Solving the SRS top-up problem using Primary 6 mathematics and sensitivity analysis
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Solving the SRS top-up problem using Primary 6 mathematics and sensitivity analysis

December 27, 2019

When comes to the Supplementary Retirement Scheme (SRS), four of the most common questions that are asked on forums and websites like Seedly and HardwareZone are the following:

"At what tax bracket would it make sense for me to contribute to my SRS account?"

"At what age should I start contributing to my SRS account?"

"How do I maximise tax savings yet minimise future tax expenses when I withdraw from my SRS account?"

"Should I keep my SRS account below $400,000 to get tax free withdrawals?"

As a former analyst in a private equity fund, I understand that these questions are something that can be better understood mathematically using a financial model.

It will be easier to understand this by articulating it in a form of a PSLE type problem sum question. We can identify the problem statement and share the SRS nuances and restrictions along the way.

Understanding SRS top up maximisation through a P6 Problem Sum

Defining the SRS top up Problem Sum

John is 35 years old this year, and he is earning a modest income that puts him inside the 7% tax bracket. He wants to maximise his personal income tax relief by utilising his SRS account, putting in the maximum $15,300 for tax relief. He intends to withdraw his SRS account over 10 years past his retirement age. He thinks that he can make a 7% return on his investments by investing in a balanced portfolios made of equities and bond unit trusts. Would topping up his SRS account now make him better off financially, assuming that the income tax rates will not change?

The "Independent Variables" defining the SRS top up problem

Moving ahead to secondary school math (yes I am cheating), the above Primary 6 Problem Sum can roughly be explained in the form of dependent and independent variables.

J = ax+ by-cz

The independent variables, or the values x, y, z in the above formula, are fairly simple. These will be things like John's

  1. Age (35 years old),
  2. Tax bracket (7% tax bracket), and
  3. Returns on investments (7% returns).

For the purpose of making this analysis simpler, we will assume that figures like the $15,300 committed in SRS, income tax rates are fixed numbers (or a, b, c in the above formula).

Understanding what are we maximising in SRS, the "Dependent Variable"

The outcome we are optimising for is simply to grow our wealth at SRS withdrawal to the largest amount possible, relative to not contributing to SRS. This has to take into account the tax brackets, returns of investments, and the 10 year tax preference treatment of SRS withdrawals.

To ensure that an apples for apples comparison is made, let us assume that John is only willing to commit $15,300 of pre-tax savings to invest.

Fleshing out the workings for the dependent variable:

Let H - I = J where J is the upside (or downside when the value is negative) from investing through SRS rather than using post-tax monies, where:

H be 10-year yearly cash flow, net of taxes that John's SRS account will give him when he withdraws his SRS monies while staying invested

I be 10-year yearly cashflow, that John's post-tax cash account will give him.

For H, do note that since John is likely to have put a huge sum of money in SRS, and given that it compounds at 7%, his portfolio would have grown to $1.14 million by the time he reaches the statutory retirement age of 62 years old. Even though only 50% of the amount withdrawn from the SRS account is taxable, the sheer size of John's portfolio means that he will be taxed.

Remember that in the case that John paid his taxes, being in the 7% tax bracket, he would be left with $14,229 to invest in a portfolio that compounds at 7% return over the 26 years.

The worked sample solution for SRS maximisation

When John is 62 years old, his SRS account will grow to $1.14 million. Net of income tax, John will have a yearly cashflow of around $159,000 liquidating his SRS account over 10 years.

If John were to invest using post-tax monies, John's portfolio will grow to $1.06 million. John will have a yearly cashflow of $151,000 investing with post-tax monies.

John (or value J) is better off by $8,000 (rounded up) a year, just by investing through SRS instead of investing through post-tax monies.

Your personal considerations before doing SRS top-ups

Your current tax bracket, and contribution age matters for SRS

Of course, you are not John -- your tax bracket is different, your age is different, your expectations of investment returns are likely to be different as well. The easy part of solving Math problems on Excel rather than through paper and pen (as is with the case of Primary 6 exams) is that we can use sensitivity tables for the analysis.

With a range of values for the independent variables, we can give you a personalised perspective of how SRS can work (or not work) for you. The sensitivity tables are as shown below (red highlights are cases where it does not work for you):

sensitivity table for age of SRS contribution vs tax bracket

John's case (35-year-old, 7% tax bracket, 7% return) is highlighted in yellow above. As you can see from the above table, the higher your tax bracket, the more you save through SRS, even though you may be paying more taxes on an absolute basis. Just like how a dollar now is worth more than a dollar in the future, a tax dollar saved now is worth more than a tax dollar paid in the future.

Tax savings can be compounded and grown to pay for higher taxes in the future.

The age you start contributing to SRS matters as well.
Do look to see how starting at different ages affect the upside that we can get
from SRS.

However, the same does not apply to investment returns. The higher the assumed return on investment, the worse off you are. The intuition behind it is very simple -- as the SRS account is a tax deferral scheme, if you are expecting a high investment return, it is better to be taxed now and invest than invest now, grow your wealth significantly and be taxed later.

Other personal considerations around SRS top ups

Investing in your SRS is ultimately a long-term commitment where your funds are locked in until retirement age. There is a trade off in terms of liquidity, and you have to ensure that you do not need the money committed into the SRS account.

You should look at your medium to long-term large ticket expenses (such as buying a new property or a new car, for example) before you commit to topping up your SRS account.

Anyway, if the analysis above makes sense to you, set up your SRS account or top it up now to reduce your taxable income. You can set up an account online and fund it immediately with local banks.

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