Saturday, 31 December 2016

Financial Studies 2 - CPP Early or Late? Part 3

In the Part 1 of my blog posts discussing whether to start CPP early or late, I talked about articles which had presented the break-even point analysis and I pointed out that this was the wrong question to ask. The break-even is the age at which the cash received from starting CPP early is the same as starting CPP at 65. 

The analysis is usually done on a spreadsheet, but there is actually a much easier way to calculate this. 

The result is:

The number of months from when your start CPP to the break-even age is the reciprocal of the actuarial adjustment discount rate. If you start CPP early the discount is 0.6% per month, or 0.006. The reciprocal of this (1/0.006) is 167 months or 13.9 years. For starting CPP at 60, the break-even is at age 74. If you live to less than 74, starting CPP at 60 is better than starting it at 65. 

So next time you're at a cocktail party and someone is going on about their spreadsheet to calculate the break-even for taking CPP early, you can one-up them by saying "Yeah, it's just the reciprocal of the actuarial adjustment discount rate".

To come up with this we need to do a little Algebra.

Make the following definitions:

P = CPP Pension benefit amount, monthly based on starting CPP at 65.
N = number of months from the time you start CPP in the early case until the cross-over point with the start CPP at 65 case.
d = discount rate for starting CPP early. This is 0.6% or 0.006
e = # of months you start CPP early before 65.

We are going to solve for N

In the "Start at 65" case the total income you receive up to the cross-over point is the CPP benefit times the number of months you receive the benefit for, which is N minus e. Remember that N starts in the early case which is e months prior to 65.

Total Income in "Start at 65" = P*(N-e)

In the "Start Early" case the total income is discounted by d for each month early and you receive it for N months.

Total Income in "Start Early" =P*(1-e*d)*N

When the cross-over occurs, these two incomes are the same. Equate them and solve for N.

P*(N-e) = P*(1-ed)*N

Divide both sides by P

N-e = N*(1-ed)

Subtract N from both sides

-e = -N*e*d

Divide both sides by e and re-arrange

N = 1/d

Wow that's a simple answer.

That says the cross-over point, in months from when you start CPP, is simply the reciprocal of the discount rate. It is independent of the age at which you start taking CPP.

The current discount rate is 0.6% (0.006) so N = 1/ 0.006 = 167 months or 13.9 years. Check this against the spreadsheet example above. When starting CPP at 60, the crossover point was at 73 (in fact it is near the end of the 73rd year), which is the same as 13.9 years (from age 60). 

If you start CPP at 61, the cross-over point is still 13.9 years after that or at 74.9 (nearly 75).

So the later you start CPP, the later the cross-over gets pushed back. 

The math is the same for starting CPP after 65, just that the discount rate (which increases the CPP benefit amount) is now 0.7% or 0.007. N=1/0.007 = 143 months or 11.9 years. If you defer taking CPP to age 70, then the cross-over is at 82. You need to be sure you will live at least to 83, to ensure that starting CPP later is a good idea.

Just remember, this is the answer to the wrong question. Go back and read Part 1 of my CPP early or late blog post here.

Disclaimer:  These posts are not fully comprehensive financial advice.  You should seek your own qualified investment, tax and legal advice.

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