## Tuesday, February 15, 2011

### How Tax-Free Compounding Helps

After reading about mental blocks on RRSPs, reader Robert asked for an explanation of the value of tax-free compounding in an RRSP. Here is my paraphrase of the essence of his question:
Starting with the example of a 40% marginal tax rate, an investor can either save \$6000 in a non-registered account or \$10,000 in an RRSP (and get a \$4000 tax refund for the same \$6000 out of pocket amount). With an 8% return in the first year, the RRSP would grow to \$10,800 and the non-registered account would grow to \$6480.

However, if the investor withdraws the RRSP money and pays taxes on it, he will have \$6480 left. This is the same amount as was in the non-registered account. How is the RRSP any better?
The short answer is that we haven’t accounted for the income taxes on the non-registered gains yet. Any interest would be taxed at 40%, capital gains at 20%, and dividends at around 19%. Even if the gains are all capital gains, the investor would have to pay taxes before he could spend the money.

In just one year the advantage of the RRSP is modest, but it can be substantial over a lifetime. I put together a spreadsheet covering 35 years of contributions and 25 years of retirement for the RRSP and non-registered cases. The following assumptions are built into the calculations:

– 8% return each year (70% capital gains, 20% dividends, 10% interest)
– 4% inflation each year
– marginal tax rate 40% (This stays constant so that we can isolate the value of tax-free compounding from changes in tax rates.)
– 10% of equities turn over each year during the saving phase (no turnover during retirement)
– \$6000 saved per year in non-registered account (\$10,000 in RRSP) growing with inflation
– find the constant yearly withdrawal amount (in today’s dollars) that exhausts the money in 25 years

Final results of yearly (after tax) withdrawals in today’s dollars:

RRSP: \$26,985
Non-registered: \$18,574

This is a substantial difference in yearly after-tax spending money. With these assumptions the RRSP is clearly the better choice. Under the assumption of a constant marginal tax rate, a TFSA works just as well as an RRSP.

There are circumstances where using an RRSP is not in an investor’s interests, but this is usually when the investor’s marginal tax rate is higher in retirement than it was while working. For most people it makes sense to use RRSPs and TFSAs.

1. Very nice spreadsheet. Where I had a problem was that I couldn't find "tax-free compounding". What you're saying is that the value is in avoiding tax leakage. And you're right, of course, that avoiding tax leakage becomes very valuable.

2. @Robert: "Tax-free compounding" in RRSPs refers to the fact that no taxes are charged from year to year (unless you make a withdrawal). Your investments get to grow for years without paying tax until you retire.

3. Fantastic. I love arguments base on data !!

4. @P2Sam: Just about all my arguments come down to numbers in one way or another. Glad you liked it.

5. Very interesting.... I made a similar one for myself last week, comparing RRSP, TFSA and unregistered investments, comparing returns, taking into account dividend taxation, withholding tax, etc. It's fascinating how quickly RRSPs turn into the best investment, and canada-only (and non-dividend) investments are fine in TFSA, but everything else suffers from tax leakage somewhere.

However, I think it would be logical to place your best assets in a TFSA, since it won't be taxed. (ie, bonds in RRSP and equities in TFSA as far as possible).

6. @Paul: You make a good point about U.S. dividend withholding taxes in TFSAs. That is one instance where RRSPs win out over TFSAs even if marginal tax rates remain the same.

7. Isn’t there one scenario where it is better to save outside an RRSP, namely, if a person’s total expected retirement income is low enough to qualify them for GIS payments?

In that case, since RRSP withdrawals are taxable, they count into total income and could cost the individual free government money.

The odds are, however, that no one reading your blog is likely to be in that situation, so you may justifiably have decided to ignore that scenario.

8. @Terry: My analysis was based on constant marginal tax rates. As I mentioned in the last paragraph, if your marginal tax rate is higher in retirement than it was while working, RRSPs may not be the best idea. The clawback on GIS payments adds a whopping 50% to your marginal tax rate. This is a clear case where RRSPs can work out badly.

9. Great examples to answer the reader's question. It might have been interesting to include a third, TFSA, condition.

1. @John: Under the assumptions I made, the TFSA case looks the same as the RRSP case. Things get different if you start looking at changes in marginal tax rates. Another smaller difference comes if you earn U.S. dividends in a TFSA. The most likely scenarios involved a mix of RRSPs and TSFAs.