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 Period1%2%3%4%5%6%7%8% 10.9900.9800.9710.9620.9520.9430.9350.926 20.9800.9610.9430.9250.9070.8900.8730.857 30.9710.9420.9150.8890.8640.8400.8160.794 40.9610.9240.8880.8550.8230.7920.7630.735 50.9510.9060.8630.8220.7840.7470.7130.681 60.9420.8880.8370.7900.7460.7050.6660.630 70.9330.8710.8130.7600.7110.6650.6230.583 80.9230.8530.7890.7310.6770.6270.5820.540 90.9140.8370.7660.7030.6450.5920.5440.500 100.9050.8200.7440.6760.6140.5580.5080.463 110.8960.8040.7220.6500.5850.5270.4750.429 120.8870.7880.7010.6250.5570.4970.4440.397 130.8790.7730.6810.6010.5300.4690.4150.368 140.8700.7580.6610.5770.5050.4420.3880.340 150.8610.7430.6420.5550.4810.4170.3620.315 160.8530.7280.6230.5340.4580.3940.3390.292

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 Period1%2%3%4%5%6%7%8% 10.9900.9800.9710.9620.9520.9430.9350.926 21.9701.9421.9131.8861.8591.8331.8081.783 32.9412.8842.8292.7752.7232.6732.6242.577 43.9023.8083.7173.6303.5463.4653.3873.312 54.8534.7134.5804.4524.3294.2124.1003.993 65.7955.6015.4175.2425.0764.9174.7674.623 76.7286.4726.2306.0025.7865.5825.3895.206 87.6527.3257.0206.7336.4636.2105.9715.747 98.5668.1627.7867.4357.1086.8026.5156.247 109.4718.9838.5308.1117.7227.3607.0246.710

12. Example: $500 received each month for 2 years, assuming 8% annual interest FV = $500 per month r = (.08/12) =.006667 n = 2(12) = 24

13. PVA = $11,055.27

14. 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

15. Present Value of a Lump Sum Period1%2%3%4%5% 10.9900.9800.9710.9620.952 20.9800.9610.9430.9250.907 30.9710.9420.9150.8890.864 40.9610.9240.8880.8550.823 50.9510.9060.8630.8220.784 60.9420.8880.8370.7900.746 70.9330.8710.8130.7600.711 80.9230.8530.7890.7310.677 90.9140.8370.7660.7030.645 100.9050.8200.7440.6760.614 110.8960.8040.7220.6500.585 120.8870.7880.7010.6250.557 130.8790.7730.6810.6010.530 140.8700.7580.6610.5770.505 150.8610.7430.6420.5550.481 160.8530.7280.6230.5340.458 170.8440.7140.6050.5130.436 180.8360.7000.5870.4940.416 190.8280.6860.5700.4750.396 200.8200.6730.5540.4560.377 250.7800.6100.4780.3750.295 300.7420.5520.4120.3080.231 350.7060.5000.3550.2530.181 400.6720.4530.3070.2080.142 500.6080.3720.2280.1410.087

16. 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

17. Present Value of an Annuity Period1%2%3%4%5% 10.9900.9800.9710.9620.952 21.9701.9421.9131.8861.859 32.9412.8842.8292.7752.723 43.9023.8083.7173.6303.546 54.8534.7134.5804.4524.329 65.7955.6015.4175.2425.076 76.7286.4726.2306.0025.786 87.6527.3257.0206.7336.463 98.5668.1627.7867.4357.108 109.4718.9838.5308.1117.722 1110.3689.7879.2538.7608.306 1211.25510.5759.9549.3858.863 1312.13411.34810.6359.9869.394 1413.00412.10611.29610.5639.899 1513.86512.84911.93811.11810.380 1614.71813.57812.56111.65210.838 1715.56214.29213.16612.16611.274 1816.39814.99213.75412.65911.690 1917.22615.67814.32413.13412.085 2018.04616.35114.87713.59012.462

18. 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.

19. 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.

20. 2009 Federal Tax Rates – Single Income betweenMarginal Tax Bracket $0 - $8,35010% $8,351 - $33,95015% $33,951 - $82,25025% $82,251 - $171,55028% $171,551 - $372,95033% > $372,95135%

21. 2009 Federal Tax Rates – Married Filing Jointly Income betweenMarginal Tax Bracket $0 - $16,70010% $16,701 - $67,90015% $67,901 - $137,05025% $137,051 - $208,85028% $208,851 - $372,95033% > $372,95135%

22. Federal Tax Brackets

23. 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%

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.