1. Chapter IV Tutorial Time Value of Money

2. Important Abbreviations N (number of periods) I/Y (interest per year) PV (present value) PMT (payment) FV (future value)

3. Overview Present/Future Value FV = PV * (1+i)ⁿ PV = FV * 1/(1+i) ⁿ PV = $100 n = 2, i = 0.05 FV = 100 * 1.05 * 1.05 = 110.25 Page 201 has some key definitions, formulas, and equations

4. Problem 4-5 You have $1,500 to invest at 7% compounded annually How much you will have accumulated over a) 3 years b) 6 years c) 9 years Calculate amount of interest earned in first 3 years, years 3-6 and years 6-9 Moodle OR Appendix A in Book for Financial Table

5. Problem 4-5 Solution

6. Problem 4-7 Time value You can deposit $10,000 into an account paying 9% annual today or in 10 years from today How much better will you be at the end of 40 years if you decide to make the deposit today rather than 10 years from today?

7. Problem 4-7 Solution A. Investing today FV = PV * (1 + 0.09)^40 FV = $10,000 * (31.409) FV = $314,090 A. Investing in 10 years FV = PV * (1 + 0.09)^30 FV = $10,000 * (13.268) FV = $132,680 You would be better off by $181,410 ($314,090 - $132,680)

8. Problem 4-9 Single payment loan repayment A person borrows $200 with annual interest 14% What will be due if the loan is repaid after: a) 1 year b) 4 years c) 8 years

9. Problem 4-9 solution a) FV = $200 * (1.14)^1 = $228 b) FV = $200 * (1.14)^4 = $200 * (1.689) = $337.80 c) FV = $200 * (1.14)^8 = $200 * (2.853) = $570.60

10. *Problem 4-15 Time value and discount rates You won a lottery that pays $1,000,000 in 10 years What is the least you would be willing to sell it for if you can earn return: a) 6% b) 9% c) 12% What if the payment will be received in 15 years? Discuss the effect of both the size of the rate of return and the time until receipt of payment on the present value of a future sum

12. Problem 4-18 Calculate the future value of the annuity assuming that it is a) An ordinary annuity b) An annuity due Compare your findings. Given all things equal which type of annuity is preferable? Why?

13. Problem 4-18 (cont.) CaseAmount of Annuity Interest Rate Deposit Period (years) A$2,5008%10 B$50012%6 C$30,00020%5

15. Problem 4-22 Value of a retirement annuity For a single payment today you can obtain $12,000 at the end of each year for the next 25 years You can currently earn 9% on comparable investment What is the most you would pay for this annuity?

16. Problem 4-22 Solution Present value of annuity

17. Exercise 4-3 Gabrielle won $2.5 million Receive $1.3 million now Get paid $100,000 at the end of each of the next 25 years Gabrielle can earn 5% annually on her investment Which option should she take?

18. Exercise 4-3 Solution PVA = $1,300,000 Compare with present value annuity of 25x $100,000 with 5% discount PVIFA = 14.094 PVB = 100,000 * 14.094 = $1,409,400 PVB > PVA Gabrielle should take the $100,000 yearly payments

19. Questions?