Investing INside or OUTside an RRSP: the Math |
Sam and Sally each have $A per year to invest, for N years. Sam invests INside an RRSP, Sally OUTside an RRSP. Sam gets a Return on his investment of R_{1} (for 12.3% Return, R_{1}=.123) and Sally gets R_{2}. If Sally is an active trader ... buying, selling, buying ... then R_{2} is her net gain after paying the taxes on the capital gains. They are both in a tax bracket of T_{1} (for a 45.6% Tax Bracket, T_{1}=.456). After paying the taxes, Sally is left with A(1-T_{1}) to invest. At the end of the N years, their portfolios are: Sam: P_{1} = A {(1+R_{1})^{N}-1}/R_{1} Sally: P_{2} = A(1-T_{1}){(1+R_{2})^{N}-1}/R_{2}
Now comes the hard part.
In retirement, Sam and Sally are each in a tax bracket of T_{2}.
So what are her gains?
We go slowly here ...
If'n it ain't capital, then y'all kin change the (3/4).
I'n y'all kin get a better return OUTside ... then ... the "miracle of compound interest" ...
Check this out: DOW vs TSE P.S. If'n ya got Excel, there's a .ZIP'd spreadsheet y'all kin download ... to play with: RRSP: IN_or_OUT? ... ain't Math wunnerful? One more thing: To get a feel for how much more you'll need (in terms of Return on Investments) in order that investing OUTside gives y'all more money than investing INside, consider this approximate, quick-and-dirty calculation: Suppose Sam begins with $A and, after umpteen years of investing INside, this money grows by a factor F, so his portfolio is now AF. He cashes it in, paying taxes at the rate T (for a 44% tax rate, we put T=0.44), and is left with:
Sally, on the other hand, invests what's left of the $A after she pays taxes at the rate T, namely A(1-T), and, after umpteen years, we suppose it grows by a factor G. She now has a portfolio worth A(1-T)G. She then cashes in, paying taxes at the rate (3/4)T ('cause her capital gains are taxed at a lower rate), leaving her with:
Does Sally have more after-tax money? She will, if A(1-T)G(1-3T/4) > AF(1-T), that is, if
Moral? Provided she gets a sufficiently bigger return on her OUTside investments, she'll come out ahead ... after taxes. For example, if Sam's return is 10% per year for 30 years, then his gain is F = 1.10^{30} = 17.4 and if the tax rate T corresponds to 44%, then T = 0.44 so F/(1-3T/4) = 17.4/(1-.33) = 26.0 and we conclude that Sally's thirty-year gain should exceed 26.0 in order to beat ol' Sam. Sounds a bunch, eh? However, it corresponds to 26.0^{1/30} - 1 = .115 or 11.5% per year^{*} (roughly). It doesn't sound like much of an increase over INside investment returns ... but what are the chances of doing that? Slim?
Of course, Sally doesn't really pay taxes on all of her portfolio - some of it
is after-tax contributions. Further, the tax rates during the investing phase needn't be
the same Maybe it's mostly dirty ...
^{*} In general, the Quick-and-Dirty formula is like so: For I = 0.10 (10% return) and g = 0.50 (Cap. gains taxed at 50%), the Quick-and-Dirty extra return required (over and above the INSIDE return) is 1.10/(1-T/2)^{1/N} - 1.10 and depends upon N and T ... look like so:
See also the Calculator |