1. Calculate Net Present Value © Dale R. Geiger 20111

2. You’ve just won a million dollars! Should you take the lump sum payment of $679,500 now or 20 annual payments of $50,000? © Dale R. Geiger 20112

3. Terminal Learning Objective Action: Recommend investment course of action based on NPV calculation 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 Net Present Value equations using macro enabled templates and make appropriate recommendation © Dale R. Geiger 20113

4. What is Net Present Value “Net” refers to the result of combining multiple values Net Pay combines wages earned (+) and payroll tax deductions (-) Net Change in Financial Position combines Revenues (+) and Costs (-) Net Present Value (NPV) refers to the combination of multiple discounted cash flows A positive NPV means that the PV of the cash inflows outweighs the PV of the outflows © Dale R. Geiger 20114

5. Multiple Cash Flows Today is Rebecca’s 16 th birthday. Her inheritance is held in trust and will be paid in the following installments: $20,000 on her 21 st birthday $40,000 on her 30 th birthday $60,000 on her 40 th birthday $100,000 on her 50 th birthday Assume a discount rate of 8% Task: Calculate the NPV of Rebecca’s inheritance © Dale R. Geiger 20115

6. Identify the Key Variables Cash Flows 1.$20,000 Inflow 2.$40,000 Inflow 3.$60,000 Inflow 4.$100,000 Inflow Time in Years …in 5 years (21 st birthday) …in 14 years (30 th birthday) …in 24 years (40 th birthday) …in 34 years (50 th birthday) Discount rate = 8% © Dale R. Geiger 20116

7. Build a Timeline 51424 $ X-Axis = number of Years The timeline helps us to visualize the cash flows and gives us a “reality check“ $20K $40K $60K $100K K © Dale R. Geiger 20117

8. Multiply by the PV Factors Cash Flow*PV Factor (8%)=Present Value $20,000*0.6806= $40,000*0.3405= $60,000*0.1577= $100,000*0.0730= Total The NPV of Rebecca’s inheritance is $43,994 © Dale R. Geiger 20118

9. Multiply by the PV Factors Cash Flow*PV Factor (8%)=Present Value $20,000*0.6806=$13,612 $40,000*0.3405= $60,000*0.1577= $100,000*0.0730= Total The NPV of Rebecca’s inheritance is $43,994 © Dale R. Geiger 20119

10. Multiply by the PV Factors Cash Flow*PV Factor (8%)=Present Value $20,000*0.6806=$13,612 $40,000*0.3405=13,620 $60,000*0.1577= $100,000*0.0730= Total The NPV of Rebecca’s inheritance is $43,994 © Dale R. Geiger 201110

11. Multiply by the PV Factors Cash Flow*PV Factor (8%)=Present Value $20,000*0.6806=$13,612 $40,000*0.3405=13,620 $60,000*0.1577=9,462 $100,000*0.0730= Total The NPV of Rebecca’s inheritance is $43,994 © Dale R. Geiger 201111

12. Multiply by the PV Factors Cash Flow*PV Factor (8%)=Present Value $20,000*0.6806=$13,612 $40,000*0.3405=13,620 $60,000*0.1577=9,462 $100,000*0.0730=7,300 Total The NPV of Rebecca’s inheritance is $43,994 © Dale R. Geiger 201112

13. Multiply by the PV Factors Cash Flow*PV Factor (8%)=Present Value $20,000*0.6806=$13,612 $40,000*0.3405=13,620 $60,000*0.1577=9,462 $100,000*0.0730=7,300 Total$43,994 The NPV of Rebecca’s inheritance is $43,994 © Dale R. Geiger 201113

14. Comparing the Cash Flows 51424 $ X-Axis = number of Years The red bars represent the Present Value of the Future Cash Flows The red bars represent the Present Value of the Future Cash Flows $20K $40K $60K $100K K $13.6K $9.5K $7.3K © Dale R. Geiger 201114

15. Questions to Think About What would happen to the Present Value of Rebecca’s inheritance if she assumed a 6% discount rate? A 12% discount rate? Rebecca has found a company that will pay her $40,000 cash now if she signs over her inheritance. What should she do? What factors should she consider? © Dale R. Geiger 201115

16. Questions to Think About What would happen to the Present Value of Rebecca’s inheritance if she assumed a 6% discount rate? A 12% discount rate? Rebecca has found a company that will pay her $40,000 cash now if she signs over her inheritance. What should she do? What factors should she consider? © Dale R. Geiger 201116

17. Check on Learning How does the Net Present Value calculation differ from the calculation of the Present Value of a single cash flow? © Dale R. Geiger 201117

18. Equal Cash Flow Example A machine may be purchased with four annual installments of $20,000. The discount rate is 4%. Task: Calculate the NPV of this course of action © Dale R. Geiger 201118

19. Identify the Key Variables Cash Flows 1.$20,000 outflow 2.$20,000 outflow 3.$20,000 outflow 4.$20,000 outflow Time in Years …in 1 year …in 2 years …in 3 years …in 4 years Discount rate = 4% © Dale R. Geiger 201119

20. Build a Timeline $K $ K -$20 X-Axis = number of Years Cash Outflows for Installment payments © Dale R. Geiger 201120

21. Multiply by the PV Factors YearCash Flow*PV Factor (4%)=Present Value 1 -20,000 * 0.962 = -19,231 2 -20,000 * 0.925 = -18,491 3 -20,000 * 0.889 = -17,780 4 -20,000 * 0.855 = -17,096 Total:-$72,598 The NPV of the Course of action is -$72,598 © Dale R. Geiger 201121

22. Annuity = Equal Cash Flows YearCash FlowPV Factor 4%PV of Cash Flow 1 -20,000 * 0.962 = -19,231 2 -20,000 * 0.925 = -18,491 3 -20,000 * 0.889 = -17,780 4 -20,000 * 0.855 = -17,096 An Annuity is a series of equal cash flows over equal time periods The four equal installment payments qualify as an Annuity This simplifies the calculation © Dale R. Geiger 201122

23. Algebra of an Annuity Essentially the NPV formula is: (Cash Flow1 * PV Factor 1) + (Cash Flow2 * PV Factor2) and so on…. If the cash flows are equal, they will factor out and this becomes: Cash Flow * (PV Factor1 + PV Factor2) © Dale R. Geiger 201123

24. Annuity = Equal Cash Flows YearCash FlowPV Factor 4%PV of Cash Flow 1 -20,000 * + 0.962 = -19,231 2 -20,000 * + 0.925 = -18,491 3 -20,000 * + 0.889 = -17,780 4 -20,000 * + 0.855 = -17,096 = 3.630 The sum of the four factors is called the Annuity Factor The Annuity Factor can be found on the PV Annuity Table © Dale R. Geiger 201124

25. Using the PV Annuity Table The PV Annuity factor on the table is equal to the sum of the PV factors for a single cash flow for Year 1 through Year 4 © Dale R. Geiger 201125

26. Annuity = Equal Cash Flows YearCash FlowPV Factor 4%PV of Cash Flow 1 -20,000 * 0.962 = -19,231 2 -20,000 * 0.925 = -18,491 3 -20,000 * 0.889 = -17,780 4 -20,000 * 0.855 = -17,096 -20,000 * 3.630 = -$72,600 The PV of an Annuity is equal to: Cash flow* PV Annuity Factor © Dale R. Geiger 201126

27. Make a Recommendation Another course of action is available: Pay $70,000 cash for the machine today Which course of action should we take? What if the discount rate is 2%? What if it is 6%? What other factors might be considered? © Dale R. Geiger 201127

28. Make a Recommendation Another course of action is available: Pay $70,000 cash for the machine today Which course of action should we take? What if the discount rate is 2%? What if it is 6%? What other factors might be considered? © Dale R. Geiger 201128

29. Check on Learning What is an annuity? How does an annuity simplify the NPV calculation? © Dale R. Geiger 201129

30. Net Present Value Reengineering a business process in your unit will cost $1 million now but will save an estimated $400,000 per year for the next three years. Assuming a discount rate of 10%, what is the NPV of this course of action? © Dale R. Geiger 201130

31. Build a Timeline X axis represents time in years 1000s © Dale R. Geiger 201131

32. Using the PV Annuity Table -Initial Investment +( Cash Flow *Annuity Factor) = NPV -1,000,000 +( 400,000*2.487) = -5,200 © Dale R. Geiger 201132

33. Should we proceed with Reengineering? NPV is negative, so we should not proceed The present value of the benefits to be received in the future is less than the initial investment What if the discount rate is 8%? -Initial Investment + Cash Flow (Savings) *Annuity Factor = NPV -1,000,000 + 400,000*2.577 = 30,800 © Dale R. Geiger 201133

34. Check on Learning What does Net Present Value represent? How can it be used to evaluate investments in property, plant and equipment? © Dale R. Geiger 201134

35. Practical Exercise © Dale R. Geiger 201135

36. Calculate NPV Spreadsheet © Dale R. Geiger 201136 Use the NPV Annuity tab when cash flows are equal

37. Screenshots © Dale R. Geiger 201137 Enter the key variables for consecutive time periods in the Cash Flow I tab The spreadsheet calculates NPV and generates the timeline graph

38. © Dale R. Geiger 201138 If cash flows are non-consecutive like Rebecca’s inheritance, use the Cash Flow II tab

39. Practical Exercise © Dale R. Geiger 201139