Present value is present value

I took a shortcut in my previous post: I said reserves in 1995 would have cost $275 per month.  This is wrong.

1. The starting point was my estimate that the near-term change to our water bills after RDOS takeover will be something like $500 per month.
2. The value of $500/month in 1995 dollars is about $295.  I am not sure where I got $275 in my original post.  Dumb math error or failing eyesight.  The consumer price index was 91.6 for 1995 and 155.2 for 2024.  So what $1 buys today could be had for $0.59 in 1995.
3. In any case, both $295 and $275 are much too high.  Solving for the correct number is a bit trickier because it involves two opposing rates: inflation and interest.

One way to make sense of this is to lay it out year-by-year in Excel.  To start with, let's keep it simple and assume the RDOS borrows what it says it wants to borrow for all phases of the water system upgrade: $33M.  I have been using the McElhanney number of connections in my calculations (244) so that means the share of the capital cost allocated to each connection is about $135K*.  Let's assume the Water Comptroller in 1995 decided to start building a reserve fund so that the Sage Mesa Water System could fully replace its aging assets in 2025.  In the first year, each household is billed an additional $157 each month on its water bill (I get that our water bills are currently quarterly, but multiply by four as required).  This amounts to $1888 per connection per year, which the Water Comptroller puts in a trust account earning 4%.  What happens to $1,888 if it is left in a bank account for 30 years earning 4%?  It is worth $5,890.70 at the end of 2024.  This is in the "Future Value" column.

Assuming that inflation is about 2%, in the following year, the Water Comptroller increases the monthly reserve contribution to $160.55 per household.  In this way, the purchasing power of the reserve contribution is kept constant.  Using such "real dollars" is how the Comptroller accounts for increases in the cost of the replacement system over time.   As before, the contributions are added to the trust and your share of the 1996 contributions is worth $5777.42 by the end of 2024.  If the Water Comptroller continues to do this for 30 years, the reserve fund will contain $135K per connection.  The $33M cost of the system can be paid for at the start of 2025 by cashing out the trust (and restarting the reserve-building process, of course).

Obviously, the Comptroller of Water chose not to do this.  One reason is the size of the numbers.  Your contribution to reserves in 2024 would have been an additional $3,354 on your water bill.  And you still would have had to put up with boil water advisories.

Note, however, that there was nothing stopping you from doing this without the Water Comptroller.  You could have opened an investment account and each month deposited the equivalent of $157.41 in 1995 dollars.  If you had done this and earned 4% per year, you would have $135K in the bank today and could easily pay your share of the capital costs of the upgrade.

But what if you did not do this?  What if instead you contributed to your pension, or paid your mortgage, or bought food and clothing?  From an economic point of view, it makes no difference.  By not contributing to either the Water Comptroller's reserved fund or your own reserve fund, you saved money and are richer as a result.  How much richer?  See above: $135,245.90.  If you don't feel richer—and I am certain you do not—you can look at it this way: you would be $135,245.90 poorer if the Water Comptroller had forced you to pay reserve contributions on the schedule above.

If, in contrast, the system is debt-financed (which is the only real option at this point), things look a bit different.  First, the initial monthly payment is much higher: $651 per connection per month (recall, I am assuming the whole $33M in Year 1 here).  However, it is important to recognize that debt payments, as opposed to the reserve contributions above, are in nominal, not real dollars.  The number never changes over the life of the loan.  This means that, thanks to inflation, the purchasing power of the payment decreases over time.  Moreover, these cashflows are in the future, so they are worth less (the "Present Value" column below).  But here is the critical point: The present value of these debt payments over 30 years is $135,245.90—which is exactly what you saved by not having to pay into a Sage Mesa Water System reserve fund for the last 30 years.

This is why I say in my original post that it does not matter whether you started paying into reserves 30 years ago or are starting to pay back debt for the next 30 years.  The present value is the same $135K.

Where this does make a difference—a big difference—if you paid into reserves for 29 years and then left the neighborhood before the upgrades.  Maybe got that money back when you sold your house (when the new buyers examined the water system's balance sheet and noted the large replacement reserve).  But my guess is not.

My point in all this is not to suggest that everything is fine.  $135K per connection is not fine at all.  Rather, my point is that ratepayers are currently on the hook for the same amount either way.  There is little use—at least for people who have been here a long time and plan to stay here a long time—in getting bent out of shape over the timing of cash flows.  It is the size of the cash flows that should be the focus.

*   As I noted in my original post, the initial capital cost will be a bit lower than this due to phased implementation.  However, the total cost will be higher since this is capital only; it does not include operations and maintenance (O&M).  It is also important to point out that the capital costs of the upgrades will be paid for over many years on our periodic water bills.  No one is getting a bill for $135K if the RDOS takes over the system.  But I get that some people like to think of this as their share of the debt.  It helps them to feel anxious.