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...

wherer = interest rate per periodn = number of periodsFV = the future value of the investment

nrFV

PV

1

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

308.1

000,12

PV

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

Implications...

_____ frequency of compounding = ___ PV

_____ length of investment = ____ PV

_____ interest rate = _____ PV

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 periodr=.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

All terms defined as previously Please note: That really is a negative n [-n]

r

rFVPVA

n11

Previous Example:$20,000 annual payment 5 year time periodr=.03

PVA = $91,594.14

03.

03.11000,20

5

PVA

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

PVA = $11,055.27

006667.

006667.11500

24

PVA

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

2503.1

000,750

PV

Present Value of a Lump SumPeriod 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

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

03.

03.11000,30

20

PVA

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, ora 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.

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%

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%

Federal Tax Brackets

0

20

40

60

80

100

Years

%

Highest

Lowest

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%

Proverb #8: A Bird in the Hand is (sometimes) Better than two in the Bush The future is riddled with uncertainty

future incomefuture inflation

But, some resource allocation options involve more risk than others.

All other things being equal, households typically like to avoid risk and uncertainty.