Tuesday, July 4, 2017

Nobody Knew Couples Budgeting Could be So Complicated

After we announced our new and improved ABC for retirees, Lori Fassman, (a fellow employee at The Wyatt Company in Boston and a singing goddess) asked us the simple question of how to use the ABC for Retirees spreadsheet to develop a spending budget or Actuarial Budget Benchmark (ABB) for a couple. This turned out to be a great question, and one that was also somewhat embarrassing to us, as we had clearly not given it sufficient thought.   So, this post will address budgeting for couples.  As we researched it, we felt a little like how our President felt about health care when he said, “Nobody knew [it] could be so complicated.”

What Makes Couples Budgeting So Complicated?

The short answer to the matter of couples budgeting is that applying the Basic Actuarial Equation is more complicated for couples than for individuals.

As we have discussed many times before, our approach to developing a spending budget in retirement is to apply the Basic Actuarial Equation, which balances the PV of total assets with the PV of total spending liabilities, of:

Accumulated Savings
PV Income from Other Sources
PV Future Non-Recurring Expenses
PV Future Recurring Annual Spending Budgets

The primary problem with the current version of the ABC for Retirees spreadsheet as it applies to couples is that it uses the same LPP to calculate
  • PV of Income from Other Sources
 as it does for the
  • PV of Future Recurring Annual Spending Budgets.
This is a problem because, if a couple’s Income from Other Sources (such as Social Security benefits, pension benefits, or life annuities) is expected to decrease or cease upon the death of one of the individuals, the left-hand side of the Basic Actuarial Equation (the assets) can be overstated by assuming the longer of the LPPs of each of the individuals in the couple.  Additionally, depending on the desired level of budget following the death of one individuals of the couple, the right-hand side of the equation (spending liabilities) may be understated.

How to Handle Couples Budgeting

We will add better budgeting for couples to our list of items to address in the next version of the ABC for Retirees.  In the meantime, this post will discuss two possible approaches that you can use in the interim:

  • a simple approximate approach and 
  • a more complicated (but more accurate) actuarial approach.
Simple Approximate Approach

The Actuaries Longevity Illustrator, which we recommend using to determine LPPs (no smoking, excellent health, 25% probability of survival) provides four planning horizons (or LPPs) for a couple:

  • Person #1 
  • Person #2 
  • Either Alive, and 
  • Both Alive
If you don’t want to crunch the numbers required under the more complicated (but more accurate) approach described below, we suggest that you use the Either Alive period for the LPP in the spreadsheet.  In most instances, this will probably produce a result that is sufficiently accurate for budgeting purposes.

More Complicated Actuarial Approach

If you want a more accurate budget, we encourage you to go back to the basics and perform the present value calculations in the Basic Actuarial Equation.  For this purpose, you can either use the PV calculation functions in the ABC for Retirees spreadsheet or the Present Value Calculator spreadsheet.

The Basic Actuarial Equation above can be restructured to solve for the current year’s spending budget as follows:

Current year’s spending budget
Accumulated Savings + PV IFOS ‒ PV Future Non-Recurring Expenses
                        PV of Future Years with Desired Increases

So, to determine current year’s spending budget, we need to determine:
  • Accumulated Savings 
  • PV Income from Other Sources (IFOS) 
  • PV Future Non-Recurring Expenses, and 
  • PV of Future Years with Desired Increases
Accumulated Savings and PV Future Non-Recurring Expenses for a couple are as determined for an individual, so they do not need to be specifically addressed here.

The first step in calculating a couple’s spending budget using the Basic Actuarial Equation is to calculate the PV of Income from Other Sources (IFOS), separately for each individual, based on the individual Person #1 and Person #2 LPPs, rather than one LPP for both and sum the results.  Remember that some benefits may continue or be reduced after the first expected death.

The second step is to calculate the PV of Future Years with Desired Increases for the couple. If you have followed us so far, this is where it just may get just a little too actuarial for you.

Depending on the desired budget after one of the couple dies as a percentage of the budget while they were both alive (Y%), the PV of Future Years with Desired Increases for the couple can be determined by applying the following formula:

PV of Future Years with Desired Increases (couple)
Y% of PV (Person #1 LPP)
Y% of PV (Person #2 LPP)
[2Y% -100%] of PV (Both Alive LPP)

Example Using More Complicated Actuarial Approach
So, for example, let’s say our couple consists of Jim, a 67-year-old male, and Mary, a 61-year-old female.  The Actuaries Longevity Illustrator tells us that the relevant LPPs for this couple, based on the recommended assumptions, are

  • 27 years for Jim 
  • 35 years for Mary 
  • 36 years for Either Alive and 
  • 24 years for Both Alive
The present values are at cell K18 of the Input and Results tab of the ABC for Retiree spreadsheet.  They are determined by entering the relevant LPPs in cell G25 of the ABC for Retiree spreadsheet with the current assumptions (4% discount rate, 2% inflation and 2% desired future increases).  In this example, they are:
PV of Future Years with Desired Increases
(from cell G25 of the Input and Results tab G25 of the ABC for Retiree spreadsheet)

Let’s assume that this couple agrees that the target spending budget after one of them dies is 67% (.6667) of the spending budget while they are both alive

Their PV of Future Years with Desired Increases is calculated as follows:

     .6667 x (21.2172) + .6667 x (25.6462) - .3333 x (19.3707) = 24.7876
Don’t want to go through these calculations?  Fine, as discussed above in the simple approximate approach, we suggest that you use the “Either Alive” years for your LPP.  In this example, you would be using a PV of Future Years with Desired Increases of 26.1530 (based on the 36-year Either Alive period in this example), but remember that you might be overstating your PV Income from other Sources (IFOS) and possibly understating your spending budget somewhat, depending on actual benefits and the desired decrease in the couple spending budget after the first death.

Thanks again to Lori Fassman for bringing this to our attention.  If anyone else has questions about the workbook or suggestions for improvement, we are always happy to receive them.