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. Implications... _____ frequency of compounding = ___ PV
_____ length of investment = ____ PV
_____ interest rate = _____ PV

7. 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)

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

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

10. PVA = $91,594.14

11. 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

12. 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

13. 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

14. 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.

15. 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.

16. 2009 Federal Tax Rates – Single
Income between
Marginal Tax Bracket
$0 - $8,350
10%
$8,351 - $33,950
15%
$33,951 - $82,250
25%
$82,251 - $171,550
28%
$171,551 - $372,950
33%
> $372,951
35%

17. 2009 Federal Tax Rates – Married Filing Jointly
Income between
Marginal Tax Bracket
$0 - $16,700
10%
$16,701 - $67,900
15%
$67,901 - $137,050
25%
$137,051 - $208,850
28%
$208,851 - $372,950
33%
> $372,951
35%

18. Federal Tax Brackets

19. 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.