Monday, January 28, 2008

Calculating Projected Asset Balances – Assuming Constant Rates

Calculating projected asset balances after retirement is complex but not too difficult (if we ignore some complicating factors like the fact that there are actually many slightly different types of stock and bond funds). To calculate the projected values –

Each month –
  • Add planned income to the money market balance.
  • Subtract planned spending (adjusted for inflation) from the money market balance.
  • Add accrued interest and dividends to money market, bond, and stock accounts. 
  • Adjust stock and bond prices changing the values of the stock and bond funds.
  • If money market balance is below zero replenish the account by moving from bond funds.
  • Record ordinary income and capital gains for the month.
And each year –
  • Adjust income for inflation (as assumed in the plan).
  • Compare total assets (adjusted for inflation) with the starting value and adjust spending as planned.
  • Use the recorded income and capital gains to calculate income tax and deduct that amount from the money market account.
  • Move the planned share of total assets into stock funds.
  • Move the planned amount into the money market account.
  • Remaining assets are in bond funds – if bond balance is below zero replenish it by moving from stock funds.
Electronic spreadsheet programs, like Excel, were developed for doing this kind of calculations – but as explained in the previous post, we do need specific values for the variables involved. There are two types of variables –

Those that are part of our plan –
  • Planned income like social security, pension, etc. (not returns on assets)
  • Planned spending
  • Total assets at the start of retirement
  • Share of total assets we plan to hold in stock funds
  • Amount we will put into the money market account each year
And those that are generated by market process through time and are beyond our control –
  • Inflation rates
  • Interest and dividend rates
  • Changes in stock and bond prices.
As an example, Chart 1 shows the projected total asset balances after retirement that are implied by the plan described below the chart and assuming the following variable values – 
  • 3.5% annual inflation rate
  • 11.5% annual increase in stock prices
  • 1% annual increase in bond prices
  • 0.04% annual dividend rate for stocks
  • 6% annual interest rate on bonds
  • 4% annual interest rate on money market accounts.


With these assumptions the assets are projected to last a little more than 40 years (you can click on the chart to make it bigger). However, small changes in our assumptions about the future rates make quite big changes in how long the assets are projected to last, with no changes in our plan variables.  
For example, Chart 2 shows four cases calculated as described above with the following assumptions.
  Annual  Case 1          Case 2          Case 3          Case 4
   rates  yellow        turquoise  red              blue
Inflation            4%  2.5%  3.5%  3%
  rate
Stock Price  8.5%  10%  11.5%  13%
  change
Bond Price  -1.0%  -0.5%  1%  0.5%
  change
Stock Div  0.02%  0.03%  0.04%  0.05%
  rate
Bond                   7%  5.5%  6%  6.5%
  rate
Mmkt  5%  3.5%  4%  4.5%
  rate

We see that the same starting assets, managed exactly the same,  can get exhausted in about 20 years or build into almost two million dollars, depending on small changes in market rates. That means the market rates are going to be awfully important – and they are totally beyond our control. 

We see that a really hard part of deciding "how much is enough to retire" is deciding what future rates are likely to be.  We can't just casually pick some rates, they make too much difference. So how do we pick the rates to use?  Let's make that the subject of our next post.

7 comments:

Charlotte said...

We are constantly trying to figure out "how much is enough." Also, trying to reconcile... some people say you should plan for retirement first, and college funds next. I'm afraid we're going to come upon college for Savannah before we think we have "enough." Any thoughts?

Tyler H said...

what is the "months draw put into money-market each year: 20" ?

the "other income" = social security?

L Huntz said...

Charlotte - Part of the point of my posts is trying to express how hard it is to figure out "how much is enough" -- mostly because future rates and prices are critically important and impossible to predict. My experience suggests that how ever much you have saved for college is how much they will need. And if you don't have "enough" they will probably find a way to go anyway. Finally more is always better.
Tyler - Yes, by other income I mean income other than the returns on the retirement assets (stock, bond, and money market accounts). For us that will be Social security and payments we receive on the SLC house (which coincidently happens to be just what we need to make what we have enough).
On the "month draw ..." The way I am projecting the assets forward is -- Each month we will receive Social Security and the house payment and also each month we plan to spend one 1/12 th of annual spending amount. The spending minus the other income is what must be drawn from the money market account. So I call it the "month's draw." It is normally negative and makes the money market account balance smaller. Once each year I replenish the money market account at the same time as we reallocate between stock and bond funds into the ratios that are specified in our plan. Does that make sense??

Tyler H said...

But where does the "20" come from?

L Huntz said...

Tyler that is a good question -- the 20 is that we plan each year to put enough in the money market account to cover 20 months of "draw." That is, if we plan to spend $1000 more than our income each month then at the start of each year we put enough in the money market account to make the balance $20,000. I had started out putting in 18 months worth but found when running out the projections that quite often that wasn't enough to last a whole year. It wasn't enough because as the year goes on inflation raises the spending but not the income -- I assume it only gets adjusted once a year because that is the way they do social security. And when you pay taxes it also comes out of the money market account. So I found that if I planned to put 20 months (of draw) in then that was usually enough. Having to make unplanned movements between accounts generates taxable income and possibly capital gains, so I wanted to try to have that happen only once a year.

Tyler H said...

So you have to put almost twice as much money is as you plan to spend ?
did I get that right?
wow! And it is mostly because of taxes?

L Huntz said...

Tyler -- yes, we need almost twice what we expect to need so that we will almost never run out; but no, it isn't primarily because of taxes. Taxes are usually only about 3 to 4 thousand a year -- because there isn't much income. Most years the money market account isn't all used up by the end of the year and so we don't have to put that much more in to bring it back up to 20 months of draw. But every so often there is a lot of inflation or higher taxes (because stock or bond prices shot up and generated big capital gains) and then the money market funds get all used up. Does that make sense? I could run more cases with smaller amounts in money market and see if it makes much difference in how long the assets last. I suspect it wouldn't make much difference just be harder to actually execute. Which is why I did the plan the way I did. You know I like things simple (or at least like to think that I do).