Calculate Net Present Value Principles of Cost Analysis

Calculate Net Present Value Principles of Cost Analysis and Management © Dale R. Geiger 2011 1

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 2011 2

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 2011 3

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 2011 4

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 2011 5

Identify the Key Variables Cash Flows Time in Years 1. 2. 3. 4. …in 5 years (21 st birthday) …in 14 years (30 th birthday) …in 24 years (40 th birthday) …in 34 years (50 th birthday) $20, 000 Inflow $40, 000 Inflow $60, 000 Inflow $100, 000 Inflow Discount rate = 8% © Dale R. Geiger 2011 6

Build a Timeline $100 K $ 100 K The timeline helps us to visualize the cash flows and gives us a “reality check“ 90 80 70 $60 K 60 50 $40 K 40 30 $20 K 20 10 0 1 5 14 24 34 X-Axis = number of Years © Dale R. Geiger 2011 7

Multiply by the PV Factors Cash Flow * PV Factor (8%) = $20, 000 * 0. 6806 = $40, 000 * 0. 3405 = $60, 000 * 0. 1577 = $100, 000 * 0. 0730 = Present Value Total The NPV of Rebecca’s inheritance is $43, 994 © Dale R. Geiger 2011 8

Multiply by the PV Factors Cash Flow * PV Factor (8%) = $20, 000 * 0. 6806 = $40, 000 * 0. 3405 = $60, 000 * 0. 1577 = $100, 000 * 0. 0730 = Present Value $13, 612 Total The NPV of Rebecca’s inheritance is $43, 994 © Dale R. Geiger 2011 9

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 2011 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 = 9, 462 $100, 000 * 0. 0730 = Total The NPV of Rebecca’s inheritance is $43, 994 © Dale R. Geiger 2011 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 = 7, 300 Total The NPV of Rebecca’s inheritance is $43, 994 © Dale R. Geiger 2011 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 $43, 994 The NPV of Rebecca’s inheritance is $43, 994 © Dale R. Geiger 2011 13

Comparing the Cash Flows $100 K $ 100 K The red bars represent the Present Value of the Future Cash Flows 90 80 70 $60 K 60 50 $40 K 40 30 $20 K $13. 6 K 20 10 0 1 5 $13. 6 K 14 $9. 5 K 24 $7. 3 K 34 X-Axis = number of Years © Dale R. Geiger 2011 14

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 2011 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 2011 16

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 2011 17

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 2011 18

Identify the Key Variables Cash Flows Time in Years 1. 2. 3. 4. …in 1 year …in 2 years …in 3 years …in 4 years $20, 000 outflow Discount rate = 4% © Dale R. Geiger 2011 19

Build a Timeline X-Axis = number of Years $ K 0 1 2 3 4 -5 Cash Outflows for Installment payments -10 -15 -20 -$20 $ -25 K © Dale R. Geiger 2011 20

Multiply by the PV Factors Year Cash Flow 1 2 3 4 -20, 000 * PV Factor (4%) * * = Present Value 0. 962 = 0. 925 = 0. 889 = 0. 855 = Total: -19, 231 -18, 491 -17, 780 -17, 096 -$72, 598 The NPV of the Course of action is -$72, 598 © Dale R. Geiger 2011 21

Annuity = Equal Cash Flows Year Cash Flow 1 -20, 000 2 -20, 000 3 -20, 000 4 -20, 000 * * PV Factor 4% 0. 962 0. 925 0. 889 0. 855 = = PV of Cash Flow -19, 231 -18, 491 -17, 780 -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 2011 22

Algebra of an Annuity • Essentially the NPV formula is: (Cash Flow 1 * PV Factor 1) + (Cash Flow 2 * PV Factor 2) and so on…. • If the cash flows are equal, they will factor out and this becomes: Cash Flow * (PV Factor 1 + PV Factor 2) © Dale R. Geiger 2011 23

Annuity = Equal Cash Flows Year Cash Flow 1 -20, 000 2 -20, 000 3 -20, 000 4 -20, 000 * * PV Factor 4% + 0. 962 + 0. 925 + 0. 889 + 0. 855 = 3. 630 = = PV of Cash Flow -19, 231 -18, 491 -17, 780 -17, 096 • 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 2011 24

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 2011 25

Annuity = Equal Cash Flows Year Cash Flow 1 -20, 000 2 -20, 000 3 -20, 000 4 -20, 000 * * * PV Factor 4% 0. 962 0. 925 0. 889 0. 855 3. 630 = = = PV of Cash Flow -19, 231 -18, 491 -17, 780 -17, 096 -$72, 600 • The PV of an Annuity is equal to: Cash flow* PV Annuity Factor © Dale R. Geiger 2011 26

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 2011 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 2011 28

Check on Learning • What is an annuity? • How does an annuity simplify the NPV calculation? © Dale R. Geiger 2011 29

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 2011 30

Build a Timeline 1000 s $ 600 X axis represents time in years $ 400 $ 200 $$ (200) 0 1 2 3 Investment Savings $ (400) $ (600) $ (800) $ (1 000) $ (1 200) © Dale R. Geiger 2011 31

Using the PV Annuity Table -Initial Investment +( Cash Flow *Annuity Factor) = NPV -1, 000 +( 400, 000*2. 487) = -5, 200 © Dale R. Geiger 2011 32

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 + 400, 000*2. 577 = 30, 800 © Dale R. Geiger 2011 33

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 2011 34

Practical Exercise © Dale R. Geiger 2011 35

Calculate NPV Spreadsheet Use the NPV Annuity tab when cash flows are equal © Dale R. Geiger 2011 36

Screenshots Enter the key variables for consecutive time periods in the Cash Flow I tab The spreadsheet calculates NPV and generates the timeline graph © Dale R. Geiger 2011 37

If cash flows are non-consecutive like Rebecca’s inheritance, use the Cash Flow II tab © Dale R. Geiger 2011 38

Practical Exercise © Dale R. Geiger 2011 39