollars.

Why did you discount it by the treasury rate?  What does that discount represent?

Assume you knew I was 100% credit worthy. Would you rather have $100 now or my promise to give you $100 adjusted for inflation in 30 years? You'd rather have the money now. There's a value to being able to use it now. That's one reason why people require loans to be paid back with interest (inflation and credit risk are the others). So I'm using the risk free rate to account for that loss of use. Not perfect since it includes a little bit for inflation. But I'm not trying to hit the moon with a rocket--just getting a decent idea of what working another year benefits me. At some point the amount of total value I'd get in return for working will fall below the amount I'd want to get in order to trade away my time and effort.

[Systems101]

You'd rather have the money now

If I have no dollars and I need to eat right now, yes.  But as part of a larger portfolio?  It depends.  If you assume no credit risk, by taking on the inflation risk in the example, you are providing value back to the person offered the future dollars.  It may make sense to have someone else bearing that risk for a portion of your portfolio, so it may actually provide value as opposed to being something where you attempt to extract value.  That transfer of risk is exactly what TIPS do vs. general treasury bills/notes/bonds.

Not perfect since it includes a little bit for inflation.

...or a lot for inflation, depending on your point of view.  The nominal rate is about 2.2%, the real rate is actually about 0.6%:
https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=realyield

So most of that 2.2% rate is expected inflation.  You'll note in the shorter time frames, people are actually paying the government to take on the risk of inflation... because the unexpected portion of the inflation is a higher risk than the expected portion that averages out over time.

At some point the amount of total value I'd get in return for working will fall below the amount I'd want to get in order to trade away my time and effort.

Of course.  At some point it's about your preferences of time / value of money.  e.g. The "what is an hour of your time worth" thread that is currently running on the forums...  And that's not to say you shouldn't ask for return above and beyond CPI-U inflation, as your personal rate of inflation may be higher... you may be more sensitive to health cost increases as you age and thus not following the CPI-U... you may want compensation for risk of Social Security law changing... lots of reasons, but the number picked for discounting is a "soft" number that will vary person to person, so it's hard for others to comment on your choice.

[forummm]

I didn't think about TIPS as the better rate to use. Looks like 30 year TIPS is yielding about 0.6% (plus inflation). That's an amazingly low interest rate.