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.

Planning with Uncertainty – When can we retire? Or How much is Enough?

As we consider retirement we want to plan prudently and arrange our affairs wisely. But results depend on future conditions that can’t be exactly predicted. We must consider questions like -- How long will we live? What rates of return will investments earn? How much inflation will there be?

Uncertainty about the answers to questions like these don't make planning impossible or less useful -- just more complicated. Prudent planning means considering the various possibilities that could result and selecting as our plan the course of action with the consequences we like best.

For example, should we retire in 2009 after I turn 62, if we –

• have $400,000 in mutual funds

• no house payments

• can receive $18,000 per year in social security benefits

• spend $45,000 a year.

Is that enough to retire? What does "enough to retire" mean? And how do we figure out whether this amount is enough?

When we ask, “Is that enough?” we mean, “Is that enough assets so that they will not be used up before we die?” And we figure this out by doing calculations to see how long the assets will last and comparing the result with how long we are likely to live.

To calculate how long our assets will last we need to use their rates of return, inflation rates, and know how inflation will affect our social security benefits and spending. Even though these values can’t be reliably predicted we must use them to carry out the calculations.

There are several techniques for producing values to use in the calculations. A common approach is picking a single “average” value for each variable we need and then making the calculation as if the variables would stay constant at those values. The term “average” is placed in quotes because sometimes mathematical averages are calculated and used for the variables, and other times values are used that represent expectations about average future conditions. The calculation procedures are the same in either case. My next post will explain an example using this approach.