How big of a deal is it to randomize the discount rate in a SPV liability calc?

This is neither very thorough nor particularly scientific. This is me going back into amateur hack territory.  In some past posts I had ginned up a stochastic present value (SPV) of a spending liability in order to get a distribution of NPVs I could perhaps choose amongst for the purposes of working on a household balance sheet. But I had only randomized the cash flow (numerator) and not the discount rate (denominator, which appears to be a "more correct" way to do it) so I was kinda cheating a little bit before.  My goal here is pretty simple. I wanted to see how big of a deal it would be and what kind of impact there would be on the shape of the NPV distribution by shaking up the denominator.  In other words, would the 95th percentile be something like $3M or would it be a hundred trazillion? I'll just use one set of parameters and see if it blows up or stays normal (normal normal not statistics normal).

Here is the basic deterministic setup. Forgive me if I botch the notation:

• Cash flow : 100k, inflated at 3% stepped down 20% at 68 and 20% at 85. No randomness.
• Mortality assumptions from the SOA IAM table with G2 extension.
• Discount rate is 4% which is entirely arbitrary and for illustration.  
• Deterministic present value is calculated like an annuity: 

Here is the basic setup for the stochastic present value calc:

• Cash flow : 100k, inflated at 3% stepped down 20% at 68 and 20% at 85 but note that here it is also now randomized with draws on US inflation history and a factor for spending variance above and beyond inflation.  Inflation is seeded at 3% +/- std dev .01 which is arbitrary and illustrative.  Spending variance, if used is +/- .10 std dev of prior period spending.   There are no current or future contributions, this is a spending outflow. 
• Mortality is embedded in the length of the sim years within each iteration as determined by a draw from a distribution based on Gompertz math that is kinda sorta tuned to the SOA IAM data.  The number of years is L-N in the equation below where L is 120 and N is the random age drawn. 
• The discount rate is randomized using (an arbitrary) 4% +/- 10% std dev.  The discount is chained into a geo return and a variance of zero would make the denominator the equivalent of (1+d)^t.  
• The result of the sim is an spv distribution.

Rather than go crazy I just wanted to see what would happen. Note that this is a rudimentary spreadsheet sim so the approach is simplified and the number of iterations are relatively small.

The scenarios can be summarized like this:

0 - the deterministic calc
A- the baseline sim with nothing varied except inflation. EV should be close to case 0
B- the sim with the denominator discount rate randomized
C- the denominator discount rate is randomized and spending in numerator is randomized
D-only the numerator spending variance (and inflation) are randomized

The resulting chart looks like this:

And some summary stats...

So this is pretty rough and it's tough, without being more thorough, to make any firm conclusions but the answer to the question is that randomizing the discount didn't "blow up" this simple scenario and make the 95th percentile a hundred trazillion.  I still favor using fixed discount rates for policy and/or sensitivity purposes but at least I know I can do this in a spreadsheet and know how I can do it in R if I have to.