## CPF Life: Is it a worthwhile investment?

In a previous post, CPF Life: A Primer, we described the features of the CPF Life scheme. As Singapore has phased out pension schemes for most of the citizens and residents, CPF Life is likely to play an important role in post-retirement finances of the CPF members, being a mandatory annuity which serves as a cross between the defunct defined benefits pension schemes, and a the defined contribution scheme which the CPF has been associated with.

In particular, as a life-long annuity, it hedges the post-retirement finances of the CPF members against longevity risk, i.e. the risk of outliving financial resources. It follows from this that CPF Life should be evaluated, not as an investment (i.e. what is the return on investment, when is the breakeven longevity), but rather as a hedge (i.e. does it protect against longevity risk – yes, is it actuarially fair, or value for money). In the following, we address the second metric for evaluating CPF Life – what is the value of CPF Life?

CPF Life hedges against longevity risk –

the risk of outliving financial resources

#### Calculating the Value of CPF Life

The assessment of the value of CPF Life is a straightforward present valuation of the cashflows:

- At the age of 55, the CPF member “invests” a sum of money into a deferred annuity, which we will assume is the Full Retirement Sum (FRS) of members turning 55 in 2019, $176,000
- At the age of 65 onwards, the CPF member receives a monthly stream of payments, which have been projected by the CPF Board based on various assumptions regarding the returns it achieves on the funds
- Should the CPF member pass on before starting to receive the monthly payments at the age of 65, the entire FRS plus the accumulated interest is refunded to deceased member’s nominees
- Should the CPF member pass on after starting to receive the monthly payments at the age of 65, the bequest amount projected by the CPF Board will be paid to the deceased member’s nominees, with the amount of the bequest depending on the age of the member.

In addition to the cashflows from the CPF Life scheme, we need two further parameters to evaluate the value of CPF Life:

- The discount rate – this is derived by computing the discount rate on a stream of payments over time from the age of 65 onwards until the exhaustion of the funds in a member’s Retirement Account (RA) such that the present value is equal to the minimum sum of $176,000. This works out to be 4.27%, which is a blended average of the RA interest rate, plus the extra 1% paid to balances up to $60,000 and the additional 1% paid on balances up to $30,000.
- The likelihood that the member will pass on at a specific age – this is derived from the preliminary Life tables for Singapore 2017

For males:

Age x (Years) | Prob of dying between age x and x+1 | Number of survivors at age x | Number of deaths between age x and x+1 | Expectation of life at age x |
---|---|---|---|---|

q(x) | l(x) | d(x) | e(x) | |

55 | 0.00424 | 95,636 | 406 | 27.6 |

60 | 0.00687 | 93,186 | 640 | 23.2 |

65 | 0.01101 | 89,353 | 984 | 19.1 |

70 | 0.01859 | 83,445 | 1,551 | 15.3 |

75 | 0.03108 | 74,243 | 2,307 | 11.8 |

80 | 0.05308 | 60,956 | 3,236 | 8.8 |

85 | 0.08923 | 43,390 | 3,872 | 6.4 |

90 | 0.14730 | 24,137 | 3,555 | 4.5 |

95 | 0.23240 | 8,988 | 2,089 | 3.1 |

100+ | 1.00000 | 1,775 | 1,775 | 2.1 |

For females:

Age x (Years) | Prob of dying between age x and x+1 | Number of survivors at age x | Number of deaths between age x and x+1 | Expectation of life at age x |
---|---|---|---|---|

q(x) | l(x) | d(x) | e(x) | |

55 | 0.00252 | 97,281 | 245 | 31.5 |

60 | 0.00380 | 95,831 | 364 | 27.0 |

65 | 0.00591 | 93,681 | 553 | 22.5 |

70 | 0.00958 | 90,351 | 865 | 18.3 |

75 | 0.01796 | 84,936 | 1,526 | 14.2 |

80 | 0.03505 | 75,301 | 2,639 | 10.7 |

85 | 0.06289 | 59,872 | 3,765 | 7.8 |

90 | 0.10926 | 39,500 | 4,316 | 5.5 |

95 | 0.18031 | 19,054 | 3,436 | 3.8 |

100+ | 1.00000 | 5,548 | 5,548 | 2.6 |

From these tables, we can compute the likelihood of a person surviving up a particular age by dividing the Number of Survivors at exact age x by the same number at an earlier age. For example, the chance that a 55-year old male will survive to the age of 90 is:

I_{90}/I_{55 } = 24,137/95,636 = 25.24%

We now have the pieces in place to value the CPF Life Scheme for a 55 year old setting aside his/her Full Retirement Sum and looking to start getting payouts from the Scheme at the age of 65.

To find the present value of a future payment at the age of 90 say, P_{90}, we normally discount this payment by the discount rate and the time until the payment is received. So from the standpoint of a 55 year old person the value of this payment at the age of 90 (i.e. in 35 years time) is:

Present Value = P_{90} / (1 + *Discount Rate*)^{t}

where *t* = 35 years, and *Discount Rate* = 4.27%. However, in the case of an annuity like CPF Life, the payment at age 70 is only received if the person survives until age 70, and hence we need to further adjust this by the likelihood of this payment happening, which is 25.24% for a male, as computed earlier. In the case of CPF Life, there may also be a bequest payable should he/she pass away in the same year, and the likelihood of this bequest being received (by the nominees, of course!) is the chance that the person survives until age 90 (which is 25.24%) and the chance that he/she then passes on in the same year *q _{90}*, which is 14.73% from the life table above.

#### Putting things together

Let’s work out some present values for the payments in the future at different ages expected for a male aged 55 years today (assuming the CPF Life payment is at the higher level projected by the CPF Board as shown earlier). Here, we make the simplifying assumptions that the entire amount of the CPF Life’s payments for a particular year is paid out at the start of the year, and that if the person passes away in a particular year, he does so at the end of the year (so he receives both the annuity payments and the bequest).

Age x (Years) | CPF Life Payout (month) | CPF Life Bequest | Chance of living to age | Chance of dying at age |
---|---|---|---|---|

P(x) | B(x) | l(x) / l(55) | q(x) | |

65 | $1,549 | $274,204 | 93.43% | 1.101% |

70 | $1,549 | $181,211 | 87.25% | 1.859% |

75 | $1,549 | $93,736 | 77.63% | 3.108% |

80 | $1,549 | $9,671 | 63.74% | 5.308% |

85 | $1,549 | $0 | 45.37% | 8.923% |

90 | $1,549 | $0 | 25.24% | 14.730% |

95 | $1,549 | $0 | 11.94% | 23.240% |

100 | $1,549 | $0 | 1.86% | 35.630% |

Age x (Years) | Expected CPF Life Payout (year) | Expected CPF Life Bequest | Present Value |
---|---|---|---|

P(x) x l(x) / l(55) | B(x) x l(x) / l(55) x q(x) | ||

65 | $11,432 | $1,857 | $13,289 |

70 | $8,662 | $1,570 | $10,232 |

75 | $6,253 | $980 | $7,233 |

80 | $4,165 | $115 | $4,280 |

85 | $2,406 | $2,406 | |

90 | $1,086 | $1,086 | |

95 | $328 | $328 | |

100 | $53 | $53 |

If we do this exercise for every single age starting from 55 onwards, and sum up all the present values, we arrive at the value of the CPF Life for a person aged 55 putting aside the Full Retirement Sum. What do these values look like? These are shown below:

For Males:

Full Retirement Sum Plan $176,000 | Present Value at Age 55 | % Value form Monthly Payments | % Value from Bequest |
---|---|---|---|

Standard | $163,244 - $178,416 | 82.4% | 17.6% |

Basic | $173,267 - $188,753 | 70.7% | 29.3% |

Escalating | $148,482 - $174,448 | 80.2% | 19.8% |

For Females:

Full Retirement Sum Plan $176,000 | Present Value at Age 55 | % Value form Monthly Payments | % Value from Bequest |
---|---|---|---|

Standard | $160,954 - $177,469 | 89.1% | 10.9% |

Basic | $170.598 - $187,226 | 79.6% | 20.4% |

Escalating | $155,082 - $172,400 | 87.2% | 12.8% |

Now, these values are the average values to the entire cohort of males and females under the CPF Life scheme, but they could be very different for each individual, as it would depend on when the person passed away – a longer-lived person would get more benefit and value than a shorter-lived one, as is the nature of annuities and longevity risk pooling. The tables following provide another view of the present value of the CPF Life Plans, depending on how long the person survived:

A longer-lived person gets more benefit than a shorter-lived one, as is the nature of annuities & longevity risk pooling

For Males:

Age of Death | Full Retirement Sum Standard Plan | Full Retirement Sum Basic Plan | Full Retirement Sum Escalating Plan |
---|---|---|---|

75 | $131,822 - $149,148 | $171,180 - $187,431 | $125,176 - $143,985 |

80 | $157,937 - $174,621 | $169,644 - $186,698 | $147,584 - $164,781 |

85 | $179,125 - $198,047 | $168,348 - $186,553 | $173,762 - $194,008 |

90 | $196,315 - $217,054 | $178,140 - $197,608 | $197,213 - $220,189 |

For Females:

Age of Death | Full Retirement Sum Standard Plan | Full Retirement Sum Basic Plan | Full Retirement Sum Escalating Plan |
---|---|---|---|

75 | $127,492 - $145,612 | $168,559 - $184,534 | $122,296 - $139,769 |

80 | $146,776 - $162,897 | $166,497 - $183,247 | $134,144 - $150,357 |

85 | $166,467 - $184,750 | $164,702 - $182,710 | $157,936 - $177,024 |

90 | $182,443 - $202,481 | $172,214 - $191,411 | $179,249 - $200,911 |

#### What can we conclude?

What do these values for the CPF Life Scheme tell us? There are a number of conclusions:

- We need to see if the inaugural cohort of members in the CPF Life scheme will be paid close to, or more than the higher of the payouts projected previously by the CPF Board. Only at this higher level of payouts will the CPF Life Scheme be expected to be worth what the CPF member puts aside as his/her Full Retirement Sum. In other words, if the payouts under CPF Life are less, the CPF Board has replaced the Retirement Sum Scheme with something that is of lesser value in practice.
- A significant amount of the value of CPF Life is allocated to bequests, which diminish over time, and in the worst case, disappears exactly when a CPF member passes away, leaving little or nothing to his/her loved ones. So even while the Basic Plan has a higher present value compared to the Standard or Escalating Plans, the additional value comes form the bequests which may not be paid out ultimately.
- In an annuity scheme, the highest value is gained by those who live the longest, and in the case of CPF Life, it is the lucky 50% who live past their life expectancy who will gain. Therefore, CPF members who are in poor health before the age of 65 (which could reduce life expectancy by 3 years or more), would be advised to choose a Plan which maximizes the value to them and their loved ones given their expected lifespans.

These conclusions should not detract from the fact that the CPF Life scheme is a valuable addition to the retirement planning tools and products, which have been lacking in many aspects previously, available for CPF members. However, we see that there is still room to improve in terms of product design, communication, and understanding of the CPF Life Scheme for the benefit of CPF members, and it is in this spirit that these conclusions are reached.

#### Other resources

Other perspectives on the returns on CPF Life can be found at:

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