Why does it seem unnecessary to fully save for irregular periodic expenses?

Question

I have been trying to plan out a budget for the next 12 months, due to a goal to pay off a certain debt in that period of time, so every penny counts. However, I have run across an unusual and non-intuitive problem and am a bit stumped on what it means.

It is my belief that in order to avoid unexpected expenses it is necessary to save ahead for those expenses so that in the month that the bill comes due, the money is completely saved and ready to pay the expense. I have ten such expenses in my budget, and I am transferring the total monthly amount for each of these expenses into a savings account. These expenses occur every 3, 6, 12, or 24 months at staggered months (*), so I divide the expense amount by the number of months between occurrences to get the monthly amount to save.

(*) i.e. one monthly expense is in January, another in May, etc. in no particular interval, instead of all being in the same month, and the same is true for the expenses with other intervals.

However, since I started this savings plan in the middle of the year, some of the expenses are occurring before the required number of months have occurred: for example, property taxes occur at the end of each year, but nothing was saved for the first four months, so I take the amount that should have been saved in those first four months and save it now for the initial balance in the account.

Now the problem is, when I run out the projected balances over the next 12 months, I see that this savings account always has a lot more money than it needs to have - it never gets anywhere close to zero. This balance usually stays at least four times the monthly amount that needs to be saved. So I created a spreadsheet for the next 5 years, and I got the same result: the actual balance never drops below 4x the monthly amount I am saving! And in fact, if I look at the average amount spent per month over time it seems to start converging on a lower amount than the monthly amount that I am saving. But when I look at all the math, I have checked and re-checked, but don't see any mistakes:

• I am dividing each expense by the number of months between occurrences to get the monthly amount to save, and summing those to get the total monthly amount
• I am pre-saving the monthly amount for all previous months since the last expense to "catch up" to where I should be.
• Each month I add the sum of calculated monthly expenses to the savings account
• Each month I subtract off the actual expenses for that month, which I have triple-checked are correct
• In the month that a given expense is actually paid, the balance for that expense reaches zero, further suggesting that there are no math errors.

So am I incorrect that I need to save in this way? Why is there all this extra money in savings that I never seem to need?

Answer 1

Another way of explaining the puzzling balance:

Right after a particular bill is paid, you have $0 saved to pay that bill the next time. Just before the bill is next due, you wisely have the whole amount saved; that's the purpose of the whole process. So, for that bill, on average over time, you'll have one-half that upcoming bill in the account.

But the same argument holds for every one of the upcoming bills. So, for a large number of bills, with varying sizes and times between occurrence, the average amount in the account will be approximately one-half of the total amount of all the bills that you're saving for.

Answer 2

I think we'd need to look at actual numbers to see where you're running into trouble.

I'm also a little confused by your use of the term "unexpected expenses". You seem to be using that to describe expenses that are quite regular, that occur every X months, and so are totally expected. But assuming this is just some clumsy wording ...

Here's the thing: Start out by taking the amount of each expense, divided by the number of months between occurrences. This is the monthly cost of each expense. Add all these up. This is the amount that you should be setting aside every month for these expenses, once you get a "base amount" set up.

So to take a simple example: Say you have to pay property taxes of $1200 twice a year. So that's $1200 every 6 months = $200 per month. Also say you have to pay a water bill once every 3 months that's typically $90. So $90 divided by 3 = $30. Assuming that was it, in the long term you'd need to put aside $230 per month to stay even.

I say "in the long term" because when you're just starting, you need to put aside an amount sufficient that your balance won't fall below zero. The easiest way to do this is to just set up a chart where you start from zero and add (in this example) $230 each month, and then subtract the amount of the bills when they will hit. Do this for some reasonable time in the future, say one year. Find the biggest negative balance. If you can add this amount to get started, you'll be safe. If not, add this amount divided by the number of months from now until it occurs and make that a temporary addition to your deposits. Check if you now are safely always positive. If not, repeat the process for the next biggest negative.

For example, let's say the property tax bills are April and October and the water bills are February, May, August, and November. Then your chart would look like this:

Month     Add    Subtract     Balance
January   $230         $0        $230
February   230         90         370
March      230          0         600
April      230       1200        -370
May        230         90        -230
June       230          0           0
July       230          0         230
August     230         90         370
September  230          0         600
October    230       1200        -370
November   230         90        -230
December   230          0           0

The biggest negative is -370 in April. So you have to add $370 in the first 4 months, or $92.50 per month. Let's say $93. That would give:

Month     Add    Subtract     Balance
January   $323         $0        $323
February   323         90         556
March      323          0         879
April      323       1200           2
May        230         90         142
June       230          0         372
July       230          0         602
August     230         90         742
September  230          0         972
October    230       1200           2
November   230         90         142
December   230          0         372

Now you stay at least barely above water for the whole year. You could extend the chart our further, but odds are the exact numbers will change next year and you'll have to recalculate anyway.

The more irregular the expenses, the more you will build up just before the big expense hits. But that's the whole point of saving for these, right? If a $1200 bill is coming next week and you don't have close to $1200 saved up in the account, where is the money coming from? If you have enough spare cash that you can just take the $1200 out of what you would have spent on lunch tomorrow, then you don't need this sort of account.

Answer 3

If you just had one expense once a year of $1200, you would put in $100 a month. The average balance is going to be $600 in that case - the 0 and $1200 months average to $600, as do the $100 and $1100, the $200 and $1000, and so on. If you had one expense twice a year of $600 and put in $100 per month it will average to $300. You have a mix of 3/6/12 months - does 8 months seem reasonable as an "average" frequency? If so, there should be about a 4 month slush all the time.

Now instead of one expense averaged over 12 months, imagine 12 accounts, each needing $100 a month. If you started at zero, you would put in $1200 the first month and immediately spend it. One account would go from +100 (its share of what you put in) to -1100 while the rest are all at +100. Overall your balance would be zero. Then the next month you would again deposit 1200 and spend 1200, bringing one account to -1000, one to -1100, and the rest to +200. You average to zero actually on deposit because some of the "accounts" have negative balances and some have positive.

But aren't doing that. You "caught up" the months you were behind. So it would be like putting in $1200 for the first account, $1100 for the second, $1000 for the third and so on - a total of $7800. Then you take out $1200 and go down to 6600. The next month you put in $1200 and take out $1200 but you will always have that $6600 amount in there. All of the accounts will have positive balances - averaging $550 in this example.

Answer 4

It totally depends on when your expenses hit and whether you might have a larger stock than necessary. If you run your projections against the monthly save and the intervals of when you'll need the money, you might be able to extract some stock from the account.

I recommend making this a bit simpler. I operate this with an "annuals" account which is a complete aggregate of expenses that I know I have several times per year (or once every two years), but are not monthly or part of a weekly non-fixed expense budget cap.

Instead of tracking each expense individually and saving for it, create a spreadsheet that lists out all of these expenses, sum them, and then divide by 12. When I first opened this account, I added a one-time deposit to "catchup" to make sure I would never need to pull money from another source for these expenses. As new expenses come into existence that I should plan for annually, I simply add them to this list and adjust the monthly auto-deposit to the account. This also adjusts my single number weekly budget.

To make it easy, whenever I see an expense on my annuals list on my amex or debit, I simply initiate a withdrawal from the annuals savings and it will balance out my weekly or monthly budget expenses.

The goal of my annuals account is to simply avoid anti-windfalls that are known quantities (insurance, annual eye exam, sprinkler flush, amazon prime, etc) that would throw a wrench in weekly/monthly budget and expense planning. The more variables you can remove from your weekly/monthly, the more regular it becomes and the more likely you will be able to stick to a budget.