1. Time Value of Money Tutorial Prepared by Ronald Moy Tobin College of Business St. John’s University

2. Solving Time Value of Money Problems To solve a time value of money problem, you need to ask yourself a number of questions in order to determine which formula you will be using. Let’s BeginLet’s Begin* * Please view as a slideshow

3. Type of Cash Flow Is the amount one lump sum of money? YesNo

4. Present or Future Value Are you trying to determine what something is worth in the future or what some future amount is worth today? Worth TodayWorth in the Future Previous slideBeginning of tutorial

5. Annuity or Multiple Cash Flow Will you be paying (or receiving) an equal sum of money made at equal intervals? YesNo Previous slideBeginning of tutorial

6. Ordinary Annuity or Annuity Due? Is the first cash flow at the beginning of the period or at the end of the period? BeginningEnd Previous slideBeginning of tutorial

7. Present or Future Value You are finding the value of multiple cash flows. Are you looking for the value of these cash flows in the future or the value today? Value in the FutureValue Today Previous slideBeginning of tutorial

8. Future Value of Multiple Cash Flows The future value of multiple cash flows is Previous slideExample Beginning of tutorial

9. Annuity Due You are dealing with an annuity due. Are you looking for the value of the annuity in the future or what the annuity is worth today? Worth in the FutureWorth Today Previous slideBeginning of tutorial

10. Present Value of Multiple Cash Flows You are finding the present value of multiple cash flows Previous slideExample Beginning of tutorial

11. Ordinary Annuity You are dealing with an ordinary annuity. Are you looking for the value of the annuity in the future or what the annuity is worth today? Worth in the FutureWorth Today Previous slideBeginning of tutorial

12. Present Value of Ordinary Annuity You are looking for the present value of an ordinary annuity. The present value of an annuity formula is, Previous slideExample Beginning of tutorial

13. Present Value of Annuity Due You are looking for the present value of an annuity due. The present value of an annuity formula is, Previous slideExample Beginning of tutorial

14. Future Value of Ordinary Annuity You are looking for the future value of an ordinary annuity. The formula for the future value of an annuity is Previous slideExample Beginning of tutorial

15. Future Value of Annuity Due You are looking for the future value of an annuity due. The formula for the future value of an annuity is Previous slideExample Beginning of tutorial

16. Present Value of a Lump Sum You are looking for the present value of a lump sum. The present value for a lump sum is Previous slidePresent value example Beginning of tutorial

17. Future Value of a Lump Sum You are looking for the future value of a lump sum. The future value of a lump sum is, Previous slideFuture Value example Beginning of tutorial

18. Future Value a Lump Sum Example Find the future value in 10 years of $100 received today, if the interest rate is 8%. Previous slideFV Calculator Beginning of tutorialTimeline example

19. Future Value Time Line Previous slideBeginning of tutorial Previous slideBeginning of tutorial 19 0 123410 $215.89 $100...

20. Present Value of a Lump Sum Example Find the present value of $1,000 received 5 years from today if the interest rate is 9%. Previous slideCalculator example Beginning of tutorialTimeline example

21. Present Value Time Line Previous slideBeginning of tutorial 012345 $ 1,000 $649.93

22. Present Value of an Ordinary Annuity You can afford to make monthly car payments of $500 per month for 48 months. If the interest rate is 12% (1% per month). How much can you afford to spend on a car? Assume that the first car payment will be made in one month. Previous slideCalculator example Beginning of tutorial

23. Present Value of an Annuity Due Example You can afford to make monthly car payments of $500 per month for 48 months. If the interest rate is 12% (1% per month). How much can you afford to spend on a car? Assume that the first car payment will be made today. Previous slideCalculator example Beginning of tutorial

24. Future Value of an Ordinary Annuity Example Suppose you want to start saving next year for your retirement. You save $1,000 per year for the next 40 years. If the interest rate is 10%, how much will you have in your account after you make the last deposit? Previous slideCalculator example Beginning tutorial

25. Future Value of an Annuity Due Example Suppose you want to start saving today for your retirement. You save $1,000 per year for the next 40 years. If the interest rate is 10%, how much will you have in your account after you make the last deposit? Previous slideCalculator example Beginning of tutorial

26. Present Value of Multiple Cash Flows Example You are considering an investment that will pay you $1,000 in one year, $2,000 in two years and $3,000 in three years. If you want to earn 10% on your money, how much would you be willing to pay? Previous slideCalculator example Beginning of tutorialTimeline example

27. PV Time Line – Multiple Cash Flows Previous slideBeginning of tutorial 27 01234 1,0002,0003,000 909.09 1,652.89 2,253.94 4,815.92

28. Future Value of Multiple Cash Flows Example Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9% annually, how much will you have in two years? Previous slideTimeline example Beginning of tutorial

29. FV Time Line – Multiple Cash Flows Previous slide Beginning of tutorial 29 $ 500 012345 $ 600 $ 654.00 $594.05 $1,248.05

30. PV Calculator Calculator solution Previous slide Beginning of tutorial NI/YPMTPVFV 591000 CPT PV649.93

31. FV Calculator Calculator solution Previous slide Beginning of tutorial NI/YPMTPVFV 108-100 CPT FV215.89

32. Calc Ex. PV Ordinary Annuity Calculator solution Make sure calculator is set for “END” – Set by 2 nd BGN 2 nd Enter Previous slide Beginning of tutorial NI/YPMTPVFV 481500 CPT PV18,986.98

33. Calc Ex PV Annuity Due Calculator solution Make sure calculator is set for “BEG” – Set by 2 nd BGN 2 nd Enter Previous slide Beginning of tutorial NI/YPMTPVFV 481500 CPT PV19,176.85

34. Calc Ex FV Ordinary Annuity Calculator solution Make sure calculator is set for “END” – Set by 2 nd BGN 2 nd Enter Previous slide Beginning of tutorial NI/YPMTPVFV 40101000 CPT FV442,592.56

35. FV Annuity Due Calculator solution Make sure calculator is set for “BEG” – Set by 2 nd BGN 2 nd Enter Previous slide Beginning of tutorial NI/YPMTPVFV 40101000 CPT FV486,851.82

36. PV Multiple Cash Flows In this case, you will use the Cash Flow Worksheet on the calculator. – CF – CF0 – CF01 1000 Enter – F01 – CF02 2000 Enter – F02 – CF03 3000 Enter – F03 – NPV 10 Enter – CPT 4,815.93Previous slideBeginning of tutorialPrevious slideBeginning of tutorial