# Calculate Present or Future Value of Cash Flows

- Slides: 50

Calculate Present or Future Value of Cash Flows Principles of Cost Analysis and Management © Dale R. Geiger 2011 1

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? © Dale R. Geiger 2011 2

Terminal Learning Objective • Action: Calculate Present Or Future Value Of A Variety Of Cash Flow Scenarios • Condition: You are a cost advisor technician with access to all regulations/course handouts, 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 © Dale R. Geiger 2011 3

Time Value of Money Concepts Money received Today: Money received in the Future: • Can be invested Today to earn interest • Has not yet begun to earn interest • Can be spent Today at Today’s prices • Can be spent in the Future at inflated prices © Dale R. Geiger 2011 4

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 © Dale R. Geiger 2011 5

Compound Interest or Future Value • Invest $1 today at 10% Interest for 3 years Principal * 10% (1 year) = Interest New Balance $1. 00 $1. 10 $1. 21 *. 10 = $. 11 = $. 12 $1. 10 $1. 21 $1. 33 • This relationship can be expressed as: Principal * (1 + Annual Interest Rate)Time in Years $1*(1+. 10)3 = $1. 33 © Dale R. Geiger 2011 6

Compound Interest or Future Value • Invest $1 today at 10% Interest for 3 years Principal * 10% (1 year) = Interest New Balance $1. 00 $1. 10 $1. 21 *. 10 = $. 11 = $. 12 $1. 10 $1. 21 $1. 33 • This relationship can be expressed as: Principal * (1 + Annual Interest Rate)Time in Years $1*(1+. 10)3 = $1. 33 © Dale R. Geiger 2011 7

Compound Interest or Future Value • Invest $1 today at 10% Interest for 3 years Principal * 10% (1 year) = Interest New Balance $1. 00 $1. 10 $1. 21 *. 10 = $. 11 = $. 12 $1. 10 $1. 21 $1. 33 • This relationship can be expressed as: Principal * (1 + Annual Interest Rate)Time in Years $1*(1+. 10)3 = $1. 33 © Dale R. Geiger 2011 8

Compound Interest or Future Value • Invest $1 today at 10% Interest for 3 years Principal * 10% (1 year) = Interest New Balance $1. 00 $1. 10 $1. 21 *. 10 = $. 11 = $. 12 $1. 10 $1. 21 $1. 33 • This relationship can be expressed as: Principal * (1 + Annual Interest Rate)Time in Years $1*(1+. 10)3 = $1. 33 © Dale R. Geiger 2011 9

Compound Interest or Future Value • Invest $1 today at 10% Interest for 3 years Principal * 10% (1 year) = Interest New Balance $1. 00 $1. 10 $1. 21 *. 10 = $. 11 = $. 12 $1. 10 $1. 21 $1. 33 • This relationship can be expressed as: Principal * (1 + Annual Interest Rate)Time in Years $1*(1+. 10)3 = $1. 33 © Dale R. Geiger 2011 10

Effect of Interest Rate and Time $ 4. 00 $ 3. 00 $ 2. 14 $ 2. 00 10% $ 1. 21 $ 1. 00 After 2 years at 10% …. . and after 8 years at 10% $- 0 2 4 6 X-Axis = Time in Years As Time increases, Future Value of $1 Increases © Dale R. Geiger 2011 8 10 11

Effect of Interest Rate and Time $ 4. 00 A higher interest rate causes the future value to increase more in the same 8 years. $ 3. 00 $ 3. 06 15% $ 2. 14 $ 2. 00 10% 5% $ 1. 48 $ 1. 00 $- 0 2 4 6 X-Axis = Time in Years As interest rate increases, Future Value of $1 Increases © Dale R. Geiger 2011 8 10 12

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. © Dale R. Geiger 2011 13

Check on Learning • How does compound interest differ from simple interest? • How does number of years affect the future value of an investment? © Dale R. Geiger 2011 14

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 © Dale R. Geiger 2011 15

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 © Dale R. Geiger 2011 16

Build a Timeline $ 120 K ? 100 $50, 000 to be invested now 80 60 Unknown amount to be received in 10 years 40 20 0 -20 0 1 2 3 4 5 6 7 8 9 10 -40 $ -60 K $50 K X-Axis = Time in Years © Dale R. Geiger 2011 17

Multiply by the FV Factor The Factor of $1 at 8% interest for 10 years is 2. 159 $50, 000 * 2. 159 = $107, 950 © Dale R. Geiger 2011 18

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 © Dale R. Geiger 2011 19

Proof Year Principal 1 $50, 000 2 $54. 000 3 $58, 320 4 5 6 7 8 9 10 $62, 986 $68, 024 $73, 466 $79, 343 $85, 690 $92, 545 $99, 949 *8% = Interest *. 08 = $4, 000 = $4, 320 = $4, 666 $54, 000 $58, 320 $62, 986 *. 08 *. 08 = $5, 039 = $5, 442 = $5, 877 = $6, 347 = $6, 855 = $7, 404 = $7, 996 $68, 024 $73, 466 $79, 343 $85, 690 $92, 545 $99, 949 $107, 945 © Dale R. Geiger 2011 New Balance 20

Check on Learning • What is the first step in solving a future value problem? • How are cash payments represented in the timeline? © Dale R. Geiger 2011 21

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? © Dale R. Geiger 2011 22

Future Value vs. Present Value The value of a dollar received today will increase in the future A dollar to be received in the future is worth less than a dollar received today © Dale R. Geiger 2011 23

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! © Dale R. Geiger 2011 24

Present Value Concepts • 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 © Dale R. Geiger 2011 25

Present Value Concepts • 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 © Dale R. Geiger 2011 26

Present Value Concepts • 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 © Dale R. Geiger 2011 27

Present Value Concepts • 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 © Dale R. Geiger 2011 28

Present Value Concepts • 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 © Dale R. Geiger 2011 29

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? © Dale R. Geiger 2011 30

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 © Dale R. Geiger 2011 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 © Dale R. Geiger 2011 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 © Dale R. Geiger 2011 33

Present Value Concepts • 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 © Dale R. Geiger 2011 34

Proof Principal * 10% (1 year) = Interest $. 75 $. 83 $. 91 *. 10 = $. 075 = $. 083 = $. 091 New Balance $. 83 $. 91 $1. 00 • There is also a table shortcut for Present Value © Dale R. Geiger 2011 35

The Present Value Table The Present Value of $1 at 10% to be received in 3 years is $. 75 © Dale R. Geiger 2011 36

Effect of Interest Rate and Time $ 1. 20 $ 1. 00 $ 0. 83 $ 0. 80 $ 0. 60 10% $ 0. 47 $ 0. 40 $ 0. 20 $- $1 to be received in 2 years at 10% …. . and in 8 years at 10% 0 2 4 6 X-Axis = Time in Years As Time increases, Present Value of $1 Decreases © Dale R. Geiger 2011 8 10 37

Effect of Interest Rate and Time $ 1. 20 A higher discount rate causes the present value to decrease more in the same 8 years. $ 1. 00 $ 0. 80 $ 0. 68 $ 0. 60 5% 10% $ 0. 47 15% $ 0. 40 $ 0. 33 $ 0. 20 $- 0 2 4 6 X-Axis = Time in Years As Time increases, Present Value of $1 Decreases © Dale R. Geiger 2011 8 10 38

Check on Learning • What does Present Value represent? • How does the Present Value table differ from the Future Value table? © Dale R. Geiger 2011 39

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 © Dale R. Geiger 2011 40

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 © Dale R. Geiger 2011 41

Build a Timeline $ 70 K $60, 000 to be received in 6 years 60 50 Unknown Present Value 40 30 20 ? 10 0 0 1 2 X-Axis = Time in Years 3 © Dale R. Geiger 2011 4 5 6 42

Multiply by the PV Factor The Factor of $1 at 12% discount for 6 years is 0. 507 $60, 000 * 0. 507 = $30, 420 © Dale R. Geiger 2011 43

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 © Dale R. Geiger 2011 44

Proof Year 1 2 3 4 5 6 Principal 30, 420 34, 070 38, 159 42, 738 47, 866 53, 610 *8% *. 12 = Interest = $3, 650 = $4, 088 = $4, 579 = $5, 129 = $5, 744 = $6, 433 © Dale R. Geiger 2011 New Balance $34, 070 $38, 159 $42, 738 $47, 866 $53, 610 $60, 044 45

Check on Learning • How does time affect the present value of a cash flow? • How does the discount rate affect the present value of a cash flow? © Dale R. Geiger 2011 46

Practical Exercise © Dale R. Geiger 2011 47

Time Value of Money Worksheet Enter key variables in the blank white cells to generate the graph shown below © Dale R. Geiger 2011 48

Time Value of Money Worksheet The spreadsheet tool also calculates Present Value © Dale R. Geiger 2011 49

Practical Exercise © Dale R. Geiger 2011 50