Eye Opening Calculations with Compact CVTVR L

I have placed Compact Calculator CVTVR L into my Yahoo Briefcase. CVTVR L is a two step calculator. It is great for long-term planning.

During the first period, you invest entirely in TIPS. You specify the number of years N and the TIPS interest rate, which is currently 2.4%. You specify your withdrawal rate during this period.

The calculator tells you how much you have drawn down your principal at the end of N years.

Following this first step is a standard, 30-Year, Compact Variable Terminal Value Rate calculator. I have adjusted its display so that all withdrawal rates are in terms of the initial balance. I have adjusted its internal calculations to report the percentage balance at the end of 30 years in terms of the initial balance.

The display shows you the withdrawal rates for the second period, the last 30 years. Using these rates, you end up with the specified percentage balance (i.e., the terminal value percentage) at year N+30.

If you wish to bypass the first step, enter N=0. Ignore the “Withdrawal Rate that lasts exactly N years.” Everything else will be in order.

As always, I have adjusted all rates to match inflation. As is usually true, I have assumed that stock portfolios have expenses equal to 0.20% of their current balances.

Here are some sample calculations:

Exceedingly pessimistic outlook:

First period: N=10 years.
Interest rate during the first period: 2.40%.
Withdrawal Rate during the first period: 3.00%.
Terminal Value Percentage: 75%. (This is 75% of the initial balance at year 40).

From cell E15, you still have 93.3% of your original balance at year 10.

Second period P/E10: 20.00.
Second period TIPS interest rate: 2.00%.

From the display, you see that you will be able to continue withdrawing 3.0% for another 30 years if you allocate 80% to stocks and 20% to TIPS. You are better off with 80% stocks than with either 50% stocks or 100% stocks.

From the table with optimized stock allocations, you can read the allocation that gives the highest Safe Withdrawal Rate in cell K32. It is 72.3%. The highest Safe Withdrawal Rate during the second period is in cell L32. It is 3.23%.

Even with this exceedingly pessimistic outlook, during which stocks remained at a historically high level of P/E10=20, you would still end up with 75% of your initial balance at year 40.

Pessimistic, but reasonable, example:

Now change the withdrawal rate during the first period to 4.00%.
Change P/E10 at the start of the second period to 14.00, which is a historically typical level.

From cell E15, we read that you would have 82.2% of your original balance at year 10.

This time, you are best off if you put all of your money into stocks during the second period. The Safe Withdrawal Rate during the second period is just above 4.00% with 100% stocks. [By looking at cell H97, we find that it is 4.05%.]

Under this more reasonable set of assumptions, with P/E10=14 at year 10, even though still pessimistic, you would be able to withdraw 4.00% of your initial balance for 40 years. At year 40, you would have still 75% of your initial balance.

Optimistic, but reasonable, example:

We change the withdrawal rate during the first period to 5.50%.
We change P/E10 at the start of the second period to 8.00, which is below the historical typical level but well above the lowest extremes.

From cell E15, we read that you would be down to 65.4% of your original balance at year 10.

Under these optimistic but reasonable assumptions, with P/E10=8 at year 10, you would be able to withdraw more than 6.00% of your initial balance during the next 30 years with 100% stocks. Or 5.40% with 80% stocks. At year 40, you would have still 75% of your initial balance.

Mixed, Optimistic and Pessimistic, Worst Case example:

Use a 4.00% withdrawal rate during the first period. But increase N from 10 years to 20 years.

From cell E15, we read that you have 59.5% of your original balance at year 20.

Use P/E10=8 for the second period. You can expect to see bargains such as this at least once during the next 20 years.

Under these conditions, with P/E10=8 at year 20, you would be able to withdraw 5.37% of your initial balance during the following 30 years with 100% stocks. Or 4.81% with 80% stocks. At year 50, you would have still 75% of your initial balance.

Excursion:

Assume a TIPS interest rate of 2.00% throughout the entire 50 year period. You would still be able to 4.00% for 50 years. You would still end up with 75% of our original balance.

Have fun.

John Walter Russell
July 28, 2006