1. Economics 173A The Time Value of Money Part 3

2. #1 - Is this a Good Investment? If I invest $100 today and expect $ 150 in 10 years, is this better than the 5 percent per year that my bank is offering me?

3. #1 Comparing investments.

4. #2 - When Do I Take My Pension? A pension is a guaranteed, fixed, annual “receipt” of money for life. So it is a life annuity. The younger you are when you take the pension, the longer the it runs, so the smaller will be the annual payment. Conversely, the older you are when you take the pension, the shorter it runs and the larger the annual payment to you. Do you want less for longer or more for shorter?

5. Quiz - When Do I Take My Social Security? This is a decision facing several million Americans each year. It is an important question and deserves thoughtful analysis. The numbers themselves provide an objective starting-point. Do I want less for longer – from age 62 to the end-of-my-life - or more for shorter – from age 66 to the end-of-my-life?

6. Starting at age 62 until Death Start at Age 66 until Death $ 1,837 / month or $ 22,044 per year $ 2,500 / month or $ 30,000 per year My Social Security as of 2/10/14 This is the decision that I will face in 10 months.

7. We need an Annuity, a rate, and a time ? Start at age 62 Start at Age 66 Here is the Annuity$ 22,044 per year$ 30,000 per year Rate - assume this …4% Years - to life expectancy, say to 85 years old. 2319 These decisions must be made now, so that means looking at this as a Present Value decision.

8. Which is Greater? Do I want $ 22,044 x PVFA ( 4%, 23) starting 10 months from now or Do I want $ 30,000 x PVFA ( 4%, 19) starting 4 years & 10 months from now For analysis, we can ignore the 10 months and just deal with the 4 year separation.

9. Remember this (from the TVM II Slides?) Summary of the Factor Tables and their Functions A Present Value Annuity Factor “PVFA” = (1 - PVF) / r turns an Annuity into a PV Which is what we need …

10. AnnuityPVFAPV Of the Annuity $ 22,044 At age 62 X 14.85 [1 point] = $ 327,504 [1 point] $ 30,000 At age 66X 13.13 [1 point] = $ 394,000 [1 point] The Annuities These results are not comparable because one is the PV of an annuity at age 62 and the other is the PV of an annuity at age 66. These values are 4 years apart

11. Annuity Present Value PVF to bring age 66 to age 62 The PV in 10 months Of each Annuity $ 327,504 At age 62X 1.00= $ 327,504 $ 394,000 At age 66X (1.04)^-4 =0.855 [2 points] = $ 336,885 A PV at age 62 [1 point] The Final Step Both results are now comparable because each is a PV of the respective annuity at the same age.

12. #3 What will my Payments be on a Loan? If you borrow money you taking a present value chunk of money and returning an annuity over a period “t” paying a rate “r”. The present value of your annuity payments must be equal to the amount of the loan.

13. #3 If you borrow $30,000 for 5 years at 8 percent, what will your monthly payments be, approximately? We want to know what five-year, annual annuity will have a present value of $30,000 at 8 percent? We know 3 of the 4 pieces of the puzzle: PV = $ 30,000 t = 5 years r = 8 percent.

14. What is a Loan? It is an exchange of a big package of money today in exchange for many small packages periodically into the future. The big package is sold by a lender to a borrower. The borrower pays the lender back through loan payments.

15. You borrow $30,000 You Know 1.$30,000 is the PV 2.For 5 years = t 3.At 8 percent per year interest = r And you want to find the monthly Payments, i.e. the amount of each “Future” payment.

16. Monthly payments on a $30,000 loan – approximated by doing annual discounting & dividing the result by 12 Solve this Value exchanged must be the same, so: $30,000 = PV sold = PV paid $ 30,000 = Payment x PVFA (8%, 5 years) $ 30,000 = $A x 3.99 from the Table Solving for $A we get the annual payment = $ 7,500 Now divide by 12 to get an approximation for the monthly payment = $ 625 per month

17. #4 - How much do I need to Save for my Retirement? 1.The amount you will have in retirement depends on: 2.When you start saving “t”. 3.How much you save “$A”. 4.How much you earn on your savings “r”.

18. #5 Should I Lease or Buy the equipment? If you “buy” you pay the full purchase price and you own the equipment! If you “lease” you make a modest down- payment followed by regular lease payments for a few years, then you return the equipment (because you don’t own it).