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... 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 = $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 0.961 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

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 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

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

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 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 0.961 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

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

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.