Calculate Present or Future Value of Cash Flows Principles of Cost Analysis and Management © Dale R Geiger 2011 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 Terminal Learning Objective • • Action: Calculate Present Or Future Value Of A Variety Of Cash Flow Scenarios • Standard: with at least 80% accuracy 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 • Identify and enter relevant report data to solve Present and Future Value equations using macro enabled cash flow templates © Dale R Geiger 2011 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 â Dale R Geiger 2011 Simple Interest • Interest earned on Principal only Principal * Annual Interest Rate * Time in Years • Invest $1 today at 10% interest for years Interest = $1 * 10 * = $.30 • $1 grows to $1.30 over years © Dale R Geiger 2011 Compound Interest or Future Value • • Invest $1 today at 10% Interest for years Principal * 10% (1 year) = Interest New Balance $1.00 * 10 = $.10 $1.10 $1.10 * 10 = $.11 $1.21 This relationship can be expressed as: $1.21 * 10 = $.12 Years Principal * (1 + Annual Interest Rate)Time in$1.33 $1*(1+.10)3 = $1.33 © Dale R Geiger 2011 Compound Interest or Future Value • • Invest $1 today at 10% Interest for years Principal * 10% (1 year) = Interest New Balance $1.00 * 10 = $.10 $1.10 $1.10 * 10 = $.11 $1.21 This relationship can be expressed as: $1.21 * 10 = $.12 Years Principal * (1 + Annual Interest Rate)Time in$1.33 $1*(1+.10)3 = $1.33 © Dale R Geiger 2011 Compound Interest or Future Value • • Invest $1 today at 10% Interest for years Principal * 10% (1 year) = Interest New Balance $1.00 * 10 = $.10 $1.10 $1.10 * 10 = $.11 $1.21 This relationship can be expressed as: $1.21 * 10 = $.12 Years Principal * (1 + Annual Interest Rate)Time in$1.33 $1*(1+.10)3 = $1.33 © Dale R Geiger 2011 Compound Interest or Future Value • • Invest $1 today at 10% Interest for years Principal * 10% (1 year) = Interest New Balance $1.00 * 10 = $.10 $1.10 $1.10 * 10 = $.11 $1.21 This relationship can be expressed as: $1.21 * 10 = $.12 Years Principal * (1 + Annual Interest Rate)Time in$1.33 $1*(1+.10)3 = $1.33 © Dale R Geiger 2011 Compound Interest or Future Value • • Invest $1 today at 10% Interest for years Principal * 10% (1 year) = Interest New Balance $1.00 * 10 = $.10 $1.10 $1.10 * 10 = $.11 $1.21 This relationship can be expressed as: $1.21 * 10 = $.12 Years Principal * (1 + Annual Interest Rate)Time in$1.33 $1*(1+.10)3 = $1.33 © Dale R Geiger 2011 10 The Present Value Table The Present Value of $1 at 10% to be received in years is $.75 © Dale R Geiger 2011 36 Effect of Interest Rate and Time 1.2 $0.83 0.8 0.6 10% $0.47 0.4 0.2 $1 to be received in years at 10% … and in years at 10% 10 X-Axis = Time in Years As Time increases, Present Value of $1 Decreases © Dale R Geiger 2011 37 Effect of Interest Rate and Time A higher discount rate causes the present value to 1.2 decrease more in the same years 0.8 $0.68 0.6 5% 10% 15% $0.47 0.4 $0.33 0.2 0 10 X-Axis = Time in Years As Time increases, Present Value of $1 Decreases © Dale R Geiger 2011 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 years from today assuming 12% discount rate? Steps: Identify the key variables • • • Cash flow Discount rate Time in years Build a timeline 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 = © Dale R Geiger 2011 41 Build a Timeline $ K 70 $60K $60,000 to be received in years 60 50 Unknown 40 Present Value 30 20 ? 10 0 X-Axis = Time in Years © Dale R Geiger 2011 42 Multiply by the PV Factor The Factor of $1 at 12% discount for 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) = $30,398 • The difference of $22 is caused by rounding in the table © Dale R Geiger 2011 44 Proof Year Principal 30,420 34,070 38,159 42,738 47,866 53,610 *8% = Interest * 12 * 12 * 12 * 12 * 12 * 12 © Dale R Geiger 2011 New Balance = $3,650 $34,070 = $4,088 $38,159 = $4,579 $42,738 = $5,129 $47,866 = $5,744 $53,610 = $6,433 $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 ... 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... 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... 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