CPF Life annuity payout is low

Recently, there have been a lot of buzz regarding Singapore's CPF Life, a form similar to pension plan in other countries.  The issues started from the ever increasing CPF Life's min sum (from $80,000 in 2003 to $155,000 in 2014) that people need to lock up in their CPF when they reach 55 years old.  

Below are certain issues that came out of my discussion with my friends.  

Just for background, CPF Life is administered by a Singapore government statutory board called CPF or Central Provident Fund Board.  CPF Life is also similar to annuity scheme sold by insurance companies in Singapore, in that you pay some money every month and at a fixed age some time later (in the case of CPF Life is when you are 65 years old), you start to receive annuity payout until you die.  However, CPF scheme is much more complicated than that.  Any way, to summarize, Singaporean workers are required to contribute about 20% of their pay to CPF every month, and employers need to co-contribute another about 15%, and these are placed into 3 accounts according to some fixed percentages, namely Ordinary Account (OA), Special Account (SA), and Medisave Account (MA).  They will contribute as long as they are working.  By the time they reach 55 years old, everyone of them who has $155,000 in OA+SA will be transferred into a Retirement Account (RA).  This sum will be held in RA under CPF Life scheme (and cannot be withdrawn) until 65 years old when by then the person can start to receive annuity payout from CPF Life scheme. 

According to current projections by CPF Board, CPF Life annuity payout for a RA sum of $155,000 will be about $1100-1223 per month.  

However, some people questioned why is this CPF Life annuity payout so low?  

To see why is this so, we can do following calculations, and we take the average payout of $1161.50 (= (1100+1223)/2) per month for our calculation: 

* CPF min sum $155,000 at 55 years old locked up with interest of 5% below $60,000 and 4% for remaining above $60,000, so total at end of 10 years at 65 years old is = $240,449.67

                             Amt below $60k           Amt $60k & above
Amount:                60,000.00                    $95,000.00
Interest:                5.00%                         4.00%
No. of Years:          10                               10
At end of 10 years: $98,820.57                   $141,629.10
Total $240,449.67

** Next come annuity payout part, to pay out $1161.50 per months mean your annuity return is only 1.93%, calculated as follow: 

No bequest - Assume Dead At 86 years old
Present value at 65 Years old      = $240,449.67
Payment per month                   = $1,161.50
Expected payout period in years = 21.00
Rate (Annualized) p.a.               = 1.93%

Now, it seems that this Government administered annuity scheme's annuity payout is even lower than annuity payout of the insurance companies in Singapore!!! 

So, therein lies another problem: Annuity payout's assumed return is low, even assuming an average person dies at 86 years old. Furthermore, CPF Life payout of this amount is not guaranteed despite giving so low return of 1.93%. Seems like people expect that a nation-wide annuity scheme should do better because of economy of scale and also the need to pay better because of the enforced scheme (i.e. you don't have the choice to opt out).