Thursday, April 16, 2009

Defined Benefit vs. Defined Contribution: Analysis

I've run a few different scenarios to work out whether I should go for the defined benefit or defined contribution option.

Scenario 1: Work 1 Year at an Australian University

This is the simplest scenario as the only variable is future rates of return in the defined contribution scheme. I don't need to project my future salary. I assume that the tax on superannuation earnings averages 7.5% (15% on general income, 10% on capital gains, and zero on fully franked dividends). All numbers are in 2009 Australian Dollars. I don't worry about projecting inflation. I am currently 44 years old.

The results of the analysis are also very clear cut. I and my employer would contribute a total after tax amount of $13,262 this year.

Under the defined benefit scheme I would receive $13,603 if I retired at age 60 (the earliest age I could access the benefits) and $14,221 if I retired at 65 or older. Clearly this rate of return is very low. A 1% real rate of return gives a lump sum of $15,450 at age 60 and $16,181 at age 65 in the defined contribution scheme. A 5% real rate of return gives $28,460 at age 60.

Selecting this option only makes sense in this scenario if you are extremely averse to market risk. Unless you expect hyperinflation and negative real interest rates in the future it will make more sense to invest in the cash option in the defined contribution scheme.

Scenario 2: Work Till Age 60 at Current Salary

Under this scenario total contributions are $225k and the age 60 defined benefit is $231k. Again, a 1% real rate of return beats the defined benefit.

Scenario 3: Smooth Rise in Salary to Full Professor (E1) at age 60

An E1 Professor currently earns $133,901. This scenario is not clear cut. The defined benefit is $505k if taken at age 65 but actually quitting at 60. A 3% real rate of return gives $508k. Continuing to work at that salary till age 65 favors the defined benefit a little bit more.

Scenario 4: Switch to Full Time Next Year and Then Smooth Rise to E1

Now the age 65 defined benefit (working till 60) is $513k and a 2% rate of return gives $516k.

Scenario 5: Switch to Full Time Next Year and Fast Promotion to E1

I assume I rise one salary notch every two years. I become a full professor in ten years. Defined Benefit is $523k at age 65 and the 2% rate of return yields $535k.

As you can see, the earlier promotion comes or if promotion doesn't come at all the lower the require rate of return in the defined contribution scheme. I reckon scenarios 1 and 5 are most likely. I'd assign them a 40% probability each and the other 3 scenarios (20/3)% each. The expected value of the defined benefit is then $299k of a 1% real rate of return defined contribution it is $273k, at a 2% real rate of return $309k , at a 3% rate of return $350k.

Using expected value assumes I am risk neutral. If I am averse to career risk then I should put a heavier weight on Scenarios 1 and 2 than on the more positive career scenarios. Those scenarios have lower required investment rates of return.

Given this low required rate of return and the advantage of portability I am going to choose the defined contribution scheme.

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