Given it's already March 1, this probably comes too late to help people calculate their optimal TFSA/RRSP usage for the 2022 tax year. However, understanding these equations will be helpful toward planning your future registered account contributions.
First, assumptions and definitions:
This is pretty straight forward. Now let's suppose you contribute to an RRSP, which lets you obtain an immediate tax refund. The tax refund can then be contributed to a TFSA.
Notice that if t0 = tn, then the expression simplifies to "A × (1 + g)[sup]n[/sup]".
This means TFSAs and RRSPs yield the identical outcome if you contribute and withdraw at the same marginal rate!
Your TFSA vs. RRSP decision requires answering three questions:
We often see this question asked:
It should be obvious that if you have sufficient TFSA room, you should always use the TFSA before RRSPs during periods of lower income. You'll likely withdraw at the same or higher marginal bracket, not lower, so TFSAs can let you arbitrage the difference in current vs. future tax rates. On the other hand, what happens if you don't have enough TFSA room?
To analyze this situation, some further assumptions:
Notice that if m converges to zero (i.e., you deduct immediately), then tm = t0 and this expression is identical to one from above.
This illustrates an important point:
This is because you actually have three options when using a RRSP (where the TFSA is nearly maximized):
Notice that if g* converges to g, then the expression becomes:
Which is superior to the deferred deduction expression! This means if you have low tax drag (e.g., mostly capital gains versus interest income), then deferring the contribution will yield a better outcome than deferring the deduction. On the other hand, high tax drag where g* is significantly less than g will yield a worse outcome (e.g., receiving interest income at a high marginal tax rate).
There is no general solution for g* versus g that gives the optimal decision. But, using this expressions will make it much easier for you to test a few numerical solutions, especially since the expressions can be further simplified.
Since "A × (1 + g)^n" appears in four expressions, we can replace it with the constant "B". This gives us:
There are just five variables of interest:
First, assumptions and definitions:
- You have the amount $A available in your bank account
- Your current marginal tax rate = t0
- You have enough TFSA/RRSP contribution room to shelter $A
- Your investment portfolio will have an expected annual growth = g
Code:
Contribute $A to TFSA
Grows at rate g for n years
Proceeds = A × (1 + g)^nThis is pretty straight forward. Now let's suppose you contribute to an RRSP, which lets you obtain an immediate tax refund. The tax refund can then be contributed to a TFSA.
Code:
Contribute $A to RRSP
Grow at g for n years
Pay tax rate = tn upon withdrawal
RRSP proceeds = A × (1 + g)^n × (1 - tn)
Deduct $A from taxable income
Obtain refund of $A × t0
Contribute A × t0 to TFSA
Grows at rate g for n years
TFSA proceeds = A × t0 × (1 + g)^n
Total proceeds = RRSP + TFSA
= A × (1 + g)^n × (1 - tn) + A × t0 × (1 + g)^n
= A × (1 + g)^n × (1 - tn + t0)Notice that if t0 = tn, then the expression simplifies to "A × (1 + g)[sup]n[/sup]".
Code:
A × (1 + g)^n × (1 - tn + t0)
= A × (1 + g)^n × (1 - t + t)
= A × (1 + g)^nThis means TFSAs and RRSPs yield the identical outcome if you contribute and withdraw at the same marginal rate!
Your TFSA vs. RRSP decision requires answering three questions:
- What is your current marginal tax rate?
- How long will your funds remain sheltered before you need to withdraw?
- What will your future marginal tax rate become?
We often see this question asked:
It should be obvious that if you have sufficient TFSA room, you should always use the TFSA before RRSPs during periods of lower income. You'll likely withdraw at the same or higher marginal bracket, not lower, so TFSAs can let you arbitrage the difference in current vs. future tax rates. On the other hand, what happens if you don't have enough TFSA room?
To analyze this situation, some further assumptions:
- You have enough RRSP room to shelter $A
- You have enough TFSA room to shelter some portion of $A, but not all of it.
Code:
Contribute $A to RRSP
Grow at g for n years
Pay tax rate = tn at withdrawal
RRSP proceeds = A × (1 + g)^n × (1 - tn)
Wait m years to reach tax rate = tm
Deduct $A from taxable income
Obtain refund of A × tm
Contribute A × tm to TFSA
Grows at g for n years
TFSA proceeds = A × tm × (1 + g)^(n-m)
= A × tm × (1 + g)^n ÷ (1 + g)^m
Total proceeds = RRSP + TFSA
= A × (1 + g)^n × (1 - tn) + A × tm × (1 + g)^n ÷ (1 + g)^m
= A × (1 + g)^n × (1 - tn + tm ÷ (1 + g)^m)Notice that if m converges to zero (i.e., you deduct immediately), then tm = t0 and this expression is identical to one from above.
Code:
A × (1 + g)^n × (1 - tn + tm ÷ (1 + g)^m)
= A × (1 + g)^n × (1 - tn + t0 ÷ (1 + g)^0)
= A × (1 + g)^n × (1 - tn + t0 ÷ 1)
= A × (1 + g)^n × (1 - tn + t0)This illustrates an important point:
- You can obtain a benefit from deferring the deduction: the differential between tm and t0
- However, this benefit must be discounted by the growing penalty of (1 + g)[sup]m.[/sup]
This is because you actually have three options when using a RRSP (where the TFSA is nearly maximized):
- Contribute to the RRSP and deduct immediately
- Contribute to the RRSP and deduct in the future
- Invest in a non-registered account and defer contributing to the RRSP
Code:
Invest $A in a non-registered account
Grow at g* for m years
Contribute the new amount to RRSP
Grow at g for n-m years
Pay tax rate = tn at withdrawal
RRSP proceeds = A × (1 + g*)^m × (1 + g)^(n-m) × (1 - tn)
Deduct from taxable income at tm
Contribute refund to TFSA
Grow at g for n-m years
TFSA proceeds = A × (1 + g*)^m × tm × (1 + g)^(n-m)
Total proceeds = RRSP + TFSA
= A × (1 + g)^n × (1 - tn + tm) × [(1 + g*)/(1 + g)]^mNotice that if g* converges to g, then the expression becomes:
Code:
A × (1 + g)^n × (1 - tn + tm) × [(1 + g*)/(1 + g)]^m
= A × (1 + g)^n × (1 - tn + tm) × [(1 + g)/(1 + g)]^m
= A × (1 + g)^n × (1 - tn + tm) × [1]^m
= A × (1 + g)^n × (1 - tn + tm)Which is superior to the deferred deduction expression! This means if you have low tax drag (e.g., mostly capital gains versus interest income), then deferring the contribution will yield a better outcome than deferring the deduction. On the other hand, high tax drag where g* is significantly less than g will yield a worse outcome (e.g., receiving interest income at a high marginal tax rate).
There is no general solution for g* versus g that gives the optimal decision. But, using this expressions will make it much easier for you to test a few numerical solutions, especially since the expressions can be further simplified.
Since "A × (1 + g)^n" appears in four expressions, we can replace it with the constant "B". This gives us:
Code:
TFSA only
= B
Contribute to RRSP with immediate deduction
= B × (1 - tn + t0)
Contribute to RRSP and defer the deduction
= B × (1 - tn + tm ÷ (1 + g)^m )
Defer the RRSP contribution and use a non-registered account
= B × (1 - tn + tm) × [(1 + g*)/(1 + g)]^mThere are just five variables of interest:
- Withdrawal tax rate = tn
- Intermediate tax rate = tm
- Tax dragged growth = g*
- Expected growth = g
- Intermediate years = m
