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Calculate Present or Future Value of Cash Flows Intermediate Cost Analysis and Management © 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? â 2011 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 © 2011 Time Value of Money Concepts Money received Today: • Can be invested Today to earn interest Money received in the Future: • Has not yet begun to earn interest • Can be spent Today at Today’s prices • Can be spent in the Future at inflated prices © 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 © 2011 Compound Interest or Future Value • Invest $1 today at 10% Interest for years Principal * 10% (1 year) = Interest New Balance $1.00 $1.10 $1.21 * 10 * 10 * 10 = $.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 © 2011 Compound Interest or Future Value • Invest $1 today at 10% Interest for years Principal * 10% (1 year) = Interest New Balance $1.00 $1.10 $1.21 * 10 * 10 * 10 = $.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 © 2011 Compound Interest or Future Value • Invest $1 today at 10% Interest for years Principal * 10% (1 year) = Interest New Balance $1.00 $1.10 $1.21 * 10 * 10 * 10 = $.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 © 2011 Compound Interest or Future Value • Invest $1 today at 10% Interest for years Principal * 10% (1 year) = Interest New Balance $1.00 $1.10 $1.21 * 10 * 10 * 10 = $.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 © 2011 Compound Interest or Future Value • Invest $1 today at 10% Interest for years Principal * 10% (1 year) = Interest New Balance $1.00 $1.10 $1.21 * 10 * 10 * 10 = $.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 © 2011 10 Proof Principal * 10% (1 year) = Interest $.75 $.83 $.91 * 10 * 10 * 10 = $.075 = $.083 = $.091 New Balance $.83 $.91 $1.00 • There is also a table shortcut for Present Value © 2011 35 The Present Value Table The Present Value of $1 at 10% to be received in years is $.75 © 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 years at 10% … and in years at 10% X-Axis = Time in Years As Time increases, Present Value of $1 Decreases © 2011 10 37 Effect of Interest Rate and Time $1.20 A higher discount rate causes the present value to decrease more in the same years $1.00 $0.80 $0.68 $0.60 5% 10% 15% $0.47 $0.40 $0.33 $0.20 $- X-Axis = Time in Years As Time increases, Present Value of $1 Decreases © 2011 10 38 Learning Check • What does Present Value represent? • How does the Present Value table differ from the Future Value table? â 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 â 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 = â 2011 41 Build a Timeline $ 70 K $60K $60,000 to be received in years 60 50 Unknown Present Value 40 30 20 ? 10 0 X-Axis = Time in Years © 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 © 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 © 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 © 2011 = $3,650 = $4,088 = $4,579 = $5,129 = $5,744 = $6,433 New Balance $34,070 $38,159 $42,738 $47,866 $53,610 $60,044 45 Practical Exercise © 2011 46 Time Value of Money Worksheet Enter key variables in the blank white cells to generate the graph shown below © 2011 47 Time Value of Money Worksheet The spreadsheet tool also calculates Present Value © 2011 48 Practical Exercise © 2011 49 ... 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... Why or why not? © 2011 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... 80% accuracy • Identify and enter relevant report data to solve Present and Future Value equations using macro enabled cash flow templates © 2011 Time Value of Money Concepts Money received Today: