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Old 02-21-2005, 08:31 AM   #1
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Lightbulb Real numbers about investment vs. Social Security

I was getting tired of seeing bunch of hypothetical arguments about how much better Social Security is than allowing workers to invest on their own. Therefore I wrote a program to investigate the matter with cold, hard numbers. There are no emotional arguments here, the numbers tell everything.

The mathematical model takes the following variables:
- Starting funds, if any (Usually set to zero.)
- Starting salary
- Number of years worked
- Average salary increase (net value, inflation included)
- Percentage of gross salary invested
- Company contribution, if any
- Average yield of investment
- Number of losses during the lifetime of investment
- Percentage of portfolio lost each time
- Yield of the portfolio at retirement

With these inputs we can get very revealing results. In most instances we shall set the percenage of investment to the actual payroll tax value, 7.65% for someone who is employed. Poor people presumably cannot afford more than that.

First, someone who is extremely poor: The 10,000 annual salary at the beginning of the employment is actually lower than the minimum wage. The average yearly raise is set to 1%, ridiculously low. The average yield is set to 6%, a very low estimate. Such a small yield comes from a very conservative investment type, so we can safely assume that there is no loss involved. Government bonds, mutual funds with heavy emphasis on utility comapnies, Cocal Cola, Nabisco etc. are examples of such investment.
Code:
Starting value, if any:             0.00
Starting salary:                    10,000.00   (833.33 monthly)
Ending salary:                      14,741.23   (1,228.44 monthly)
Number of years worked:             40
Yearly raise of salary (%):         1.00
Percent of salary invested:         7.65
Company contribution:               0.00
Investment portfolio yield:         6.00
Chance of loss (yearly):            0.00
Pecent of portfolio lost:           0.00
Retirement interest of portfolio:   6.00
Results ----------------------------
Lifetime earnings:                  488,863.73
Lifetime invested:                  37,398.08
Company matching:                   0,000.00
Amount at retirement:               144,085.52
Monthly income at retirement:       720.43
At the end, this person has 144 thousand dollars in the bank, which yields 720 dollars a month, with the principal untouched.

This is much better than a Social Security check of a few hundred dollars. I don't know how much exactly someone recieves whose income at the age of retirement is under 15,000 dollars.

The next example will be the same starting conditions, but we shall assume a little bit more aggressive investment portfolio. The more aggressive the investment is, the higher the chance of periodic setbacks, so we shall assume that twice during the life of the investment there will be a loss of 20%. This means that 20% of the current portfolio is lost:

Code:
Starting value, if any:             0.00
Starting salary:                    10,000.00   (833.33 monthly)
Ending salary:                      14,741.23   (1,228.44 monthly)
Number of years worked:             40
Yearly raise of salary (%):         1.00
Percent of salary invested:         7.65
Company contribution:               0.00
Investment portfolio yield:         10.00
Chance of loss (yearly):            2.00
Pecent of portfolio lost:           20.00
Retirement interest of portfolio:   6.00
Results ----------------------------
Lifetime earnings:                  488,863.73
Lifetime invested:                  37,398.08
Company matching:                   0,000.00
Amount at retirement:               303,778.41
Monthly income at retirement:       1,518.89
There were losses 2 times:
In year 14   5,570.16 was lost.
In year 28   23,626.24 was lost.
The results are much better, even when there were two losses.

In the next example we shall go little higher, the person in question now works for a company which offers a 401K plan with matching contributions.

Code:
Starting value, if any:             0.00
Starting salary:                    10,000.00   (833.33 monthly)
Ending salary:                      14,741.23   (1,228.44 monthly)
Number of years worked:             40
Yearly raise of salary (%):         1.00
Percent of salary invested:         7.65
Company contribution:               3.00
Investment portfolio yield:         10.00
Chance of loss (yearly):            2.00
Pecent of portfolio lost:           20.00
Retirement interest of portfolio:   6.00
Results ----------------------------
Lifetime earnings:                  488,863.73
Lifetime invested:                  37,398.08
Company matching:                   14,665.91
Amount at retirement:               422,907.20
Monthly income at retirement:       2,114.54
There were losses 2 times:
In year 14   7,754.54 was lost.
In year 28   32,891.43 was lost.
Look at the retirement income: 422 thousand in the bank, which yields over 2100 dollars a month. Much higher than the ending salary. And that is due to the 401K company matching contributions.

All of these examples are about someone whose skills are way below the average, and still with a moderately aggressive investment scheme they can preprare for their retirement.

Just for the hell of it, a more realistic scenario for a low middle class person:

Code:
Starting value, if any:             0.00
Starting salary:                    20,000.00   (1,666.67 monthly)
Ending salary:                      43,294.90   (3,607.91 monthly)
Number of years worked:             40
Yearly raise of salary (%):         2.00
Percent of salary invested:         7.65
Company contribution:               3.00
Investment portfolio yield:         12.00
Chance of loss (yearly):            4.00
Pecent of portfolio lost:           30.00
Retirement interest of portfolio:   6.00
Results ----------------------------
Lifetime earnings:                  1,208,039.66
Lifetime invested:                  92,415.03
Company matching:                   36,241.19
Amount at retirement:               797,929.90
Monthly income at retirement:       3,989.65
There were losses 4 times:
In year 08   10,961.22 was lost.
In year 16   30,729.92 was lost.
In year 24   68,550.44 was lost.
In year 32   139,533.89 was lost.
If you still are dubious about these results, you can calculate them for yourself.

If you want the source code for the program, or the executable itself, I will be happy to email them to you. If you are curious about the results of more input parameters, just post them and I will run the program for you.

Have fun with the numbers. That is so cool about them, no need for ideology, no need for emotionalism.

Behold the power of compounded interest!
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Old 02-21-2005, 09:02 AM   #2
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Quote:
Originally Posted by Hitetlen
This is much better than a Social Security check of a few hundred dollars. I don't know how much exactly someone recieves whose income at the age of retirement is under 15,000 dollars.

This is much better than something you don't know? How does one make a claim that something is "much better than" a value that the person"doesn't know"?

Are all of your calculations like this?

Just kidding on the question, kind of, since you explain some of your methodology, but you don't explain it all, so should I assume that there are other things in it that you compare one thing to an unknown thing and make a claim about the relative value?


...


On another note, what portion of the 7+ percent goes toward non-retirment items and should therefore be removed from your calculation? On another thread, it looks like the amount of FICA that goes to non-retirement OASI is not trivial. Does this change your determination of the relative rank of the two balances (one of which is unknown to you?)
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Old 02-21-2005, 09:13 AM   #3
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You missed the operating word: "exactly"!

Quote:
Originally Posted by Rhea
This is much better than something you don't know? How does one make a claim that something is "much better than" a value that the person"doesn't know"?
I don't know the exact amount, but I have a good guess. With income getting close to 70K, my predicted SS income is around 800 dollars, so with 15K closing income it cannot be more than 3-400 dollars a month.

Quote:
Originally Posted by Rhea
On another note, what portion of the 7+ percent goes toward non-retirment items and should therefore be removed from your calculation?
Today, the percentage going to retirement is 6.2%, the Medicare insurance is 1.45%.

Here is the original calculation redone with 6.2%:

Code:
Starting value, if any:             0.00
Starting salary:                    10,000.00   (833.33 monthly)
Ending salary:                      14,741.23   (1,228.44 monthly)
Number of years worked:             40
Yearly raise of salary (%):         1.00
Percent of salary invested:         6.20
Company contribution:               0.00
Investment portfolio yield:         6.00
Chance of loss (yearly):            0.00
Pecent of portfolio lost:           0.00
Retirement interest of portfolio:   6.00
Results ----------------------------
Lifetime earnings:                  488,863.73
Lifetime invested:                  30,309.55
Company matching:                   0,000.00
Amount at retirement:               116,775.19
Monthly income at retirement:       583.88
As you can see, there is a little drop in the final result, which was to be expected.

However, this example shows an irrationally low income, with a starting salary under the minimum wage and only 1% increase in the yearly income. I wanted to show that even in such a case, the investment option is better.
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Old 02-21-2005, 09:16 AM   #4
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Default For those who want to see the code itself.

This is a very simple VB (Visual Basic) code:

Code:
Option Explicit

    Dim start_amount As Double
    Dim start_salary As Double
    Dim num_years As Long
    Dim num_months As Long
    Dim yearly_raise As Double
    Dim percent_invested As Double
    Dim company_contrbution As Double
    Dim yearly_interest As Double
    Dim monthly_interest As Double
    Dim num_loss As Long
    Dim percent_of_fund_lost As Double
    Dim amt_fund_lost As Double
    Dim annuity_interest As Double
    '

Private Sub cmd_calc_Click()

    Dim x As Long
    Dim y As Long
    Dim yy As Long
    Dim amt_lost() As Double
    Dim year_lost() As Double
    Dim sum_income As Double
    Dim sum_inv As Double
    Dim sum_matching As Double
    Dim sum_extra As Double
    Dim str1 As String
    
    start_amount = CDbl(txt_value.Text)
    start_salary = CDbl(txt_salary.Text)
    num_years = CLng(txt_years.Text)
    num_months = 12 * num_years
    yearly_raise = 1 + CDbl(txt_raise.Text) / 100
    percent_invested = CDbl(txt_perc_inv.Text) / 100
    company_contrbution = CDbl(txt_comp_contr.Text) / 100
    yearly_interest = CDbl(txt_yearly_int.Text) / 100
    monthly_interest = 1 + yearly_interest / 12
    num_loss = CLng(txt_loss.Text)
    If num_loss > 5 Then
        num_loss = 5
        txt_loss.Text = "5"
        txt_loss.Refresh
    End If
    percent_of_fund_lost = CDbl(txt_perc_lost.Text) / 100
    annuity_interest = CDbl(txt_annuity.Text) / 1200
    
    ReDim yearly_income(num_years)
    ReDim monthly_income(num_months)
    ReDim monthly_invest(num_months)
    ReDim matching_portion(num_months)
    
    ReDim Preserve amt_lost(num_loss + 1)
    ReDim Preserve year_lost(num_loss + 1)
    
    If num_loss > 0 Then
        Select Case num_loss
            Case 1:
                year_lost(0) = 20
            Case 2:
                year_lost(0) = 14
                year_lost(1) = 28
            Case 3:
                year_lost(0) = 10
                year_lost(1) = 20
                year_lost(2) = 30
            Case 4:
                year_lost(0) = 8
                year_lost(1) = 16
                year_lost(2) = 24
                year_lost(3) = 32
            Case 5:
                year_lost(0) = 7
                year_lost(1) = 14
                year_lost(2) = 21
                year_lost(3) = 28
                year_lost(4) = 35
        End Select
    End If
    
    lst1.Clear
    
    x = 0
    yearly_income(x) = start_salary
    lst1.AddItem "Year " & Format(x + 1, "00") & "   " & Format(yearly_income(x), "0.00")
    For x = 1 To num_years - 1
        yearly_income(x) = yearly_income(x - 1) * yearly_raise
        lst1.AddItem "Year " & Format(x + 1, "00") & "   " & Format(yearly_income(x), "0.00")
    Next x
    lst1.AddItem String(20, "-")
    
    sum_income = 0
    sum_inv = 0
    sum_extra = start_amount
    For x = 0 To num_years - 1
        For y = 0 To 11
            monthly_income(x * 12 + y) = yearly_income(x) / 12
            monthly_invest(x * 12 + y) = monthly_income(x * 12 + y) * percent_invested
            matching_portion(x * 12 + y) = monthly_income(x * 12 + y) * company_contrbution
            sum_income = sum_income + monthly_income(x * 12 + y)
            sum_inv = sum_inv + monthly_invest(x * 12 + y)
            sum_matching = sum_matching + matching_portion(x * 12 + y)
            sum_extra = sum_extra * monthly_interest + monthly_invest(x * 12 + y) + matching_portion(x * 12 + y)
            lst1.AddItem "Y/" & Format(x + 1, "00") & "  M/" & Format(y + 1, "00") & "   " & Format(monthly_income(x * 12 + y), "#,##0.00") & "   " & Format(monthly_invest(x * 12 + y), "#,##0.00") & "   " & Format(matching_portion(x * 12 + y), "0.00") & "   " & Format(sum_extra, "#,##0.00")
        Next y
        If num_loss > 0 Then
            For yy = 0 To num_loss - 1
                If x = year_lost(yy) Then
                    amt_lost(yy) = sum_extra * percent_of_fund_lost
                    lst1.AddItem String(40, "-")
                    lst1.AddItem "Loss occurred: " & Format(sum_extra * percent_of_fund_lost, "#,##0.00") & " is lost"
                    sum_extra = sum_extra * (1 - percent_of_fund_lost)
                End If
            Next yy
        End If
        lst1.AddItem String(50, "-")
    Next x
    Label9.Caption = Format(sum_inv, "#,##0,000.00")
    Label18.Caption = Format(sum_income, "#,##0,000.00")
    Label11.Caption = Format(sum_extra, "#,##0.00")
    Label15.Caption = Format(sum_extra * annuity_interest, "#,##0.00")
    If txt_save_file.Text <> "" Then
        Open App.Path & "\" & txt_save_file.Text For Output As #1
        Print #1, "Starting value, if any:             " & Format(start_amount, "#,##0.00")
        Print #1, "Starting salary:                    " & Format(start_salary, "#,##0.00") & "   (" & Format(start_salary / 12, "#,##0.00") & " monthly)"
        Print #1, "Ending salary:                      " & Format(yearly_income(num_years - 1), "#,##0.00") & "   (" & Format(yearly_income(num_years - 1) / 12, "#,##0.00") & " monthly)"
        Print #1, "Number of years worked:             " & Format(num_years, "0")
        Print #1, "Yearly raise of salary (%):         " & Format(txt_raise.Text, "#,##0.00")
        Print #1, "Percent of salary invested:         " & Format(txt_perc_inv.Text, "#,##0.00")
        Print #1, "Company contribution:               " & Format(txt_comp_contr.Text, "#,##0.00")
        Print #1, "Investment portfolio yield:         " & Format(txt_yearly_int.Text, "#,##0.00")
        Print #1, "Chance of loss (yearly):            " & Format(txt_loss.Text, "#,##0.00")
        Print #1, "Pecent of portfolio lost:           " & Format(txt_perc_lost.Text, "#,##0.00")
        Print #1, "Retirement interest of portfolio:   " & Format(txt_annuity.Text, "#,##0.00")
        Print #1, "Results ----------------------------"
        Print #1, "Lifetime earnings:                  " & Format(sum_income, "#,##0,000.00")
        Print #1, "Lifetime invested:                  " & Format(sum_inv, "#,##0,000.00")
        Print #1, "Company matching:                   " & Format(sum_matching, "#,##0,000.00")
        Print #1, "Amount at retirement:               " & Format(sum_extra, "#,##0,000.00")
        Print #1, "Monthly income at retirement:       " & Format(sum_extra * annuity_interest, "#,##0.00")
        If num_loss > 0 Then
            Print #1, "There were losses " & num_loss & " times:"
            For x = 0 To num_loss - 1
                Print #1, "In year " & Format(year_lost(x), "00") & "   " & Format(amt_lost(x), "#,##0.00") & " was lost."
            Next x
        End If
        Close #1
        Open App.Path & "\" & txt_save_file.Text For Input As #1
        txt_res = ""
        Do While Not EOF(1)
            Line Input #1, str1
            txt_res = txt_res & str1 & vbCrLf
        Loop
        Close #1
    End If

End Sub

Private Sub cmd_exit_Click()

    End
    
End Sub

Private Sub Form_Load()

    txt_save_file = "res.txt"
    txt_salary = "10000"
    txt_years = "40"
    txt_raise = "1"
    txt_perc_inv = "7.65"
    txt_comp_contr = "0"
    txt_yearly_int = "8"
    txt_loss = "4"
    txt_perc_lost = "10"
    txt_annuity = "4"
    
End Sub
Copy and paste into the VB editor, create the proper screen, and execute. the whole algorithm is spelled out. Nothing is hidden!
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Old 02-21-2005, 09:34 AM   #5
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Nice effort.

* warning 'but' monkey * BUT in accounting or programming the saying is:

Garbage in, Garbage out.

Error: 7.65% Percent of salary invested
True value is around double that.
Reason: Fundamental economics. If you cannot grasp that, then there is no point going further. The lower value is an EMOTIONAL response.

Error: 2 times 20% loss Pecent of portfolio lost
This is arbitrary and fallacious.
True value is no loss. Market equities average 9.5% over 40 years time.
Reason: Proven in many financial journals.
Inserting arbitrary losses is an EMOTIONAL response not based in sound economics.

Unfortunately, due to copyrights, Google may not be useful. Historical charts are NOT available to general public. There exists a historical chart of Bills Stocks etc. but it is copyrighted. I do not remember the name but it cost $200 for the chart.


Finally, Excel spreadsheet using FV and PV functions is much simpler and more transparent.

But great initial try.
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Old 02-21-2005, 09:35 AM   #6
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Default

As I pointed out elsewhere, in the absence of government deductions from one's paycheck the scenario of starting to save for retirement at age 20 is extremely unrealistic. Knock a decade or two off of those scenarios and see what you come up with.

Then add in the cost of disability insurance.

If you eliminate Social Security, I presume you are also eliminating Medicare, so you also need to factor in costs for medical care in retirement.

And unlike Social Security, personal reirement funds are not untouchable. Many people will dip into their funds for one reason or another and will sometimes be unable to replace them.

Oh, and don't forget to throw in a catastrophic investment loss in year 42.
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Old 02-21-2005, 09:41 AM   #7
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Also it is missing the Inflation (Tax) Rate. My fuzzy guess is 2% loss per year.

Also over 40 years a salary more than doubles due to lower value of the dollar. The dollar, as a reference, is like a rubber yardsitck, it is always sadly changing & cheapens.

Doubling in prices, due to a crappy cheap dollar, occurs every 7 years or decade in general. CRAPPY, LOUSY, STINKING, CHEAP, WORTHLESS Fed Reserve United States garbage Dollar.
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Old 02-21-2005, 09:42 AM   #8
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Thanks for the response. That clears things up. A few more questions because I'm neither an economist nor a financial expert.


1. The current system, if I understand correctly, invests in Government bonds. The rate of return on these is often called 3% Is it correct that this is steady, or does it fluctuate? Can you do a calc on 3% instead of 6%? I'm curious if the Soc Sec gives a return "equal to" the purported income.

2. This value you give for income, this is interest? Or is this an annuity that was purchased with the money? If it's interest, as I'm thinking it appears to be, is 6% a reasonable return for an ULTRA CONSERVATIVE investment? Seems like if you're talking about your retirement income, you can no longer afford ups and downs, right? You can't afford to weather a year or two at 2% interest or a loss (what would you eat? principle?). So is 6% representative of an ultra-conservative rock-steady investment? If I'm only geting $600/mo, I can't afford to have it fluctuate or the rent doesn't get paid.

3. Does this interest income ever provide a cost of living increase, the way Social Security does? Or am I stuck on $600/mo for the next 30 years (assuming it doesn't fluctuate and force me to dip into principle)


Thanks, I'm pretty new at this. I'm just an engineer.
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Old 02-21-2005, 09:46 AM   #9
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In other words,

2% loss to Inflation Tax

9.5% per annum increase in Market equitites

Overall expected rate = 7.5% per year. (no bonds, no money market)
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Old 02-21-2005, 09:56 AM   #10
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Quote:
Originally Posted by Rhea
1. The current system, if I understand correctly, invests in Government bonds. The rate of return on these is often called 3% Is it correct that this is steady, or does it fluctuate? Can you do a calc on 3% instead of 6%? I'm curious if the Soc Sec gives a return "equal to" the purported income.
Here it is:
Code:
Starting value, if any:             0.00
Starting salary:                    10,000.00   (833.33 monthly)
Ending salary:                      14,741.23   (1,228.44 monthly)
Number of years worked:             40
Yearly raise of salary (%):         1.00
Percent of salary invested:         6.20
Company contribution:               0.00
Investment portfolio yield:         3.00
Chance of loss (yearly):            0.00
Pecent of portfolio lost:           0.00
Retirement interest of portfolio:   3.00
Results ----------------------------
Lifetime earnings:                  488,863.73
Lifetime invested:                  30,309.55
Company matching:                   0,000.00
Amount at retirement:               56,230.34
Monthly income at retirement:       140.58
Quote:
Originally Posted by Rhea
2. This value you give for income, this is interest? Or is this an annuity that was purchased with the money? If it's interest, as I'm thinking it appears to be, is 6% a reasonable return for an ULTRA CONSERVATIVE investment?
Straight interest, not an annuity that you may purchase. Local bonds, very conservative mutual funds can yield such a return.

Quote:
Originally Posted by Rhea
3. Does this interest income ever provide a cost of living increase, the way Social Security does? Or am I stuck on $600/mo for the next 30 years (assuming it doesn't fluctuate and force me to dip into principle)
No adjustment. What you see is what you get.

It is very interesting to see more aggressive funds. The results, though prone to have setbacks are are absolutely staggering.

And don't forget that people are not satisfied with 1% salary, increase. They will "shop" around to get better income.
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