1. Calculate Present or Future Value of Cash Flows © 20111

2. Time Value of Money Concepts Is $1 received today worth the same as $1 to be received one year from today? Is $1 received today worth the same as $1 to be received one hundred years from today? Why or why not? © 20112

3. Terminal Learning Objective Action: Calculate Present or Future Value of a Variety of Cash Flow Scenarios Condition: You are training to become an ACE with access to ICAM course handouts, readings, and spreadsheet tools and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors Standard: with at least 80% accuracy Identify and enter relevant report data to solve Present and Future Value equations using macro enabled cash flow templates © 20113

4. Time Value of Money Concepts Money received Today: Can be invested Today to earn interest Can be spent Today at Today’s prices Money received in the Future: Has not yet begun to earn interest Can be spent in the Future at inflated prices © 20114

5. Simple Interest Interest earned on Principal only Principal * Annual Interest Rate * Time in Years Invest $1 today at 10% interest for 3 years Interest = $1 *.10 * 3 = $.30 $1 grows to $1.30 over 3 years © 20115

6. Compound Interest or Future Value Invest $1 today at 10% Interest for 3 years This relationship can be expressed as: Principal * (1 + Annual Interest Rate) Time in Years $1*(1+.10) 3 = $1.33 Principal* 10% (1 year)= InterestNew Balance $1.00*.10= $.10$1.10 *.10= $.11$1.21 *.10= $.12$1.33 © 20116

7. Compound Interest or Future Value Invest $1 today at 10% Interest for 3 years This relationship can be expressed as: Principal * (1 + Annual Interest Rate) Time in Years $1*(1+.10) 3 = $1.33 Principal* 10% (1 year)= InterestNew Balance $1.00*.10= $.10$1.10 *.10= $.11$1.21 *.10= $.12$1.33 © 20117

8. Compound Interest or Future Value Invest $1 today at 10% Interest for 3 years This relationship can be expressed as: Principal * (1 + Annual Interest Rate) Time in Years $1*(1+.10) 3 = $1.33 Principal* 10% (1 year)= InterestNew Balance $1.00*.10= $.10$1.10 *.10= $.11$1.21 *.10= $.12$1.33 © 20118

9. Compound Interest or Future Value Invest $1 today at 10% Interest for 3 years This relationship can be expressed as: Principal * (1 + Annual Interest Rate) Time in Years $1*(1+.10) 3 = $1.33 Principal* 10% (1 year)= InterestNew Balance $1.00*.10= $.10$1.10 *.10= $.11$1.21 *.10= $.12$1.33 © 20119

10. Compound Interest or Future Value Invest $1 today at 10% Interest for 3 years This relationship can be expressed as: Principal * (1 + Annual Interest Rate) Time in Years $1*(1+.10) 3 = $1.33 Principal* 10% (1 year)= InterestNew Balance $1.00*.10= $.10$1.10 *.10= $.11$1.21 *.10= $.12$1.33 © 201110

11. Effect of Interest Rate and Time X-Axis = Time in Years As Time increases, Future Value of $1 Increases After 2 years at 10% …..and after 8 years at 10% © 2011 11

12. Effect of Interest Rate and Time X-Axis = Time in Years As interest rate increases, Future Value of $1 Increases A higher interest rate causes the future value to increase more in the same 8 years. © 2011 12

13. The Future Value Table The Value of $1 at 10% interest after 8 years is $2.14 The Factors are pre-calculated on the FV Table. © 2011 13

14. Learning Check How does compound interest differ from simple interest? How does number of years affect the future value of an investment? © 201114

15. Demonstration Problem If I invest $50,000 today at 8%, what will it be worth in 10 years? Steps: 1.Identify the key variables Cash flow Interest rate Time in years 2.Build a timeline 3.Multiply cash flow by FV factor from the Table © 201115

16. Identify Key Variables Cash Flows $50,000 to be paid now Cash Payments are negative numbers Some unknown amount to be received ten years in the future Cash Receipts are positive numbers Interest Rate = 8% Time in Years = 10 © 201116

17. Build a Timeline $50,000 to be invested now $ $ X-Axis = Time in Years Unknown amount to be received in 10 years K K $50K ? © 201117

18. Multiply by the FV Factor The Factor of $1 at 8% interest for 10 years is 2.159 $50,000 * 2.159 = $107,950 © 2011 18

19. Using the Formula The formula proves that the answer from the table is correct: $50,000 * (1 +.08) 10 = $107,946 The difference of $4 is caused by rounding in the table © 201119

20. Proof YearPrincipal* 8 %= InterestNew Balance 1$50,000*.08= $4,000$54,000 2$54.000*.08= $4,320$58,320 3 *.08= $4,666$62,986 4 *.08= $5,039$68,024 5 *.08= $5,442$73,466 6 *.08= $5,877$79,343 7 *.08= $6,347$85,690 8 *.08= $6,855$92,545 9 *.08= $7,404$99,949 10$99,949*.08= $7,996 © 201120

21. Learning Check What is the first step in solving a future value problem? How are cash payments represented in the timeline? © 201121

22. Future Value vs. Present Value Future Value answers the question: To what value will $1 grow in the Future? Present Value answers the question: What is the value Today of $1 to be received in the Future? -or- How much must be invested today to achieve $1 in the Future? © 201122

23. Future Value vs. Present Value A dollar to be received in the future is worth less than a dollar received today The value of a dollar received today will increase in the future © 201123

24. Present Value Concepts What is the value Today of $1 to be received one year in the Future? How much must be invested Today to grow to $1 one year from Today? The answer to these two questions is the same! © 201124

25. Present Value Concepts Discount Rate Discount Rate represents interest or inflation Assume a rate of 10% What is the cost expression for this relationship? $Investment Today + Interest = $1.00 -or- $Investment + ($Investment *.10) = $1.00 $Investment * (1+.10) = $1.00 $Investment = $1/(1.10) $Investment = $.91 © 201125

26. Present Value Concepts Discount Rate Discount Rate represents interest or inflation Assume a rate of 10% What is the cost expression for this relationship? $Investment Today + Interest = $1.00 -or- $Investment + ($Investment *.10) = $1.00 $Investment * (1+.10) = $1.00 $Investment = $1/(1.10) $Investment = $.91 © 201126

27. Present Value Concepts Discount Rate Discount Rate represents interest or inflation Assume a rate of 10% What is the cost expression for this relationship? $Investment Today + Interest = $1.00 -or- $Investment + ($Investment *.10) = $1.00 $Investment * (1+.10) = $1.00 $Investment = $1/(1.10) $Investment = $.91 © 201127

28. Present Value Concepts Discount Rate Discount Rate represents interest or inflation Assume a rate of 10% What is the cost expression for this relationship? $Investment Today + Interest = $1.00 -or- $Investment + ($Investment *.10) = $1.00 $Investment * (1+.10) = $1.00 $Investment = $1/(1.10) $Investment = $.91 © 201128

29. Present Value Concepts Discount Rate Discount Rate represents interest or inflation Assume a rate of 10% What is the cost expression for this relationship? $Investment Today + Interest = $1.00 -or- $Investment + ($Investment *.10) = $1.00 $Investment * (1+.10) = $1.00 $Investment = $1/(1.10) $Investment = $.91 © 201129

30. Proof Plug $.91 in to the original equation: $.91 + ($.91 *.10) = $1.00 $.91 +.09 = $1.00 This relationship is fairly simple for one period, but what about multiple periods? © 201130

31. Present Value Concepts How much must be invested today to achieve $1.00 three years from today? What is the cost expression for this relationship? $Investment * (1 + Rate) #Years = $Future Value $Investment = $Future Value / (1 + Rate) #Years -or- $Investment * (1+.10) 3 = $1.00 $Investment = $1.00 / (1+.10) 3 $Investment = $.75 © 201131

32. Present Value Concepts How much must be invested today to achieve $1.00 three years from today? What is the cost expression for this relationship? $Investment * (1 + Rate) #Years = $Future Value $Investment = $Future Value / (1 + Rate) #Years -or- $Investment * (1+.10) 3 = $1.00 $Investment = $1.00 / (1+.10) 3 $Investment = $.75 © 201132

33. Present Value Concepts How much must be invested today to achieve $1.00 three years from today? What is the cost expression for this relationship? $Investment * (1 + Rate) #Years = $Future Value $Investment = $Future Value / (1 + Rate) #Years -or- $Investment * (1+.10) 3 = $1.00 $Investment = $1.00 / (1+.10) 3 $Investment = $.75 © 201133

34. Present Value Concepts Present Value The Investment amount is known as the Present Value The Present Value relationship is expressed in the formula: Future Cash Flow * 1/(1 + Rate) #Years -or- $1 * 1/(1.10) 3 = $.75 © 201134

35. Proof There is also a table shortcut for Present Value Principal* 10% (1 year)= InterestNew Balance $.75*.10= $.075$.83 *.10= $.083$.91 *.10= $.091 © 201135

36. The Present Value Table The Present Value of $1 at 10% to be received in 3 years is $.75 © 201136

37. Effect of Interest Rate and Time X-Axis = Time in Years As Time increases, Present Value of $1 Decreases $1 to be received in 2 years at 10% …..and in 8 years at 10% © 2011 37

38. Effect of Interest Rate and Time X-Axis = Time in Years As Time increases, Present Value of $1 Decreases A higher discount rate causes the present value to decrease more in the same 8 years. © 2011 38

39. Learning Check What does Present Value represent? How does the Present Value table differ from the Future Value table? © 201139

40. Demonstration Problem What is the Present Value of a $60,000 cash flow to be received 6 years from today assuming 12% discount rate? Steps: 1.Identify the key variables Cash flow Discount rate Time in years 2.Build a timeline 3.Multiply cash flow by the Factor from the PV Table © 201140

41. Identify Key Variables Cash Flow $60,000 to be received in the Future Is equal to some unknown amount Today Discount Rate = 12% Time in Years = 6 © 201141

42. Build a Timeline Unknown Present Value Unknown Present Value $ X-Axis = Time in Years $60,000 to be received in 6 years K ? $60K © 201142

43. Multiply by the PV Factor The Factor of $1 at 12% discount for 6 years is 0.507 $60,000 * 0.507 = $30,420 © 201143

44. Using the Formula The formula proves that the answer from the table is correct: $60,000 * 1/(1 +.12) 6 = $30,398 The difference of $22 is caused by rounding in the table © 201144

45. Proof YearPrincipal* 8 %= InterestNew Balance 1 30,420 *.12 = $3,650 $34,070 2 34,070 *.12 = $4,088 $38,159 3 38,159 *.12 = $4,579 $42,738 4 42,738 *.12 = $5,129 $47,866 5 47,866 *.12 = $5,744 $53,610 6 53,610 *.12 = $6,433 © 201145

46. Practical Exercise © 201146

47. Time Value of Money Worksheet © 2011 Enter key variables in the blank white cells to generate the graph shown below 47

48. Time Value of Money Worksheet © 2011 The spreadsheet tool also calculates Present Value 48

49. Practical Exercise © 201149