1 / 27

Lecture 5: Time Value of Money

Learn the fundamentals of time value of money, including future value, present value, compound interest, annuities, and more. Discover how to calculate values and rates for smarter financial decisions.

buckners
Download Presentation

Lecture 5: Time Value of Money

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 5: Time Value of Money Money has a time value. It can be expressed in multiple ways: A dollar today held in savings will grow. A dollar received in a year is not worth as much as a dollar received today.

  2. Future Values Future Value: Amount to which an investment will grow after earning interest. Let r = annual interest rate Let t = # of years Simple Interest- Interest earned only on the original investment. Compound Interest- Interest earned on interest. Simple Interest Compound Interest

  3. Simple Interest: Example Interest earned at a rate of 7% for five years on a principal balance of $100. Example - Simple Interest Today Future Years 12345 Interest Earned Value 100 Value at the end of Year 5: $135 7 107 7 114 7 121 7 128 7 135

  4. Compound Interest: Example Interest earned at a rate of 7% for five years on the previous year’s balance. Example - Compound Interest Today Future Years 12345 Interest Earned Value 100 7 107 7.49 114.49 8.01 122.50 8.58 131.08 9.18 140.26 Value at the end of Year 5 = $140.26

  5. The Power of Compounding Interest earned at a rate of 7% for the first forty years on the $100 invested using simple and compound interest.

  6. Present Value What is it? Present Value– Value today of a future cash flow Why is it useful?

  7. Present Value Discount Rate: Interest rate used to compute present values of future cash flows Discount Factor: Present value of a $1 future payment • Present Value: Value today of a future cash flow Recall: t = number of years

  8. Present Value: Example Example Always ahead of the game, Tommy, at 8 years old, believes he will need $100,000 to pay for college. If he can invest at a rate of 7% per year, how much money should he ask his rich Uncle GQ to give him? Note: Ignore inflation/taxes

  9. Time Value of Money(applications) The PV formula has many applications. Given any variables in the equation, you can solve for the remaining variable.

  10. Present Values: Changing Discount Rates The present value of $100 to be received in 1 to 20 years at varying discount rates: Discount Rates

  11. PV of Multiple Cash Flows The present value of multiple cash flows can be calculated: Recall: r = the discount rate

  12. Multiple Cash Flows: Example Example Your auto dealer gives you the choice to pay $15,500 cash now or make three payments: $8,000 now and $4,000 at the end of the following two years. If your cost of money (discount rate) is 8%, which do you prefer? * The initial payment occurs immediately and therefore would not be discounted.

  13. Perpetuities What are they? Perpetuity – A stream of level cash payments that never ends. Let C = Yearly Cash Payment PV of Perpetuity: Recall: r = the discount rate

  14. Perpetuities: Example Example : In order to create an endowment, which pays $185,000 per year forever, how much money must be set aside today if the rate of interest is 8%? What if the first payment won’t be received until 3 years from today?

  15. Annuities What are they? Annuities are equally-spaced, level streams of cash flows lasting for a limited period of time. Why are they useful?

  16. Present Value of an Annuity Let: C = yearly cash payment r = interest rate t = number of years cash payment is received The terms within the brackets are collectively called the “annuity factor.”

  17. Annuities: Example Example: You are purchasing a home and are scheduled to make 30 annual installments of $10,000 per year. Given an interest rate of 5%, what is the price you are paying for the house (i.e. what is the present value)?

  18. Future Value of Annuities Example - Future Value of annual payments You plan to save $4,000 every year for 20 years and then retire. Given a 10% rate of interest, how much will you have saved by the time you retire?

  19. Annuity Due • What is it? • Annuity Due: Level stream of cash flows starting immediately. How does it differ from an ordinary annuity? How does the future value differ from an ordinary annuity? Recall: r = the discount rate

  20. Annuities Due: Example Example: Suppose you invest $429.59 annually at the beginning of each year at 10% interest. After 50 years, how much would your investment be worth?

  21. Interest Rates: EAR & APR What is EAR? Effective annual interest rate: - Interest rate that is annualized using compound interest What is APR? Annual percentage rate: Interest rate that is annualized using simple interest. How do they differ?

  22. EAR & APR Calculations Effective Annual Interest Rate (EAR): Annual Percentage Rate (APR): *where MR = monthly interest rate

  23. EAR and APR: Example Example: Given a monthly rate of 1%, what is the Effective Annual Rate(EAR)? What is the Annual Percentage Rate (APR)?

  24. Inflation What is it? What determines inflation rates? What is deflation?

  25. Inflation and Real Interest Exact calculation: Approximation:

  26. Inflation: Example Example If the nominal interest rate on your interest-bearing savings account is 2.0% and the inflation rate is 3.0%, what is the real interest rate?

  27. Appendix A: Inflation Annual U.S. Inflation Rates from 1900 - 2010

More Related