# Hypothetical Situation by C48y311X

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```									Hypothetical Situation...

   Suppose you win the Publisher’s
Clearinghouse Sweepstakes and are
given a choice of taking
 \$10,000 today or
 \$12,000 three years from today

   Which should you choose?
   Re-stated, what is the promise of
\$12,000 three years from now worth
to you today?
Present Value Calculations

   Present value calculation - assessing
what a future dollar amount is worth to
you today.
 Present value of a future lump sum –
PV
 Present value of future periodic
payments – PVA
Present value of a future
lump sum...
FV
PV 
1  r n

   where
 r = interest rate per period
 n = number of periods
 FV = the future value of the
investment
Back to our example...
   FV = \$12,000
   Use r = .08
   Get your money in 3 years

12 ,000
PV 
1  .08 3
   = \$9,525.99
   Implies that, based on economic considerations, you should
take the \$10,000 today
Present Value of a lump sum

Period            1%      2%      3%      4%      5%      6%      7%      8%

1     0.990   0.980   0.971   0.962   0.952   0.943   0.935   0.926

2     0.980   0.961   0.943   0.925   0.907   0.890   0.873   0.857

3     0.971   0.942   0.915   0.889   0.864   0.840   0.816   0.794

4     0.961   0.924   0.888   0.855   0.823   0.792   0.763   0.735

5     0.951   0.906   0.863   0.822   0.784   0.747   0.713   0.681

6     0.942   0.888   0.837   0.790   0.746   0.705   0.666   0.630

7     0.933   0.871   0.813   0.760   0.711   0.665   0.623   0.583

8     0.923   0.853   0.789   0.731   0.677   0.627   0.582   0.540

9     0.914   0.837   0.766   0.703   0.645   0.592   0.544   0.500

10     0.905   0.820   0.744   0.676   0.614   0.558   0.508   0.463

11     0.896   0.804   0.722   0.650   0.585   0.527   0.475   0.429

12     0.887   0.788   0.701   0.625   0.557   0.497   0.444   0.397

13     0.879   0.773   0.681   0.601   0.530   0.469   0.415   0.368

14     0.870   0.758   0.661   0.577   0.505   0.442   0.388   0.340

15     0.861   0.743   0.642   0.555   0.481   0.417   0.362   0.315

16     0.853   0.728   0.623   0.534   0.458   0.394   0.339   0.292
How do these calculations change if the
payment is repeated periodically?

   Suppose you want to know how much a
retirement annuity is worth to you today if it
claims…
 \$20,000 annual payment
 5 year time period
 r=.03
   Need to calculate the present value of future
periodic payments (also called the present
value of annuity payments → PVA)
Present Value of an Annuity

1  1  r                n
PVA  FV              
      r      
 All terms defined as previously
 Please note: That really is
a negative n [-n]
   Previous Example:
 \$20,000  annual payment
 5 year time period
 r=.03
1  1  .03 
5
PVA  20,000              
      .03     

   PVA = \$91,594.14
Present value of an annuity

Period          1%      2%      3%      4%      5%      6%      7%      8%

1   0.990   0.980   0.971   0.962   0.952   0.943   0.935   0.926

2   1.970   1.942   1.913   1.886   1.859   1.833   1.808   1.783

3   2.941   2.884   2.829   2.775   2.723   2.673   2.624   2.577

4   3.902   3.808   3.717   3.630   3.546   3.465   3.387   3.312

5   4.853   4.713   4.580   4.452   4.329   4.212   4.100   3.993

6   5.795   5.601   5.417   5.242   5.076   4.917   4.767   4.623

7   6.728   6.472   6.230   6.002   5.786   5.582   5.389   5.206

8   7.652   7.325   7.020   6.733   6.463   6.210   5.971   5.747

9   8.566   8.162   7.786   7.435   7.108   6.802   6.515   6.247

10   9.471   8.983   8.530   8.111   7.722   7.360   7.024   6.710
Example:

 \$500 received each month for 2
years, assuming 8% annual interest
 FV = \$500 per month

 r = (.08/12) = .006667

 n = 2(12) = 24
1  1  .00666724

PVA  500                       
       .006667         

   PVA = \$11,055.27
Let’s try it...
   Uncle Bob dies and leaves you \$750,000, but
you cannot collect it for 25 years. Assuming a
3% inflation rate, what is the money worth to
you today?
   PV
         750 ,000
PV 
1  .03 25

   PV = \$358,204.18
Present Value of a Lump Sum
Period         1%      2%      3%      4%      5%
1    0.990   0.980   0.971   0.962   0.952

2    0.980   0.961   0.943   0.925   0.907

3    0.971   0.942   0.915   0.889   0.864

4    0.961   0.924   0.888   0.855   0.823

5    0.951   0.906   0.863   0.822   0.784

6    0.942   0.888   0.837   0.790   0.746

7    0.933   0.871   0.813   0.760   0.711

8    0.923   0.853   0.789   0.731   0.677

9    0.914   0.837   0.766   0.703   0.645

10   0.905   0.820   0.744   0.676   0.614

11   0.896   0.804   0.722   0.650   0.585

12   0.887   0.788   0.701   0.625   0.557

13   0.879   0.773   0.681   0.601   0.530

14   0.870   0.758   0.661   0.577   0.505

15   0.861   0.743   0.642   0.555   0.481

16   0.853   0.728   0.623   0.534   0.458

17   0.844   0.714   0.605   0.513   0.436

18   0.836   0.700   0.587   0.494   0.416

19   0.828   0.686   0.570   0.475   0.396

20   0.820   0.673   0.554   0.456   0.377

25   0.780   0.610   0.478   0.375   0.295

30   0.742   0.552   0.412   0.308   0.231

35   0.706   0.500   0.355   0.253   0.181

40   0.672   0.453   0.307   0.208   0.142

50   0.608   0.372   0.228   0.141   0.087
Let’s try it some more...
   Your work is offering an incentive for you to
retire early. Should you take \$500,000 now or
\$30,000 per year for the next 20 years?
   PVA
               1  1  .0320 
PVA  30,000                 
       .03       
   PVA = \$446,324.25
   So, take the \$500,000 now
Present Value of an Annuity
Period           1%       2%       3%       4%       5%

1    0.990    0.980    0.971    0.962    0.952

2    1.970    1.942    1.913    1.886    1.859

3    2.941    2.884    2.829    2.775    2.723

4    3.902    3.808    3.717    3.630    3.546

5    4.853    4.713    4.580    4.452    4.329

6    5.795    5.601    5.417    5.242    5.076

7    6.728    6.472    6.230    6.002    5.786

8    7.652    7.325    7.020    6.733    6.463

9    8.566    8.162    7.786    7.435    7.108
10    9.471    8.983    8.530    8.111    7.722

11   10.368    9.787    9.253    8.760    8.306

12   11.255   10.575    9.954    9.385    8.863

13   12.134   11.348   10.635    9.986    9.394

14   13.004   12.106   11.296   10.563    9.899

15   13.865   12.849   11.938   11.118   10.380

16   14.718   13.578   12.561   11.652   10.838
17   15.562   14.292   13.166   12.166   11.274

18   16.398   14.992   13.754   12.659   11.690

19   17.226   15.678   14.324   13.134   12.085

20   18.046   16.351   14.877   13.590   12.462
Proverb #7: The Only Two
Certainties in Life are Death and
Taxes
   Costs and benefits of alternative
resource allocation options should
only be assessed net of taxes.

 Some choices of how to spend
resources are nontaxable and
therefore they are worth more than
taxable options.
 Some choices reduce your amount of
taxable income while others do not.
Example

   Finance the purchase of a car using…
 a 7% loan from your credit union, or
 a 7% home equity loan

   On the surface, the financing options
appear to be equivalent, but interest
paid on a home equity loan can be
deducted from taxable income while
interest paid on a credit union loan
cannot.
2012 Federal Tax Rates –
Single
Income between        Marginal Tax Bracket
\$0 - \$8,700           10%
\$8,700 - \$35,350      15%
\$35,350 - \$85,650     25%
\$85,650 - \$217,470    28%
\$217,470 - \$178,650   33%
> \$178,650            35%
2009 Federal Tax Rates –
Married Filing Jointly
Income between        Marginal Tax Bracket
\$0 - \$17,400          10%
\$17,400 - \$70,700     15%
\$70,700 - \$142,700    25%
\$142,700 - \$217,470   28%
\$217,470 - \$388,350   33%
> \$388,350            35%
Federal Tax Brackets
Interesting note:

 Highest marginal tax bracket now is
35%
 1952-1963 = 91%

 1964-1982 = btw 65-75%

 Then dropped to 45% for a while

 1988-1990 = bottomed out at 28%

 1992 = back up to 38%
Tax rates for 2013 are
scheduled to be:
 10% rate will collapse into the 15%
rate
 25% rate will become 28%

 28% rate will become 31%

 33% rate will become 36%

 35% rate will become 39.6%

These rate changes will take effect beginning in 2013 absent further
legislation.
Proverb #8: A Bird in the Hand is
(sometimes) Better than two in the
Bush
   The future is riddled with uncertainty
 future income
 future inflation

 But, some resource allocation options
involve more risk than others.
 All other things being equal,
households typically like to avoid risk
and uncertainty.

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