1. 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?

2. 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

3. Present value of a future lump sum...
where
r = interest rate per period
n = number of periods
FV = the future value of the investment

4. Back to our example... FV = $12,000 Use r = .08
Get your money in 3 years
= $9,525.99
Implies that, based on economic considerations, you should take the $10,000 today

5. 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
0.961
0.925
0.907
0.890
0.873
0.857 3
0.942
0.915
0.889
0.864
0.840
0.816
0.794 4
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
0.837
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
0.766
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
0.601
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
0.728
0.534
0.458
0.394
0.339
0.292

6. 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)

7. Present Value of an Annuity
All terms defined as previously
Please note: That really is
a negative n [-n]

8. Previous Example:
$20,000 annual payment
5 year time period
r=.03

9. PVA = $91,594.14

10. 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

11. Example:
$500 received each month for 2 years, assuming 8% annual interest
FV = $500 per month
r = (.08/12) =
n = 2(12) = 24

12. PVA = $11,055.27

13. 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
PV = $358,204.18

14. Present Value of a Lump Sum
Period 1% 2% 3% 4% 5% 1
0.990
0.980
0.971
0.962
0.952 2
0.961
0.943
0.925
0.907 3
0.942
0.915
0.889
0.864 4
0.924
0.888
0.855
0.823 5
0.951
0.906
0.863
0.822
0.784 6
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
0.766
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
0.728
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
0.673
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

15. 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
PVA = $446,324.25
So, take the $500,000 now

16. 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

17. 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.

18. 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.

19. 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%

20. 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%

21. Federal Tax Brackets

22. Interesting note: Highest marginal tax bracket now is 35%
= 91%
= btw 65-75%
Then dropped to 45% for a while
= bottomed out at 28%
1992 = back up to 38%

23. 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.

24. 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.