1. Finanças Sept 21

2. Topics covered  Time value of money  Future value  Simple interest  Compound interest  Present value  Net present value

3. Time Value of Money  People always prefer to receive $1 today than $1 in the future  The relationship between $1 today and (possibly uncertain) $1 in the future shows the time value of money

4. Future Values Future Value Compound Interest Simple Interest

5. Future Values Example - Simple Interest Interest earned at a rate of 6% for five years on a principal balance of $100.

6. Example - Simple Interest Interest earned at a rate of 6% for five years on a principal balance of $100. TodayFuture Years 1 2 3 4 5 Interest Earned Value100 Future Values

7. Example - Compound Interest Interest earned at a rate of 6% for five years on the previous year’s balance. Interest Earned Per Year =

8. Example - Compound Interest Interest earned at a rate of 6% for five years on the previous year’s balance. TodayFuture Years 1 2 3 4 5 Interest Earned Value100 Future Values

9. Future Value of C = FV

10. Future Values Example - FV What is the future value of $100 if interest is compounded annually at a rate of 6% for five years?

11. Future Values with Compounding Interest Rates

12. Manhattan Island Sale Peter Minuit bought Manhattan Island for $24 in 1626. Was this a good deal? To answer, determine $24 is worth in the year 2006, compounded at 8%.

13. Present Values  Present Value:  PV Factor:  Discount Rate:

14. Present Values

15. Example You just bought a new computer for $3,000. The payment terms are 2 years same as cash. If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years?

16. Present Values PV Factor = PV of $1  Discount Factors can be used to compute the present value of any cash flow.

17. Present Values with Compounding Interest Rates

18. Net Present Value NPV = - cost + PV  Example: A project costs $50,000. The project will generate profits of $25,000 one year from now, $20,000 two years from now, and $15,000 three years from now. The discount rate is 7% for this project. What is the NPV of the project?

19. Cash flows PV factorPV Year 0 -50,000 1 25,000 2 20,000 3 15,000 NPV